An introduction to geophysical exploration

  • An Introduction to Geophysical Exploration Philip Kearey Department of Earth Sciences University of Bristol

    Michael Brooks Ty Newydd, City Near Cowbridge Vale of Glamorgan

    An Introduction to Geophysical Exploration Philip Kearey Department of Earth Sciences University of Bristol

    Michael Brooks Ty Newydd, City Near Cowbridge Vale of Glamorgan

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    Contents Preface, ix 1 The principles and limitations of geophysical exploration methods, 1 1.1 Introduction, 1 3.7 1.2 The survey methods, 1 3.8 1.3 The problem of ambiguity in geophysical interpretation, 6 1.4 The structure of the book, 7

    7.8 Aeromagnetic and marine surveys, 164 9.1 7.9 Reduction of magnetic observations, 165 9.2 7.9.1 Diurnal variation correction, 165 7.9.2 Geomagnetic correction, 166 9.3 7.9.3 Elevation and terrain corrections, 166 9.4 7.10 Interpretation of magnetic anomalies, 166 7.10.1 Introduction, 166 7.10.2 Direct interpretation, 168 7.10.3 Indirect interpretation, 170 7.11 Potential ?eld transformations, 172 9.5 7.12 Applications of magnetic surveying, 173 9.6 Problems, 180 9.7 Further reading, 181 9.8 8 Electrical surveying, 183 8.1 Introduction, 183 9.9 8.2 Resistivity method, 183 9.10 8.2.1 Introduction, 183 9.11 8.2.2 Resistivities of rocks and minerals, 183 8.2.3 Current ?ow in the ground, 184 8.2.4 Electrode spreads, 186 8.2.5 Resistivity surveying equipment, 186 9.12 8.2.6 Interpretation of resistivity data, 187 9.13 8.2.7 Vertical electrical sounding interpretation, 188 8.2.8 Constant separation traversing interpretation, 193 10 8.2.9 Limitations of the resistivity method, 196 10.1 8.2.10 Applications of resistivity surveying, 196 10.2 8.3 Induced polarization (IP) method, 199 10.3 8.3.1 Principles, 199 10.4 8.3.2 Mechanisms of induced polarization, 199 8.3.3 Induced polarization measurements, 200 8.3.4 Field operations, 201 8.3.5 Interpretation of induced polarization data, 201 10.5 8.3.6 Applications of induced polarization 10.6 surveying, 202 8.4 Self-potential (SP) method, 203 8.4.1 Introduction, 203 11 8.4.2 Mechanism of self-potential, 203 11.1 8.4.3 Self-potential equipment and survey 11.2 procedure, 203 11.3 8.4.4 Interpretation of self-potential 11.4 anomalies, 204 Problems, 205 Further reading, 207 Contents vii

    Preface This book provides a general introduction to the most important methods of geophysical exploration. These methods represent a primary tool for investigation of the subsurface and are applicable to a very wide range of problems. Although their main application is in prospecting for natural resources, the methods are also used, for example, as an aid to geological surveying, as a means of deriving information on the Earth’s internal physical properties, and in engineering or archaeological site investigations. Consequently, geophysical explo- ration is of importance not only to geophysicists but also The book covers the physical principles, methodology, interpretational procedures and ?elds of application of the various survey methods.The main emphasis has been placed on seismic methods because these represent the most extensively used techniques, being routinely and widely employed by the oil industry in prospecting for hydrocarbons. Since this is an introductory text we have not attempted to be completely comprehensive in our coverage of the subject. Readers seeking further infor- mation on any of the survey methods described should refer to the more advanced texts listed at the end of each We hope that the book will serve as an introductory course text for students in the above-mentioned disci- plines and also as a useful guide for specialists who wish to be aware of the value of geophysical surveying to their own disciplines. In preparing a book for such a wide possible readership it is inevitable that problems arise concerning the level of mathematical treatment to be adopted. Geophysics is a highly mathematical subject and, although we have attempted to show that no great mathematical expertise is necessary for a broad under- standing of geophysical surveying, a full appreciation of the more advanced data processing and interpretational techniques does require a reasonable mathematical abil- ity. Our approach to this problem has been to keep the mathematics as simple as possible and to restrict full mathematical analysis to relatively simple cases.We con- sider it important, however, that any user of geophysical surveying should be aware of the more advanced tech- niques of analysing and interpreting geophysical data since these can greatly increase the amount of useful information obtained from the data. In discussing such techniques we have adopted a semiquantitative or quali- tative approach which allows the reader to assess their scope and importance, without going into the details of Earlier editions of this book have come to be accepted as the standard geophysical exploration textbook by nu- merous higher educational institutions in Britain, North America, and many other countries. In the third edition, we have brought the content up to date by taking account of recent developments in all the main areas of geophysical exploration.We have extended the scope of the seismic chapters by including new material on three-component and 4D re?ection seismology, and by providing a new section on seismic tomography. We have also widened the range of applications of refrac- tion seismology considered, to include an account of engineering site investigation.

    geophysical exploration methods 1.1 Introduction This chapter is provided for readers with no prior knowledge of geophysical exploration methods and is pitched at an elementary level. It may be passed over by readers already familiar with the basic principles and The science of geophysics applies the principles of physics to the study of the Earth. Geophysical investiga- tions of the interior of the Earth involve taking measure- ments at or near the Earth’s surface that are in?uenced by the internal distribution of physical properties. Analysis of these measurements can reveal how the physical properties of the Earth’s interior vary vertically and By working at different scales, geophysical methods may be applied to a wide range of investigations from studies of the entire Earth (global geophysics; e.g. Kearey & Vine 1996) to exploration of a localized region of Vogelsang 1995, McCann et al. 1997). In the geophysical exploration methods (also referred to as geophysical sur- veying) discussed in this book, measurements within geographically restricted areas are used to determine the distributions of physical properties at depths that re?ect An alternative method of investigating subsurface geology is, of course, by drilling boreholes, but these are expensive and provide information only at discrete locations. Geophysical surveying, although sometimes prone to major ambiguities or uncertainties of interpre- tation, provides a relatively rapid and cost-effective means of deriving areally distributed information on subsurface geology. In the exploration for subsurface resources the methods are capable of detecting and delineating local features of potential interest that could Geophysical surveying does not dispense with the need for drilling but, properly applied, it can optimize explo- ration programmes by maximizing the rate of ground coverage and minimizing the drilling requirement. The importance of geophysical exploration as a means of deriving subsurface geological information is so great that the basic principles and scope of the methods and their main ?elds of application should be appreciated by any practising Earth scientist. This book provides a gen- eral introduction to the main geophysical methods in widespread use.

    Method Measured parameter Operative physical property Seismic

    Gravity Magnetic Electrical Resistivity Induced polarization

    Self-potential Electromagnetic Radar Travel times of re?ected/refracted seismic waves

    Spatial variations in the strength of the gravitational ?eld of the Earth Spatial variations in the strength of the geomagnetic ?eld Earth resistance Polarization voltages or frequency- dependent ground resistance Electrical potentials Response to electromagnetic radiation Travel times of re?ected radar pulses Density and elastic moduli, which determine the propagation velocity of seismic waves Density

    Magnetic susceptibility and remanence Electrical conductivity Electrical capacitance

    Electrical conductivity Electrical conductivity and inductance Dielectric constant

    being able to survey areas where ground access is dif?cult A wide range of geophysical surveying methods exists, for each of which there is an `operative’ physical property to which the method is sensitive.The methods The type of physical property to which a method Thus, for example, the magnetic method is very suitable for locating buried magnetite ore bodies because of their high magnetic susceptibility. Similarly, seismic or elec- trical methods are suitable for the location of a buried water table because saturated rock may be distinguished from dry rock by its higher seismic velocity and higher Other considerations also determine the type of methods employed in a geophysical exploration pro- gramme. For example, reconnaissance surveys are often carried out from the air because of the high speed of operation. In such cases the electrical or seismic methods are not applicable, since these require physical contact Thus, the initial search for metalliferous mineral deposits often utilizes airborne magnetic and electromagnetic surveying. Similarly, routine reconnaissance of conti- nental shelf areas often includes simultaneous gravity, magnetic and seismic surveying. At the interpretation stage, ambiguity arising from the results of one survey method may often be removed by consideration of results from a second survey method.

    Principles of Exploration Methods 3 Application Appropriate survey methods* Exploration for fossil fuels (oil, gas, coal) S, G, M, (EM) Exploration for metalliferous mineral deposits M, EM, E, SP, IP, R Exploration for bulk mineral deposits (sand and gravel) S, (E), (G) Exploration for underground water supplies E, S, (G), (Rd) Engineering/construction site investigation E, S, Rd. (G), (M) Archaeological investigations Rd, E, EM, M, (S) * G, gravity; M, magnetic; S, seismic; E, electrical resistivity; SP, self-potential; IP, induced polarization; EM, electromagnetic; R, radiometric; Rd, ground-penetrating radar. Subsidiary methods in brackets.

    +10 0 km 5 0 –40 –30 –20 –10

    0 N 0 Fig. 1.1 The gravity anomaly over the Grand Saline Salt Dome,Texas, USA (contours in gravity units — see Chapter 6).The stippled area represents the subcrop of the dome. (Redrawn from Peters & Dugan 1945.)

    20 80 60 80 N 100 0 km 5 40 40 Fig. 1.2 Magnetic anomalies over the Grand Saline Salt Dome,Texas, USA (contours in nT — see Chapter 7).The stippled area represents the subcrop of the dome. (Redrawn from Peters & Dugan 1945.)

    Principles of Exploration Methods 5 Fig. 1.3 (a) Seismic re?ection section across a buried salt dome (courtesy Prakla-Seismos GmbH). (b) Simple structural interpretation of the seismic section, illustrating some possible ray paths for re?ected rays.

    50 35 35 50 35 70 140 100 35 50 35 50 35 50 0 km 2 50 Fig. 1.4 Perturbation of telluric currents over the Haynesville The stippled area represents the subcrop of the dome. (Redrawn from Boissonas & Leonardon 1948.)

    con?guration of closely-spaced shots and detectors is moved systematically along a pro?le line and the travel times of rays re?ected back from any subsurface geologi- cal interfaces are measured. If a salt dome is encountered, rays re?ected off its top surface will delineate the shape of 4. Earth materials with anomalous electrical resistivity may be located using either electrical or electromagnetic geophysical techniques. Shallow features are normally investigated using arti?cial ?eld methods in which an electrical current is introduced into the ground and potential differences between points on the surface are measured to reveal anomalous material in the subsurface (Chapter 8). However, this method is restricted in its depth of penetration by the limited power that can be introduced into the ground. Much greater penetration can be achieved by making use of the natural Earth cur- rents (telluric currents) generated by the motions of charged particles in the ionosphere. These currents ex- tend to great depths within the Earth and, in the absence of any electrically anomalous material, ?ow parallel to the surface. A salt dome, however, possesses an anom- alously high electrical resistivity and electric currents preferentially ?ow around and over the top of such a structure rather than through it. This pattern of ?ow causes distortion of the constant potential gradient at the surface that would be associated with a homogeneous subsurface and indicates the presence of the high- resistivity salt. Figure 1.4 presents the results of a telluric current survey of the Haynesville Salt Dome, Texas, USA.The contour values represent quantities describing the extent to which the telluric currents are distorted by subsurface phenomena and their con?guration re?ects the shape of the subsurface salt dome with some accuracy.

    conversion of this travel time into a depth requires knowledge of the velocity with which the pulse travelled along the re?ection path and, unlike the velocity of If a velocity is assumed, a depth estimate can be derived And since rocks differ signi?cantly in the velocity with which they propagate seismic waves, it is by no means a straightforward matter to translate the travel time of a seismic pulse into an accurate depth to the geological in- The solution to this particular problem, as discussed in Chapter 4, is to measure the travel times of re?ected pulses at several offset distances from a seismic source because the variation of travel time as a function of range provides information on the velocity distribution with depth. However, although the degree of uncertainty in geophysical interpretation can often be reduced to an acceptable level by the general expedient of taking additional (and in some cases different kinds of ) ?eld measurements, the problem of inherent ambiguity The general problem is that signi?cant differences from an actual subsurface geological situation may give rise to insigni?cant, or immeasurably small, differences in the quantities actually measured during a geophysical survey. Thus, ambiguity arises because many different geological con?gurations could reproduce the observed measurements. This basic limitation results from the unavoidable fact that geophysical surveying attempts to solve a dif?cult inverse problem. It should also be noted that experimentally-derived quantities are never exactly determined and experimental error adds a Principles of Exploration Methods 7

    further degree of indeterminacy to that caused by the incompleteness of the ?eld data and the ambiguity associated with the inverse problem. Since a unique solution cannot, in general, be recovered from a set of ?eld measurements, geophysical interpretation is concerned either to determine properties of the subsurface that all possible solutions share, or to introduce assumptions to restrict the number of admissible solutions (Parker 1977). In spite of these inherent problems, however, geophysical surveying is an invaluable tool for the investigation of subsurface geology and occupies a key role in exploration programmes for geological resources.

    1.4 The structure of the book The above introductory sections illustrate in a simple way the very wide range of approaches to the geophysical investigation of the subsurface and warn Chapter 2 provides a short account of the more important data processing techniques of general applicability to geophysics. In Chapters 3 to 10 the individual survey methods are treated systematically in terms of their basic principles, survey procedures, Chapter 11 describes the application of these methods to specialized surveys undertaken in boreholes. All these chapters contain suggestions for further reading which provide a more extensive treatment of the material covered in this book. A set of problems is given for all the major geophysical methods.

    2.1 Introduction Geophysical surveys measure the variation of some physical quantity, with respect either to position or to time. The quantity may, for example, be the strength of the Earth’s magnetic ?eld along a pro?le across an igneous intrusion. It may be the motion of the ground surface as a function of time associated with the passage of seismic waves. In either case, the simplest way to pre- sent the data is to plot a graph (Fig. 2.1) showing the vari- ation of the measured quantity with respect to distance or time as appropriate. The graph will show some more or less complex waveform shape, which will re?ect physical variations in the underlying geology, superim- posed on unwanted variations from non-geological fea- tures (such as the effect of electrical power cables in the magnetic example, or vibration from passing traf?c for the seismic case), instrumental inaccuracy and data col- lection errors. The detailed shape of the waveform may be uncertain due to the dif?culty in interpolating the curve between widely spaced stations.The geophysicist’s task is to separate the`signal’from the`noise’and interpret Analysis of waveforms such as these represents an es- sential aspect of geophysical data processing and inter- pretation. The fundamental physics and mathematics of such analysis is not novel, most having been discovered in the 19th or early 20th centuries.The use of these ideas is also widespread in other technological areas such as radio, television, sound and video recording, radio- astronomy, meteorology and medical imaging, as well as military applications such as radar, sonar and satellite imaging. Before the general availability of digital com- puting, the quantity of data and the complexity of the processing severely restricted the use of the known tech- niques. This no longer applies and nearly all the tech- niques described in this chapter may be implemented in The fundamental principles on which the various methods of data analysis are based are brought together in this chapter.These are accompanied by a discussion of the techniques of digital data processing by computer that are routinely used by geophysicists.Throughout this chapter, waveforms are referred to as functions of time, but all the principles discussed are equally applicable to functions of distance. In the latter case, frequency (num- ber of waveform cycles per unit time) is replaced by spatial frequency or wavenumber (number of waveform cycles per unit distance).

    Geophysical Data Processing 9 600 500 400 300 (a) 200 0 10 Magnetic field (nT) 20 30 40 50 Distance (m) Fig. 2.1 (a) A graph showing a typical magnetic ?eld strength variation which may be measured along a pro?le. (b) A graph of a typical seismogram, showing variation of particle velocities in the ground as a function of time during the passage of a seismic wave.

    (a) f (t ) Ground velocity (10-6 m/s) 15 10 5 0 –5 (b) –10

    1.0 0 10 20 30 40 50 60 70 80 Time (milliseconds)

    ?ne electrical power ratios: the ratio of two power values P and P is given by 10 log (P /P ) dB. Since power is 1 2 10 1 2 proportional to the square of signal amplitude A

    2 10 log (P P ) = 10 log (A A ) 10 1 2 10 1 2 = 20 log (A A ) (2.1) 10 1 2 t

    Thus, if a digital sampling scheme measures ampli- tudes over the range from 1 to 1024 units of amplitude, the dynamic range is given by –1.0 20 log (A A ) = 20 log 1024 ª 60 dB 10 max min 10

    0.9 0.9 0.5 0.5 ? 2? 3? 0.0 t (b) g(t ) 1.0

    signi?cant loss of information content as long as the fre- quency of sampling is much higher than the highest frequency component in the sampled function. Mathe- matically, it can be proved that, if the waveform is a sine curve, this can always be reconstructed provided that there are a minimum of two samples per period of the Thus, if a waveform is sampled every two milliseconds (sampling interval), the sampling frequency is 500 sam- ples per second (or 500 Hz). Sampling at this rate will preserve all frequencies up to 250 Hz in the sampled function. This frequency of half the sampling frequency is known as the Nyquist frequency ( f ) and the Nyquist N interval is the frequency range from zero up to f N

    f = 1 (2Dt) N (2.2)

    If frequencies above the Nyquist frequency are pre- sent in the sampled function, a serious form of distortion results known as aliasing, in which the higher frequency Consider the example illustrated in Fig. 2.3 in which sine waves at different frequencies are sampled. The lower frequency wave (Fig. 2.3(a)) is accurately repro- duced, but the higher frequency wave (Fig. 2.3(b), solid line) is rendered as a ?ctitious frequency, shown by the dashed line, within the Nyquist interval. The relation- ship between input and output frequencies in the case of a sampling frequency of 500 Hz is shown in Fig. 2.3(c). It is apparent that an input frequency of 125 Hz, for exam- ple, is retained in the output but that an input frequency To overcome the problem of aliasing, the sampling frequency must be at least twice as high as the highest fre- quency component present in the sampled function. If the function does contain frequencies above the Nyquist frequency determined by the sampling, it must be passed through an antialias ?lter prior to digitization. The antialias ?lter is a low-pass frequency ?lter with a sharp cut-off that removes frequency components above the Nyquist frequency, or attenuates them to an insigni?cant amplitude level.

    2.3 Spectral analysis An important mathematical distinction exists between periodic waveforms (Fig. 2.4(a)), that repeat themselves at a ?xed time period T, and transient waveforms (Fig. 2.4(b)), (a)

    (b) (c) f 2f 3f 4f NNNN 250 Output frequency (Hz) 125

    0 125 250 500 625 750 1000 Input frequency (Hz) (b) Sine wave frequency greater than Nyquist frequency (solid line) showing the ?ctitious frequency that is generated by aliasing (c) Relationship between input and output frequencies for a N

    Geophysical Data Processing 11 T (a) 8 8 (b) (a) 2 Amplitude 1

    0 (a) (b) Fig. 2.5 Complex waveforms resulting from the summation of two sine wave components of frequency f and 2f. (a)The two sine wave components are of equal amplitude and in phase. (b)The higher frequency component has twice the amplitude of the lower frequency component and is p/2 out of phase. (After Anstey 1965.)

    (b) 2 Amplitude 1 0 f 2f Frequency ?/2?/2

    0 0 2f Frequency Phase Fig. 2.6 Representation in the frequency domain of the waveforms illustrated in Fig. 2.5, showing their – ?/2 amplitude and phase spectra.

    Phase f produce the quite different waveform illustrated in From the above it follows that a periodic waveform can be expressed in two different ways: in the familiar time domain, expressing wave amplitude as a function of time, or in the frequency domain, expressing the amplitude and phase of its constituent sine waves as a function of frequency. The waveforms shown in Fig. 2.5(a) and (b) are represented in Fig. 2.6(a) and (b) in terms of their am- plitude and phase spectra. These spectra, known as line spectra, are composed of a series of discrete values of the amplitude and phase components of the waveform at set frequency values distributed between 0 Hz and the Nyquist frequency.

    – ?/2 f 2f Frequency f 2f Frequency

    Amplitude density Frequency Phase Frequency Fig. 2.7 Digital representation of the continuous amplitude and phase spectra associated with a transient waveform.

    thin frequency slices, with each slice having a frequency equal to the mean frequency of the slice and an ampli- tude and phase proportional to the area of the slice of the appropriate spectrum (Fig. 2.7). This digital expression of a continuous spectrum in terms of a ?nite number of discrete frequency components provides an approximate representation in the frequency domain of a transient waveform in the time domain. Increasing the sampling frequency in the time domain not only improves the time-domain representation of the waveform, but also increases the number of frequency slices in the frequen- cy domain and improves the accuracy of the approxima- Fourier transformation may be used to convert a time function g(t) into its equivalent amplitude and phase spectra A( f ) and f( f ), or into a complex function of frequency G( f ) known as the frequency spectrum, where

    G ( f ) = A( f )e if ( f ) (2.3) The time- and frequency-domain representations of a waveform, g(t) and G( f ), are known as a Fourier pair, represented by the notation g (t) ´ G( f ) (2.4) Components of a Fourier pair are interchangeable, such that, if G( f ) is the Fourier transform of g(t ), then g(t) is the Fourier transform of G( f ). Figure 2.8 illus- trates Fourier pairs for various waveforms of geophysical signi?cance. All the examples illustrated have zero phase spectra; that is, the individual sine wave components of the waveforms are in phase at zero time. In this case f( f ) = 0 for all values of f. Figure 2.8(a) shows a spike func- tion (also known as a Dirac function), which is the shortest possible transient waveform. Fourier transformation shows that the spike function has a continuous frequency thus, a spike function contains all frequencies from zero to in?nity at equal amplitude.The`DC bias’waveform of Fig. 2.8(b) has, as would be expected, a line spectrum comprising a single component at zero frequency. Note that Fig. 2.8(a) and (b) demonstrate the principle of interchangeability of Fourier pairs stated above (equa- tion (2.4)). Figures 2.8(c) and (d) illustrate transient waveforms approximating the shape of seismic pulses, together with their amplitude spectra. Both have a band- limited amplitude spectrum, the spectrum of narrower bandwidth being associated with the longer transient waveform. In general, the shorter a time pulse the wider is its frequency bandwidth and in the limiting case a spike Waveforms with zero phase spectra such as those illus- trated in Fig. 2.8 are symmetrical about the time axis and, for any given amplitude spectrum, produce the maximum peak amplitude in the resultant waveform. If phase varies linearly with frequency, the waveform re- mains unchanged in shape but is displaced in time; if the phase variation with frequency is non-linear the shape of the waveform is altered. A particularly important case in seismic data processing is the phase spectrum associated with minimum delay in which there is a maximum con- Analysis of seismic pulses sometimes assumes that they Fourier transformation of digitized waveforms is readily programmed for computers, using a `fast Fourier transform’ (FFT) algorithm as in the Cooley–Tukey method (Brigham 1974). FFT subroutines can thus be routinely built into data processing programs in order to Fourier transformation is supplied as a function to standard spreadsheets such as Microsoft Excel. Fourier transformation can be extended into two dimensions (Rayner 1971), and can thus be applied to areal distribu- tions of data such as gravity and magnetic contour maps.

    Geophysical Data Processing 13 Time domain Frequency domain

    (a) (b) (c) (d) Fig. 2.8 Fourier transform pairs for (b)A`DCbias’.(c)and(d)Transient Time Frequency waveforms approximating seismic pulses. t = 0

    In this case, the time variable is replaced by horizontal distance and the frequency variable by wavenumber (number of waveform cycles per unit distance). The application of two-dimensional Fourier techniques to the interpretation of potential ?eld data is discussed in Chapters 6 and 7.

    2.4 Waveform processing The principles of convolution, deconvolution and cor- relation form the common basis for many methods of geophysical data processing, especially in the ?eld of seis- mic re?ection surveying. They are introduced here in general terms and are referred to extensively in later chapters.Their importance is that they quantitatively de- scribe how a waveform is affected by a ?lter. Filtering modi?es a waveform by discriminating between its con- stituent sine wave components to alter their relative am- plitudes or phase relations, or both. Most audio systems are provided with simple ?lters to cut down on high- frequency `hiss’, or to emphasize the low-frequency `bass’. Filtering is an inherent characteristic of any system through which a signal is transmitted.

    Amplitude Input displacement W Output displacement Input

    Output Time Fig. 2.9 The principle of ?ltering illustrated by the perturbation of a suspended weight system.

    response which is de?ned as the output of the ?lter when the input is a spike function (Fig. 2.10). The impulse re- sponse is a waveform in the time domain, but may be transformed into the frequency domain as for any other waveform. The Fourier transform of the impulse re- sponse is known as the transfer function and this speci?es the amplitude and phase response of the ?lter, thus de?ning its operation completely.The effect of a ?lter is described mathematically by a convolution operation such that, if the input signal g(t) to the ?lter is convolved with the impulse response f(t) of the ?lter, known as the con- volution operator, the ?ltered output y(t) is obtained:

    y(t) = g (t) * f (t) (2.5)

    Figure 2.11(a) shows a spike function input to a ?lter whose impulse response is given in Fig. 2.11(b). Clearly the latter is also the ?ltered output since, by de?nition, the impulse response represents the output for a spike input. Figure 2.11(c) shows an input comprising two 2.11(d)) is now the superposition of the two impulse re- sponse functions offset in time by the separation of the

    Spike input input spikes and scaled according to the individual spike amplitudes. Since any transient wave can be represented as a series of spike functions (Fig. 2.11(e)), the general form of a ?ltered output (Fig. 2.11(f )) can be regarded as the summation of a set of impulse responses related to a succession of spikes simulating the overall shape of the The mathematical implementation of convolution involves time inversion (or folding) of one of the func- tions and its progressive sliding past the other function, the individual terms in the convolved output being de- rived by summation of the cross-multiplication products over the overlapping parts of the two functions. In gen- eral, if g (i = 1, 2, . . . , m) is an input function and f ( j = ij 1, 2, . . . , n) is a convolution operator, then the convolu- tion output function y is given by k

    m y = Â g f (k = 1, 2, . . . , m + n – 1) (2.6) k i k-i i =1

    In Fig. 2.12 the individual steps in the convolution process are shown for two digital functions, a double spike function given by g = g , g , g = 2, 0, 1 and an im- i123 pulse response function given by f = f , f , f , f = 4, 3, 2, i1234 1, where the numbers refer to discrete amplitude values 2.11 it can be seen that the convolved output y = y , y , i12 y , y , y , y = 8, 6, 8, 5, 2, 1. Note that the convolved 3456 output is longer than the input waveforms; if the func- tions to be convolved have lengths of m and n, the con- The convolution of two functions in the time domain becomes increasingly laborious as the functions become longer. Typical geophysical applications may have func- tions which are each from 250 to a few thousand samples long. The same mathematical result may be obtained by transforming the functions to the frequency domain, then multiplying together equivalent frequency terms of their amplitude spectra and adding terms of their phase spectra. The resulting output amplitude and phase spec- Thus, digital ?ltering can be enacted in either the time

    Geophysical Data Processing 15 (a) (c) (e) (b) (d) (f) Fig. 2.11 Examples of ?ltering. (a) A spike input. (b) Filtered output equivalent to impulse response of ?lter. (c) An input comprising two spikes. (d) Filtered output given by summation of two impulse response functions offset in time. (e) A complex input represented by a series of contiguous spike functions. (f) Filtered output given by the summation of a set of impulse responses.

    4 3 2 1 Cross-products Sum 1 0 2 4×2 = 1 0 2 1 0 2 4×0+3×2 = 4×1+3×0+2×2 = 1 0 2 3×1+2×0+2×1 = 1 0 2 2×1+1×0 = Fig. 2.12 A method of calculating the convolution of two digital functions.

    domain or the frequency domain. With large data sets, ?ltering by computer is more ef?ciently carried out in the frequency domain since fewer mathematical opera- Convolution, or its equivalent in the frequency 1 0 2 1×1 = 8 6 8 5 2 1

    domain, ?nds very wide application in geophysical data processing, notably in the digital ?ltering of seismic and potential ?eld data and the construction of synthetic seismograms for comparison with ?eld seismograms (see Chapters 4 and 6).

    2.4.2 Deconvolution Deconvolution or inverse ?ltering (Kanasewich 1981) is a process that counteracts a previous convolution (or ?ltering) action. Consider the convolution operation given in equation (2.5) y(t) = g (t) * f (t)

    y(t) is the ?ltered output derived by passing the input Knowing y(t) and f(t), the recovery of g(t) represents a de- convolution operation. Suppose that f ¢(t) is the function that must be convolved with y(t) to recover g(t) g(t ) = y(t ) * f ¢(t ) (2.7)

    Substituting for y(t) as given by equation (2.5) g(t ) = g(t ) * f (t ) * f ¢(t ) (2.8) Now recall also that

    g(t ) = g(t ) * d (t ) (2.9) where d(t) is a spike function (a unit amplitude spike at zero time); that is, a time function g(t) convolved with a spike function produces an unchanged convolution output function g(t). From equations (2.8) and (2.9) it follows that

    f (t ) * f ¢(t ) = d (t ) (2.10)

    Thus, provided the impulse response f(t) is known, f¢(t) can be derived for application in equation (2.7) to re- cover the input signal g(t). The function f ¢(t) represents Deconvolution is an essential aspect of seismic data processing, being used to improve seismic records by re- moving the adverse ?ltering effects encountered by seis- mic waves during their passage through the ground. In the seismic case, referring to equation (2.5), y(t) is the seismic record resulting from the passage of a seismic wave g(t) through a portion of the Earth, which acts as a ?lter with an impulse response f(t). The particular prob- lem with deconvolving a seismic record is that the input waveform g(t) and the impulse response f(t) of the Earth ?lter are in general unknown. Thus the `deterministic’ approach to deconvolution outlined above cannot be employed and the deconvolution operator has to be designed using statistical methods.This special approach to the deconvolution of seismic records, known as pre- dictive deconvolution, is discussed further in Chapter 4.

    2.4.3 Correlation Cross-correlation of two digital waveforms involves cross- multiplication of the individual waveform elements and summation of the cross-multiplication products over the common time interval of the waveforms.The cross- correlation function involves progressively sliding one waveform past the other and, for each time shift, or lag, summing the cross-multiplication products to derive the cross-correlation as a function of lag value. The cross- correlation operation is similar to convolution but does not involve folding of one of the waveforms. Given two digital waveforms of ?nite length, x and y (i = 1, 2, . . . , ii n), the cross-correlation function is given by n -t

    f (t ) = Â x y (-m < t < +m) (2.11) xy i+t i i =1

    Geophysical Data Processing 17 Waveform 1 Waveform 2 lag Cross-correlation function

    – ve lag + ve lag Fig. 2.13 Cross-correlation of two Zero identical waveforms. lag

    centred on the time value at which the signal function and its concealed equivalent in the waveform are in A special case of correlation is that in which a wave- form is cross-correlated with itself, to give the autocorre- lation function f (t).This function is symmetrical about xx a zero lag position, so that

    fxx (t ) = fxx (-t ) (2.12)

    The autocorrelation function of a periodic waveform is also periodic, with a frequency equal to the repetition frequency of the waveform.Thus, for example, the auto- correlation function of a cosine wave is also a cosine wave. For a transient waveform, the autocorrelation These differing properties of the autocorrelation func- tion of periodic and transient waveforms determine one of its main uses in geophysical data processing, namely, the detection of hidden periodicities in any given wave- 2.15) are an indication of the existence of periodicities in the original waveform, and the spacing of the side lobes de?nes the repetition period.This property is particular- ly useful in the detection and suppression of multiple re?ections in seismic records (see Chapter 4).

    The autocorrelation function contains all the am- plitude information of the original waveform but none of the phase information, the original phase relation- ships being replaced by a zero phase spectrum. In fact, the autocorrelation function and the square of the am- plitude spectrum A( f ) can be shown to form a Fourier pair

    2 f (t ) ´ A( f ) (2.13) xx

    Since the square of the amplitude represents the power term (energy contained in the frequency component) the autocorrelation function can be used to compute the power spectrum of a waveform.

    Waveform Signal function Cross-correlation function (a) ? (b) S SS 1 23 Fig. 2.14 Cross-correlation to detect Signal positions occurrences of a known signal concealed in waveform in noise. (After Sheriff 1973.)

    ? (?) xx Fig. 2.15 Autocorrelation of the waveform exhibiting periodicity shown in (a) produces the autocorrelation function with side lobes shown in (b).The spacing of the side lobes de?nes the repetition period of the original ? waveform.

    random, and usually due to effects unconnected with the geophysical survey. Coherent noise is, on the other hand, components of the waveform which are generated by the geophysical experiment, but are of no direct interest for the geological interpretation. For example, in a seismic survey the signal might be the seismic pulse arriving at a detector after being re?ected by a geological boundary at depth. Random noise would be back- Coherent noise would be the surface waves generated by the seismic source, which also travel to the detector In favourable circumstances the signal-to-noise ratio (SNR) is high, so that the signal is readily identi?ed and extracted for subsequent analysis. Often the SNR is low and special processing is necessary to enhance the infor- mation content of the waveforms. Different approaches are needed to remove the effect of different types of noise. Random noise can often be suppressed by re- peated measurement and averaging. Coherent noise may be ?ltered out by identifying the particular charac- teristics of that noise and designing a special ?lter to re- move it.The remaining signal itself may be distorted due to the effects of the recording system, and again, if the nature of the recording system is accurately known, suit- able ?ltering can be designed. Digital ?ltering is widely employed in geophysical data processing to improve SNR or otherwise improve the signal characteristics. A very wide range of digital ?lters is in routine use in geo- physical, and especially seismic, data processing (Robin- son & Treitel 2000). The two main types of digital ?lter are frequency ?lters and inverse (deconvolution) ?lters.

    Geophysical Data Processing 19 Frequency domain Time domain (a) (b)

    Sinc function ff ct (c) (d)

    Filter operator Fig. 2.16 Design of a digital low-pass ff ?lter. ct

    (BR) in terms of their frequency response. Frequency ?lters are employed when the signal and noise compo- nents of a waveform have different frequency character- Analogue frequency ?ltering is still in widespread use and analogue antialias (LP) ?lters are an essential compo- nent of analogue-to-digital conversion systems (see Sec- tion 2.2). Nevertheless, digital frequency ?ltering by computer offers much greater ?exibility of ?lter design and facilitates ?ltering of much higher performance than can be obtained with analogue ?lters. To illustrate the design of a digital frequency ?lter, consider the case of a LP ?lter whose cut-off frequency is f . The desired out- c put characteristics of the ideal LP ?lter are represented by the amplitude spectrum shown in Fig. 2.16(a).The spec- trum has a constant unit amplitude between 0 and f and c zero amplitude outside this range: the ?lter would there- fore pass all frequencies between 0 and f without atten- c c This amplitude spectrum represents the transfer func- Inverse Fourier transformation of the transfer func- tion into the time domain yields the impulse response of the ideal LP ?lter (see Fig. 2.16(b)). However, this im- pulse response (a sinc function) is in?nitely long and must therefore be truncated for practical use as a convo- lution operator in a digital ?lter. Figure 2.16(c) repre- sents the frequency response of a practically realizable LP ?lter operator of ?nite length (Fig. 2.16(d)). Convolu- tion of the input waveform with the latter will result in LP ?ltering with a ramped cut-off (Fig. 2.16(c)) rather HP, BP and BR time-domain ?lters can be designed in a similar way by specifying a particular transfer func- tion in the frequency domain and using this to design a ?nite-length impulse response function in the time do- main.As with analogue ?ltering, digital frequency ?lter- ing generally alters the phase spectrum of the waveform and this effect may be undesirable. However, zero phase ?lters can be designed that facilitate digital ?ltering with- out altering the phase spectrum of the ?ltered signal.

    2.5.2 Inverse (deconvolution) ?lters The main applications of inverse ?ltering to remove the adverse effects of a previous ?ltering operation lie in the ?eld of seismic data processing. A discussion of inverse ?ltering in the context of deconvolving seismic records is given in Chapter 4.

    forms themselves are presented in a form in which they simulate an image of the subsurface structure. The most obvious examples of this are in seismic re?ection (Chapter 4) and ground-penetrating radar (Chapter 9) sections, where the waveform of the variation of re?ect- ed energy with time is used to derive an image related to the occurrence of geological boundaries at depth. Often magnetic surveys for shallow engineering or archaeo- logical investigations are processed to produce shaded, coloured, or contoured maps where the shading or colour correlates with variations of magnetic ?eld which are expected to correlate with the structures being sought. Imaging is a very powerful tool, as it provides a way of summarizing huge volumes of data in a format which can be readily comprehended, that is, the visual image. A disadvantage of imaging is that often it can be dif?cult or impossible to extract quantitative informa- In modelling, the geophysicist chooses a particular type of structural model of the subsurface, and uses this The model is then adjusted to give the closest match be- tween the predicted (modelled) and observed wave- forms. The goodness of the match obtained depends on both the signal-to-noise ratio of the waveforms and the initial choice of the model used.The results of modelling are usually displayed as cross-sections through the struc- ture under investigation. Modelling is an essential part of most geophysical methods and is well exempli?ed in gravity and magnetic interpretation (see Chapters 6 and 7).

    Problems 1. Over the distance between two seismic recording sites at different ranges from a seismic source, seismic waves have been attenuated by 5 dB. What is the ratio of the wave amplitudes ob- 2. In a geophysical survey, time-series data are (a) What is the Nyquist frequency? (b) In the absence of antialias ?ltering, at what frequency would noise at 200 Hz be aliased back into the 3. If a digital recording of a geophysical time series is required to have a dynamic range of 120 dB, what number of bits is required in each binary word?

    4. If the digital signal (-1, 3, -2, -1) is convolved with the ?lter operator (2, 3, 1), what is the con- 5. Cross-correlate the signal function (-1, 3, -1) with the waveform (-2, -4, -4, -3, 3, 1, 2, 2) con- taining signal and noise, and indicate the likely position of the signal in the waveform on the 6. A waveform is composed of two in-phase components of equal amplitude at frequencies f and 3f. Draw graphs to represent the waveform in the time domain and the frequency domain.

    Further reading Brigham, E.O. (1974) The Fast Fourier Transform. Prentice-Hall, Camina, A.R. & Janacek, G.J. (1984) Mathematics for Seismic Data Dobrin, M.B. & Savit, C.H. (1988) Introduction to Geophysical Kanasewich, E.R. (1981) Time Sequence Analysis in Geophysics (3rd edn). University of Alberta Press.

    Rayner, J.N. (1971) An Introduction to Spectral Analysis. Pion, Sheriff, R.E. & Geldart, L.P. (1983) Exploration Seismology Vol 2: Data-Processing and Interpretation. Cambridge University Press, Cambridge.

    3.1 Introduction In seismic surveying, seismic waves are created by a con- Some waves will return to the surface after refraction or re?ection at geological boundaries within the subsur- face. Instruments distributed along the surface detect the ground motion caused by these returning waves and hence measure the arrival times of the waves at different ranges from the source. These travel times may be con- verted into depth values and, hence, the distribution of subsurface geological interfaces may be systematically Seismic surveying was ?rst carried out in the early 1920s. It represented a natural development of the already long-established methods of earthquake seis- mology in which the travel times of earthquake waves recorded at seismological observatories are used to de- Earthquake seismology provides information on the gross internal layering of the Earth, and measurement of the velocity of earthquake waves through the various Earth layers provides information about their physical properties and composition. In the same way, but on a smaller scale, seismic surveying can provide a clear and detailed picture of subsurface geology. It undoubtedly represents the single most important geophysical survey- ing method in terms of the amount of survey activity and the very wide range of its applications. Many of the principles of earthquake seismology are applicable to seismic surveying. However, the latter is concerned solely with the structure of the Earth down to tens of kilometres at most and uses arti?cial seismic sources, such as explosions, whose location, timing and source characteristics are, unlike earthquakes, under the direct control of the geophysicist. Seismic surveying also uses specialized recording systems and associated data pro- Seismic methods are widely applied to exploration problems involving the detection and mapping of sub- surface boundaries of, normally, simple geometry.They also identify signi?cant physical properties of each sub- surface unit. The methods are particularly well suited to the mapping of layered sedimentary sequences and are therefore widely used in the search for oil and gas. The methods are also used, on a smaller scale, for the mapping of near-surface sediment layers, the location of the water table and, in an engineering context, site investigation of foundation conditions including the determination of depth to bedrock. Seismic surveying can be carried out on land or at sea and is used extensively in offshore geological surveys and the exploration for offshore In this chapter the fundamental physical principles on which seismic methods are based are reviewed, starting with a discussion of the nature of seismic waves and going on to consider their mode of propagation through the ground, with particular reference to re?ection and refraction at interfaces between different rock types. To understand the different types of seismic wave that propagate through the ground away from a seismic source, some elementary concepts of stress and strain need to be considered.

    Stress Chapter 3 Elastic field Ductile field Yield point Fracture point

    Strain known as the principal axes of stress, and the normal stresses acting in these directions are known as the princi- pal stresses. Each principal stress represents a balance of equal-magnitude but oppositely-directed force compo- nents.The stress is said to be compressive if the forces are directed towards each other and tensile if they are If the principal stresses are all of equal magnitude within a body the condition of stress is said to be hydro- static, since this is the state of stress throughout a ?uid body at rest. A ?uid body cannot sustain shearing stresses (since a ?uid has no shear strength), hence there cannot be shear stresses in a body under hydrostatic stress. If the principal stresses are unequal, shearing stresses exist along all surfaces within the stressed body, except for the three orthogonal planes intersecting in the principal A body subjected to stress undergoes a change of shape and/or size known as strain. Up to a certain limit- ing value of stress, known as the yield strength of a ma- terial, the strain is directly proportional to the applied stress (Hooke’s Law). This elastic strain is reversible so that removal of stress leads to a removal of strain. If the yield strength is exceeded the strain becomes non-linear and partly irreversible (i.e. permanent strain results), and this is known as plastic or ductile strain. If the stress is in- creased still further the body fails by fracture. A typical The linear relationship between stress and strain in the elastic ?eld is speci?ed for any material by its various elas- tic moduli, each of which expresses the ratio of a particu- lar type of stress to the resultant strain. Consider a rod of original length l and cross-sectional area A which is ex- tended by an increment Dl through the application of a stretching force F to its end faces (Fig. 3.2(a)). The rele- vant elastic modulus isYoung’ s modulus E, de?ned by

    longitudinal stress F A E= longitudinal strain Dl l Note that extension of such a rod will be accompanied by a reduction in its diameter; that is, the rod will suffer lateral as well as longitudinal strain.The ratio of the lateral The bulk modulus K expresses the stress–strain ratio in the case of a simple hydrostatic pressure P applied to a cubic element (Fig. 3.2(b)), the resultant volume strain being the change of volume Dv divided by the original volume v

    volume stress P K= volume strain Dv v In a similar manner the shear modulus (m) is de?ned as the ratio of shearing stress (t) to the resultant shear strain tan q (Fig. 3.2(c))

    shear stress t m= shear strain tan q Finally, the axial modulus y de?nes the ratio of longi- tudinal stress to longitudinal strain in the case when there is no lateral strain; that is, when the material is con- strained to deform uniaxially (Fig. 3.2(d))

    longitudinal stress F A y= longitudinal strain (uniaxial) Dl l

    Elements of Seismic Surveying 23 P (a) l (b)

    F F P P l + ?l longitudinal stress F/A volume stress P E= K= longitudinal strain ?l/l volume strain ?v/v

    ? (c) (d) l ? F F

    l + ?l Fig. 3.2 The elastic moduli. (a)Young’ s shear stress ? longitudinal stress F/A µ= ?= modulus E. (b) Bulk modulus K. (c) Shear shear strain tan ? longitudinal strain ?l/l modulus m. (d) Axial modulus y. (no lateral strain)

    which they pass. There are two groups of seismic waves, 3.3.1 Body waves Body waves can propagate through the internal volume of an elastic solid and may be of two types. Compressional waves (the longitudinal, primary or P-waves of earth- quake seismology) propagate by compressional and dila- Particle motion associated with the passage of a com- pressional wave involves oscillation, about a ?xed point, in the direction of wave propagation (Fig. 3.3(a)). Shear waves (the transverse, secondary or S-waves of earth- quake seismology) propagate by a pure shear strain in a Individual particle motions involve oscillation, about a ?xed point, in a plane at right angles to the direction of wave propagation (Fig. 3.3(b)). If all the particle oscilla- tions are con?ned to a plane, the shear wave is said to be The velocity of propagation of any body wave in any homogeneous, isotropic material is given by:

    12 È appropriate elastic modulus of material ? v= Hence the velocity v of a compressional body wave, p which involves a uniaxial compressional strain, is given by 12 v = Èy ? r

    or, since y = K + 43 m, by 12 È K + 43 m ? v= r and the velocity v of a shear body wave, which involves a s pure shear strain, is given by

    12 v =Èm? r It will be seen from these equations that compres- sional waves always travel faster than shear waves in the same medium. The ratio v /v in any material is deter- ps mined solely by the value of Poisson’s ratio (s ) for that material

    (a) P-wave Compressions Undisturbed medium Dilatations (b) S-wave

    Fig. 3.3 Elastic deformations and ground particle motions associated with the passage (From Bolt 1982.)

    independent of density and can be used to derive Pois- son’s ratio, which is a much more diagnostic lithological indicator. If this information is required, then both v p s These fundamental relationships between the veloc- ity of the wave propagation and the physical properties of the materials through which the waves pass are inde- pendent of the frequency of the waves. Body waves are non-dispersive; that is, all frequency components in a wave train or pulse travel through any material at the same velocity, determined only by the elastic moduli and Historically, most seismic surveying has used only compressional waves, since this simpli?es the survey technique in two ways. Firstly, seismic detectors which record only the vertical ground motion can be used, and these are insensitive to the horizontal motion of S- waves. Secondly, the higher velocity of P-waves ensures that they always reach a detector before any related S-waves, and hence are easier to recognize. Recording S-waves, and to a lesser extent surface waves, gives greater information about the subsurface, but at a cost of greater data acquisition (three-component recording) and consequent processing effort. As technology ad- vances multicomponent surveys are becoming more One application of shear wave seismology is in engi- neering site investigation where the separate measure- ment of v and v for near-surface layers allows direct ps calculation of Poisson’s ratio and estimation of the elas- tic moduli, which provide valuable information on the in situ geotechnical properties of the ground.These may be of great practical importance, such as the value of rip- pability (see Section 5.11.1).

    Elements of Seismic Surveying (a) (b) 25 Fig. 3.4 Elastic deformations and ground particle motions associated with the passage of surface waves. (a) Rayleigh wave. (b) Love wave. (From Bolt 1982.)

    interior.Analysisoftheobservedpatternofdispersionof earthquake waves is a powerful method of studying the velocity structure of the lithosphere and asthenosphere (Knopoff 1983). The same methodology, applied to the surface waves generated by a sledgehammer, can be used to examine the strength of near-surface materials for If the surface is layered and the surface layer shear wave velocity is lower than that of the underlying layer, a second set of surface waves is generated. Love waves are polarized shear waves with a particle motion parallel to the free surface and perpendicular to the direction of wave propagation (Fig. 3.4(b)). The velocity of Love waves is intermediate between the shear wave velocity of the surface layer and that of deeper layers, and Love waves are inherently dispersive. The observed pattern of Love wave dispersion can be used in a similar way to Rayleigh wave dispersion to study the subsurface structure.

    3.3.3 Waves and rays A seismic pulse propagates outwards from a seismic source at a velocity determined by the physical proper- ties of the surrounding rocks. If the pulse travels through a homogeneous rock it will travel at the same velocity in all directions away from the source so that at any subse- quent time the wavefront, de?ned as the locus of all points which the pulse has reached at a particular time, will be a sphere. Seismic rays are de?ned as thin pencils of seismic energy travelling along ray paths that, in isotropic media, are everywhere perpendicular to wavefronts (Fig. 3.5).

    Wavefront Source Ray path Fig. 3.5 The relationship of a ray path to the associated wavefront.

    of only about 10-10 m.The detection of seismic waves in- 3.4 Seismic wave velocities of rocks grain shape and degree of sorting), porosities and con- tained pore ?uids, rocks differ in their elastic moduli and densities and, hence, in their seismic velocities. Informa- tion on the compressional and shear wave velocities, v p and v , of rock layers encountered by seismic surveys is s important for two main reasons: ?rstly, it is necessary for secondly, it provides an indication of the lithology of a rock or, in some cases, the nature of the pore ?uids To relate rock velocities to lithology, the assumption that rocks are uniform and isotropic in structure must be reviewed. A typical rock texture can be regarded as having mineral grains making up most of the rock (the matrix), with the remaining volume being occupied by void space (the pores). The fractional volume of pore space is the porosity (f) of the rock. For simplicity it may be assumed that all the matrix grains have the same physical properties. This is a surprisingly good approxi- mation since the major rock-forming minerals, quartz, feldspar and calcite, have quite similar physical proper- ties. In this case, the properties of the bulk rock will be an average of the properties of the matrix minerals and the pore ?uid, weighted according to the porosity.The sim- plest case is for the density of a rock, where the bulk density r can be related to the matrix and pore ?uid b densities (r , r ): mf

    r = r f + (1 – f ) r bf m For P-wave velocity a similar relationship exists, but the velocity weighting is proportional to the percentage of travel-time spent in each component of the system, which is inversely proportional to velocity, giving the relationship: 1 f (1 – f ) =+ vvv bfm

    From the above equations it is possible to produce cross-plot graphs (Fig. 3.6) which allow the estimation of the matrix grain type and the porosity of a rock, purely from the seismic P-wave velocity and density.

    6500 6000 5500 5000 -1 4500 4000 3500 Seismic P-wave velocity in m s 3000

    2500 2000 1500 1000 Density–Velocity Cross-plot Sandstone Limestone

    0% 50% 100% 1000 1500 2000 2500 3000 Density in kg m-3

    Fig. 3.6 The relationship of seismic velocity and density to porosity, calculated for mono-mineralic granular solids: open circles – sandstone, calculated for a quartz matrix; solid circles – limestone, calculated for a calcite matrix. Points annotated with the corresponding porosity value 0–100%. Such relationships are useful in borehole log interpretation (see Chapter 11).

    and 5. If boreholes exist in the vicinity of a seismic survey, it may be possible to correlate velocity values so derived with individual rock units encountered within borehole sequences. As discussed in Chapter 11, veloc- ity may also be measured directly in boreholes using a sonic probe, which emits high-frequency pulses and measures the travel time of the pulses through a small vertical interval of wall rock. Drawing the probe up through the borehole yields a sonic log, or continuous velocity log (CVL), which is a record of velocity varia- In the laboratory, velocities are determined by meas- uring the travel-time of high-frequency (about 1 MHz) acoustic pulses transmitted through cylindrical rock specimens. By this means, the effect on velocity of vary- ing temperature, con?ning pressure, pore ?uid pressure or composition may be quantitatively assessed. It is im- portant to note that laboratory measurements at low con?ning pressures are of doubtful validity.The intrinsic velocity of a rock is not normally attained in the labora- tory below a con?ning pressure of about 100 MPa (megapascals), or 1 kbar, at which pressure the original solid contact between grains characteristic of the pristine The following empirical ?ndings of velocity studies are noteworthy: 1. Compressional wave velocity increases with con?n- 2. Sandstone and shale velocities show a systematic increase with depth of burial and with age, due to the combined effects of progressive compaction and 3. For a wide range of sedimentary rocks the compres- sional wave velocity is related to density, and well- established velocity–density curves have been published Hence, the densities of inaccessible subsurface layers may be predicted if their velocity is known from seismic 4. The presence of gas in sedimentary rocks reduces the elastic moduli, Poisson’s ratio and the v /v ratio. v /v ra- ps ps tios greater than 2.0 are characteristic of unconsolidated sand, whilst values less than 2.0 may indicate either a consolidated sandstone or a gas-?lled unconsolidated sand. The potential value of v in detecting gas-?lled s sediments accounts for the current interest in shear wave Typical compressional wave velocity values and ranges forawidevarietyof EarthmaterialsaregiveninTable3.1.

    Elements of Seismic Surveying 27 v (km s-1) p Unconsolidated materials Sand (dry) 0.2–1.0 Sand (water-saturated) 1.5–2.0 Clay 1.0–2.5 Glacial till (water-saturated) 1.5–2.5 Permafrost 3.5–4.0 Sedimentary rocks Sandstones 2.0–6.0 Tertiary sandstone 2.0–2.5 Pennant sandstone (Carboniferous) 4.0–4.5 Cambrian quartzite 5.5–6.0 Limestones 2.0–6.0 Cretaceous chalk 2.0–2.5 Jurassic oolites and bioclastic limestones 3.0–4.0 Carboniferous limestone 5.0–5.5 Dolomites 2.5–6.5 Salt 4.5–5.0 Anhydrite 4.5–6.5 Gypsum 2.0–3.5 Igneous/Metamorphic rocks Granite 5.5–6.0 Gabbro 6.5–7.0 Ultrama?c rocks 7.5–8.5 Serpentinite 5.5–6.5 Pore ?uids Air 0.3 Water 1.4–1.5 Ice 3.4 Petroleum 1.3–1.4 Other materials Steel 6.1 Iron 5.8 Aluminium 6.6 Concrete 3.6

    3.5 Attenuation of seismic energy along ray paths As a seismic pulse propagates in a homogeneous ma- terial, the original energy E transmitted outwards from the source becomes distributed over a spherical shell, the wavefront, of expanding radius. If the radius of the wave- front is r, the amount of energy contained within a unit area of the shell is E/4pr2.With increasing distance along a ray path, the energy contained in the ray falls off as r-2 due to the effect of the geometrical spreading of the energy.

    Wave amplitude, which is proportional to the square A further cause of energy loss along a ray path arises because, even at the low strains involved, the ground is imperfectly elastic in its response to the passage of seismic waves. Elastic energy is gradually absorbed into the medium by internal frictional losses, leading eventually to the total disappearance of the seismic disturbance.The mechanisms for the absorption of energy are complex, but the loss of energy is usually regarded as being a ?xed proportion of the total energy, for each oscillation of the rock particles involved, during which time the wave- front will have moved forward one wavelength. The ab- sorption coef?cient a expresses the proportion of energy lost during transmission through a distance equivalent to a complete wavelength l.Values of a for common Earth materials range from 0.25 to 0.75 dB l-1 (for a de?nition Over the range of frequencies used in seismic survey- ing the absorption coef?cient is normally assumed to be independent of frequency. If the amount of absorp- tion per wavelength is constant, it follows that higher frequency waves attenuate more rapidly than lower frequency waves as a function of time or distance. To illustrate this point, consider two waves with frequencies of 10 Hz and 100 Hz to propagate through a rock in which v = 2.0 km s-1 and a = 0.5 dB l-1. The 100 Hz p wave (l = 20 m) will be attenuated due to absorption by 5 dB over a distance of 200 m, whereas the 10 Hz wave (l = 200 m) will be attenuated by only 0.5 dB over the same distance. The shape of a seismic pulse with a broad fre- quency content therefore changes continuously during propagation due to the progressive loss of the higher fre- quencies. In general, the effect of absorption is to pro- 3.7). This effect of absorption is a familiar experience as it applies to P-waves in air, sound. The sharp crack of a nearby lightning ?ash is heard far away as the distant `rumble’ of thunder.

    3.6 Ray paths in layered media At an interface between two rock layers there is gen- erally a change of propagation velocity resulting from At such an interface, the energy within an incident seis- mic pulse is partitioned into transmitted and re?ected pulses. The relative amplitudes of the transmitted and re?ected pulses depend on the velocities and densities Input spike

    20 ms After 1 s After 2 s After 3 s After 4 s After 5 s Fig. 3.7 The progressive change of shape of an original spike pulse during its propagation through the ground due to the effects of absorption. (After Anstey 1977.)

    of the two layers, and the angle of incidence on the 3.6.1 Re?ection and transmission of normally incident seismic rays Consider a compressional ray of amplitude A normally 0 incident on an interface between two media of differ- ing velocity and density (Fig. 3.8). A transmitted ray of amplitude A travels on through the interface in the 2 same direction as the incident ray and a re?ected ray of amplitude A returns back along the path of the 1 The total energy of the transmitted and re?ected rays must equal the energy of the incident ray. The relative proportions of energy transmitted and re?ected are de- termined by the contrast in acoustic impedance Z across the interface. The acoustic impedance of a rock is the prod- uct of its density (r) and its wave velocity(v); that is, Z = rv

    Incident ray, amplitude A0 Elements of Seismic Surveying 29

    Reflected ray, v1, ?1 amplitude A1 Transmitted ray, v2, ?2 amplitude A2 ?2v2 =/ ?1v1 Fig. 3.8 Re?ected and transmitted rays associated with a ray normally incident on an interface of acoustic impedance contrast.

    interface, and more energy is re?ected the greater the contrast. From common experience with sound, the best echoes come from rock or brick walls. In terms of physical theory, acoustic impedance is closely analogous to elec- trical impedance and, just as the maximum transmission of electrical energy requires a matching of electrical im- pedances, so the maximum transmission of seismic ener- The re?ection coef?cient R is a numerical measure of the effect of an interface on wave propagation, and is calcu- lated as the ratio of the amplitude A of the re?ected ray 1 to the amplitude A of the incident ray 0

    R=A A 10 To relate this simple measure to the physical properties of the materials at the interface is a complex problem. As we have already seen, the propagation of a P-wave de- pends on the bulk and shear elastic moduli, as well as the density of the material. At the boundary the stress and strain in the two materials must be considered. Since the materials are different, the relations between stress and strain in each will be different. The orientation of stress and strain to the interface also becomes important. The formal solution of this physical problem was derived early in the 20th century, and the resulting equations are named the Zoeppritz equations (Zoeppritz 1919; and for explanation of derivations see Sheriff & Geldart 1982). Here, the solutions of these equations will be accepted. For a normally incident ray the relationships are fairly simple, giving:

    rv-rv Z-Z R= 22 11= 2 1 rv+rv Z+Z 22 11 2 1 where r , v , Z and r , v , Z are the density, P-wave 111 222 velocity and acoustic impedance values in the ?rst and second layers, respectively. From this equation it follows that -1 £ R £ +1. A negative value of R signi?es a phase The transmission coef?cient T is the ratio of the ampli- tude A of the transmitted ray to the amplitude A of the 20 incident ray

    T=A A 20 For a normally incident ray this is given, from solution of Zoeppritz’s equations, by

    2Z T= 1 Z +Z 21 Re?ection and transmission coef?cients are some- times expressed in terms of energy rather than wave am- plitude. If energy intensity I is de?ned as the amount of energy ?owing through a unit area normal to the direc- tion of wave propagation in unit time, so that I , I and I 01 2 are the intensities of the incident, re?ected and trans- mitted rays respectively, then

    where R¢ and T¢ are the re?ection and transmission coef- This is the case when there is no contrast of acoustic im- pedance across an interface, even if the density and ve- 12 A good approximation to this situation occurs at the free surface of a water layer: rays travelling upwards from an explosion in a water layer are almost totally re?ected back from the water surface with a phase change of p (R Values of re?ection coef?cient R for interfaces be- tween different rock types rarely exceed ±0.5 and are typically much less than ±0.2.Thus, normally the bulk of seismic energy incident on a rock interface is transmitted and only a small proportion is re?ected. By use of an em- pirical relationship between velocity and density (see also Section 6.9), it is possible to estimate the re?ection coef?cient from velocity information alone (Gardner et al. 1974, Meckel & Nath 1977):

    R=0.625ln(v1v2) Such relationships can be useful, but must be applied with caution since rock lithologies are highly variable and laterally heterogeneous as pointed out in Section 3.4.

    3.6.2 Re?ection and refraction of obliquely incident rays When a P-wave ray is obliquely incident on an inter- face of acoustic impedance contrast, re?ected and trans- mitted P-wave rays are generated as in the case of normal incidence. Additionally, some of the incident com- pressional energy is converted into re?ected and trans- mitted S-wave rays (Fig. 3.9) that are polarized in a vertical plane. Zoeppritz’s equations show that the am- plitudes of the four phases are a function of the angle of incidence q. The converted rays may attain a signi?cant magnitude at large angles of incidence. Detection and identi?cation of converted waves can be dif?cult in seis- mic surveys, but they do have potential to provide more constraints on the physical properties of the media at the interface. Here consideration will be con?ned to the In the case of oblique incidence, the transmitted P- wave ray travels through the lower layer with a changed direction of propagation (Fig. 3.10) and is referred to as a refracted ray.The situation is directly analogous to the be- Reflected S

    Incident P ? Reflected P v1 v2 > v1 Refracted P

    Refracted S Fig. 3.9 Re?ected and refracted P- and S-wave rays generated by a P-wave ray obliquely incident on an interface of acoustic impedance contrast.

    Incident P ?1 ?1 Reflected P

    v1 v2 > v1 Refracted P ?2 Fig. 3.10 Re?ected and refracted P-wave rays associated with a P-wave rays obliquely incident on an interface of acoustic impedance contrast.

    haviour of a light ray obliquely incident on the boundary between, say, air and water and Snell’s Law of Refraction applies equally to the optical and seismic cases. Snell de- ?ned the ray parameter p = sin i/v, where i is the angle of inclination of the ray in a layer in which it is travelling with a velocity v. The generalized form of Snell’s Law states that, along any one ray, the ray parameter remains a For the refracted P-wave ray shown in Fig. 3.10, therefore

    sin q v 1=1 sin q v 22 Note that if v > v the ray is refracted away from the 21 normal to the interface; that is, q > q . Snell’s Law also 21 applies to the re?ected ray, from which it follows that the 3.10).

    3.6.3 Critical refraction When the velocity is higher in the underlying layer there is a particular angle of incidence, known as the critical angle q , for which the angle of refraction is 90°. This c gives rise to a critically refracted ray that travels along the interface at the higher velocity v . At any greater angle of 2 incidence there is total internal re?ection of the incident energy (apart from converted S-wave rays over a further range of angles).The critical angle is given by

    sin q sin 90? 1 c= = vvv 122 so that q = sin – 1 ( ) c v1 v 2

    The passage of the critically refracted ray along the top of the lower layer causes a perturbation in the upper layer that travels forward at the velocity v , which is greater 2 than the seismic velocity v of that upper layer. The 1 situation is analogous to that of a projectile travelling through air at a velocity greater than the velocity of sound in air and the result is the same, the generation of a shock wave.This wave is known as a head wave in the seis- Elements of Seismic Surveying 31

    mic case, and it passes up obliquely through the upper layer towards the surface (Fig. 3.11). Any ray associated with the head wave is inclined at the critical angle i . By c means of the head wave, seismic energy is returned to the surface after critical refraction in an underlying layer of higher velocity.

    3.6.4 Diffraction In the above discussion of the re?ection and transmission of seismic energy at interfaces of acoustic impedance contrast it was implicitly assumed that the interfaces were continuous and approximately planar. At abrupt discontinuities in interfaces, or structures whose radius of curvature is shorter than the wavelength of incident waves, the laws of re?ection and refraction no longer apply. Such phenomena give rise to a radial scattering of incident seismic energy known as diffraction. Common sources of diffraction in the ground include the edges of faulted layers (Fig. 3.12) and small isolated objects, such as boulders, in an otherwise homogeneous layer.

    Ray paths Head wave generated in overlying layer ?c

    v1 A B v2 > v1

    Wavefront expanding in lower layer Fig. 3.11 Generation of a head wave in the upper layer by a wave propagating through the lower layer.

    (a) (b) t 1 v 1 1 v 2 xx x crit cros (c) Fig. 3.13 (a) Seismogram showing the S D output traces of 24 geophones distributed X along the Earth’s surface as a function of time. (b)Travel-time curves for direct, z re?ected and refracted rays in the case of a v1 simple two-layer model. (c) Direct, re?ected and refracted ray paths from a near surface source to a surface detector v2 in the case of a simple two-layer model.

    Diffracted phases are commonly observed in seismic recordings and are sometimes dif?cult to discriminate from re?ected and refracted phases, as discussed in Chapter 4.

    refracted ray travels obliquely down to the interface at ve- locity v , along a segment of the interface at the higher 1 21 The travel time of a direct ray is given simply by t =xv dir 1

    which de?nes a straight line of slope l/v passing through 1 The travel time of a re?ected ray is given by

    12 (x2 + 4z2) t= refl v 1 which, as discussed in Chapter 4, is the equation of an The travel time of a refracted ray (for derivation see Chapter 5) is given by

    x 2z cosq t=+ c refr vv 21 which is the equation of a straight line having a slope of l/v and an intercept on the time axis of 2

    2z cosq c v 1 Travel-time curves, or time–distance curves, for 3.13. By suitable analysis of the travel-time curve for re?ected or refracted rays it is possible to compute the depth to the underlying layer. This provides two inde- pendent seismic surveying methods for locating and mapping subsurface interfaces, re?ection surveying and refraction surveying. These have their own distinctive methodologies and ?elds of application and they are dis- cussed separately in detail in Chapters 4 and 5. However, some general remarks about the two methods may be made here with reference to the travel-time curves and seismogram of Fig. 3.13. The curves are more compli- cated in the case of a multilayered model, but the follow- The ?rst arrival of seismic energy at a surface detector offset from a surface source is always a direct ray or a re- fracted ray. The direct ray is overtaken by a refracted ray at the crossover distance x . Beyond this offset distance cros the ?rst arrival is always a refracted ray. Since critically re- Elements of Seismic Surveying 33

    fracted rays travel down to the interface at the critical angle there is a certain distance, known as the critical dis- tance x , within which refracted energy will not be re- cr it turned to the surface. At the critical distance, the travel times of re?ected rays and refracted rays coincide because they follow effectively the same path. Re?ected rays are never ?rst arrivals; they are always preceded by direct rays The above characteristics of the travel-time curves determine the methodology of refraction and re?ection surveying. In refraction surveying, recording ranges are chosen to be suf?ciently large to ensure that the cross- over distance is well exceeded in order that refracted rays Indeed, some types of refraction survey consider only these ?rst arrivals, which can be detected with unsophis- ticated ?eld recording systems. In general, this approach means that the deeper a refractor, the greater is the range over which recordings of refracted arrivals need to be In re?ection surveying, by contrast, re?ected phases are sought that are never ?rst arrivals and are normally of very low amplitude because geological re?ectors tend to have small re?ection coef?cients. Consequently, re?ec- tions are normally concealed in seismic records by higher amplitude events such as direct or refracted body Re?ection surveying methods therefore have to be capable of discriminating between re?ected energy and many types of synchronous noise. Recordings are nor- mally restricted to small offset distances, well within the critical distance for the re?ecting interfaces of main interest. However, in multichannel re?ection surveying recordings are conventionally taken over a signi?cant range of offset distances, for reasons that are discussed fully in Chapter 4.

    · record and display the seismic waveforms on a suitable The general methodology of examining hidden structures by studying their effects on arti?cially gener- ated acoustic or seismic waves has an enormously wide range of applications covering a wide range of spatial scales. Perhaps the smallest scale is ultrasound imaging in medicine, which can also be applied industrially to examining engineering structures. Within the more geophysical applications, the scales range from depths of a metre or less in engineering, environmental or archae- ological surveys to tens of kilometres for crustal and For each application there is a limit to the smallest structures that can be detected, known as the resolution of the survey.The resolution is basically determined by the pulse length: for a pulse of any particular length there is a minimum separation below which the pulses will overlap in time in the seismic recording. Although the pulse length may be shortened at the processing stage by deconvolution (see Section 4.8.2), this is only possible if the data are of good quality, and is a complement to, not a substitute for, good survey design. The pulse width is determined by both the maximum frequency Since Earth materials absorb seismic energy in a fre- quency-selective way (Section 3.5), the optimum wave- form will be speci?c to each survey. It is an important characteristic of all geophysical surveys, and particularly seismic ones, that they must be designed individually for each speci?c case. The general aspects of the equipment used for seismic surveys are reviewed here; speci?c variations for re?ection and refraction surveying are described in Chapters 4 and 5.

    3.8.1 Seismic sources and the seismic/acoustic spectrum A seismic source is a localized region within which the sudden release of energy leads to a rapid stressing of the surrounding medium. The archetypal seismic source is an explosion. While explosives are still used, there is an increasing number of more sophisticated and ef?cient The main requirements of the seismic source are: · Suf?cient energy across the broadest possible fre- quency range, extending up to the highest recordable · Energy should be concentrated in the type of wave energy which is required for a speci?c survey, either P- wave or S-wave, and generate minimum energy of other wave types. Such other unwanted energy would degrade · The source waveform must be repeatable. Seismic sur- veys almost always involve comparing the seismograms Variations on the seismograms should be diagnostic of the ground structure, not due to random variations of · The source must be safe, ef?cient, and environmen- tally acceptable. Most seismic surveys are commercial operations which are governed by safety and environ- mental legislation.They must be as cost-effective as pos- sible. Sometimes the requirements for ef?ciency lead to higher safety and environmental standards than legally enforced.Whether involving personal injury or not, ac- cidents are referred to as `lost-time incidents’. Safety aids ef?ciency as well as being desirable from many other The complete seismic/acoustic spectrum is shown in Fig. 3.14.There is a very wide variety of seismic sources, characterized by differing energy levels and frequency characteristics. In general, a seismic source contains a wide range of frequency components within the range from 1 Hz to a few hundred hertz, though the energy is Source characteristics can be modi?ed by the use of several similar sources in an array designed, for example, to improve the frequency spectrum of the transmitted pulse. This matter is taken up in Chapter 4 when dis- cussing the design parameters of seismic re?ection surveys.

    Elements of Seismic Surveying 35 Echo sounders Pingers Boomers Sparkers Air guns Vibroseis Quarry blasts Earthquake body waves Earthquake surface waves

    10–2 10–1 1 101 102 103 104 105 Frequency (Hz) (log scale)

    and usually three, of the basic requirements for modern surveys, their use is steadily declining and limited to lo- cations where alternative sources cannot be used.

    Vibroseis sweep signal Reflection from base of layer 1 Reflection from base of layer 2

    Reflection from base of layer 3 (phase inverted) Field recording (superposition of above reflections)

    Output trace resulting from correlation of field recording with sweep signal t=0 Time

    Fig. 3.15 Cross-correlation of aVibroseis® seismogram with the input sweep signal to locate the positions of occurrence of re?ected arrivals.

    Firing pin pulse-encoded signal from buried interfaces. Peaks in the cross-correlation function reveal the positions of Weight drops and hammers. Perhaps the simplest land seismic source is a large mass dropped on to the ground surface. Weight drops have been manufactured in a wide variety of forms from eight-wheel trucks dropping a weight of several tonnes, to a single person with a sledgehammer. If the source energy required is relatively low, these types of sources can be fast and ef?cient. The horizontal impact of a weight or hammer on to one side of a vertical plate partially embedded in the ground can be used as a source for shear wave Shotguns, buffalo guns and ri?es. One solution to gaining additional energy for small-scale surveys is to use the Ri?es have been used as seismic sources by ?ring the bullet into the ground. While effective as a very high- frequency source, this is banned by legislation in many countries. An alternative is to ?re a blank shotgun car- tridge in a hole using a suitable device, commonly termed a buffalo gun (Fig 3.16).The blank shotgun car- tridge offers an impulsive source giving considerably more energy than a sledgehammer, with few of the safety problems of explosives.

    Ground surface Auger flight Firing chamber Fig. 3.16 Schematic cross-section of a typical buffalo gun.The cartridge is ?red by dropping a simple ?ring pin on to the cartridge.

    (a) Variable chamber size (b) Air Elements of Seismic Surveying 37

    Water Fig. 3.17 Schematic cross-sections through (a) a Bolt air gun and (b) a Sodera water gun to illustrate the principles of operation. (Redrawn with permission of Bolt Associates and Sodera Ltd.)

    (a) Single 270 in3 air gun 0 (b) 0.1 0.2 0.3 0.4 0.5 0.6

    Seven – gun array (1222 in3 total volume) water.When the piston stops, a vacuum cavity is created behind the advancing water jet and this implodes under the in?uence of the ambient hydrostatic pressure, gener- Since the implosion represents collapse into a vacuum, no gaseous material is compressed to ` bounce back’ as a bubble pulse. The resulting short pulse length offers a potentially higher resolution than is achieved with air guns but at the expense of a more complex initial source Several marine sources utilize explosive mixtures of gases, but these have not achieved the same safety and reliability, and hence industry acceptance, as air guns. In sleeve exploders, propane and oxygen are piped into a sub- merged ?exible rubber sleeve where the gaseous mix- 0.7 0.8 s

    Fig. 3.18 Comparison of the source signatures of (a) a single air gun (peak pressure: 4.6 bar metres) and (b) a seven- Note the effective suppression of bubble pulses in the latter case. (Redrawn with permission of Bolt Associates.)

    behind the survey vessel. Operating voltages are typi- This electrical discharge leads to the formation and rapid growth of a plasma bubble and the consequent genera- tion of an acoustic pulse. For safety reasons, sparkers are Boomers comprise a rigid aluminium plate attached below a heavy-duty electrical coil by a spring-loaded mounting. A capacitor bank is discharged through the coil and the electromagnetic induction thus generated forces the aluminium plate rapidly downwards, setting up a compressional wave in the water. The device is typically towed behind the survey vessel in a catamaran Sparkers and boomers generate broad-band acoustic pulses and can be operated over a wide range of energy levels so that the source characteristics can to some ex- tent be tailored to the needs of a particular survey. In gen- eral, boomers offer better resolution (down to 0.5 m) but more restricted depth penetration (a few hundred metres Pingers consist of small ceramic piezoelectric transducers, mounted in a towing ?sh, which, when ac- tivated by an electrical impulse, emit a very short, high- frequency acoustic pulse of low energy.They offer a very high resolving power (down to 0.1 m) but limited pene- tration (a few tens of metres in mud, much less in sand or rock). They are useful in offshore engineering applica- tions such as surveys of proposed routes for submarine Chirp systems are electro-mechanical transducers that produce an extended, repeatable, source waveform which allows greater energy output. This longer signal can be compressed in processing to give greater resolu- Further discussion of the use of air guns, sparkers, boomers and pingers in single-channel seismic re?ec- tion pro?ling systems is given in Section 4.15.

    3.8.2 Seismic transducers Conversion of the ground motion to an electrical signal requires a transducer which is sensitive to some compo- nent of the ground motion, and can record the required The ?rst issue is which component of the motion to measure. As the ground oscillates, it is possible to mea- sure either the displacement, velocity or acceleration of the ground particles as the wave passes.The ground mo- tion also takes place in three dimensions. To record it Elements of Seismic Surveying 39

    Shunt resistor Leaf spring supportCoil output to seismic amplifier

    Coil N S N Permanent magnet Fig. 3.19 Schematic cross-section through a moving-coil geophone.

    Resonant frequency (a) (b) 180 0.80 150 – 1 ) 0.40h = 0.2 120 s –1 0.20h = 0.5 90 h = 0.7 60 Output phase Output (V cm 0.10 30

    0 0 10 20 30 40 Frequency (Hz) Resonant frequency

    10 20 30 40 Frequency (Hz) h = 0.7 h = 0.5 h = 0.2 Fig. 3.20 Amplitude and phase responses of a geophone with a resonant frequency of 7 Hz, for different damping factors h. Output phase is expressed relative to input phase. (AfterTelford et al. 1976.)

    hydrophones are made up into hydrophone streamers by distributing them along an oil-?lled plastic tube. The tube is arranged to have neutral buoyancy and is manu- factured from materials with an acoustic impedance close to that of water to ensure good transmission of seismic energy to the hydrophone elements. Since piezoelectric elements are also sensitive to accelerations, hydrophones are often composed of two elements mounted back to back and connected in series so that the effects of accelerations of the streamer as it is towed through the water are cancelled out in the hydrophone outputs. The response of each element to pressure change is, however, unaffected and the seismic signal is Arrays of geophones or hydrophones may be con- nected together into linear or areal arrays containing tens or even hundreds of transducers whose individual out- puts are summed. Such arrays provide detectors with a directional response that facilitates the enhancement of signal and the suppression of certain types of noise as dis- cussed further in Chapter 4.

    3.8.3 Seismic recording systems Recording a seismogram is a very dif?cult technical operation from at least three key aspects: 1. The recording must be timed accurately relative to 2. Seismograms must be recorded with multiple trans- ducers simultaneously, so that the speed and direction of The least dif?cult of these problems is the timing. For nearly all seismic surveys, times need to be accurate to better than one thousandth of a second (one milli- second). For very small-scale surveys the requirement may be for better than 0.1 ms. In fact, with modern electronics, measuring such short time intervals is not dif?cult. Usually the biggest uncertainty is in deciding how to measure the instant when the seismic source started the wave. Even in a simple case, as for a sledge- hammer hitting the ground, is the correct instant when the hammer ?rst hits the ground, or when it stops compressing the ground and a seismic wave radiates out- ward?The ?rst is easy to measure, the second is probably more important, and they are usually separated by more In order to determine the subsurface path of the seis- mic energy, the direction from which the wave arrives at the surface must be determined.This is achieved by hav- Elements of Seismic Surveying 41

    and potentially reveals more information about the Distributed systems In seismic surveying the outputs of several detectors are fed to a multichannel recording system mounted in a recording vehicle. The individual detector outputs may be fed along a multicore cable.The weight and complex- ity of multicore cables becomes prohibitive as the num- ber of channels of data rises into the hundreds. Modern systems distribute the task of ampli?cation, digitization and recording of data from groups of detectors to indi- vidual computer units left unattended in the ?eld.These are connected together to make a ?eld computer net- work using lightweight ?bre-optic cables or telemetry links. The separate units can then be controlled by a central recording station, and upload their digital seis- mograms to it on command.

    Problems 1. How does the progressive loss of higher fre- quencies in a propagating seismic pulse lead to 2. A 10 Hz seismic wave travelling at 5 km s-1 propagates for 1000 m through a medium with an absorption coef?cient of 0.2 dB l-1. What is the wave attenuation in decibels due solely to 3. A wave component with a wavelength of 100 m propagates through a homogeneous medium from a seismic source at the bottom of a borehole. Between two detectors, located in boreholes at radial distances of 1 km and 2 km from the source, the wave amplitude is found to be attenuated by 10 dB. Calculate the contribu- tion of geometrical spreading to this value of at- tenuation and, thus, determine the absorption coef?cient of the medium.

    4. What is the crossover distance for direct and critically refracted rays in the case of a horizontal interface at a depth of 200 m separating a top layer of velocity 3.0 km s-1 from a lower layer of 5. A seismic pulse generated by a surface source is returned to the surface after re?ection at the tenth of a series of horizontal interfaces, each of which has a re?ection coef?cient R of 0.1. What is the attenuation in amplitude of the pulse caused by energy partitioning at all interfaces 6. At what frequency would a 150 Hz signal be recorded by a digital recording system with a sampling rate of 100 Hz?

    Further reading Al-Sadi, H.N. (1980) Seismic Exploration. Birkhauser Verlag, Anstey, N.A. (1981) Seismic Prospecting Instruments. Vol 1: Signal Characteristics and Instrument Speci?cations. Gebruder Born- Dobrin, M.B. & Savit, C.H. (1988) Introduction to Geophysical Gregory, A.R. (1977) Aspects of rock physics from laboratory and log data that are important to seismic interpretation. In: Payton, C.E. (ed.), Seismic Stratigraphy — Applications to Hydrocarbon Exploration. Memoir 26, American Association of Petroleum Geologists,Tulsa.

    SEG (1997) Digital Tape Standards (SEG-A, SEG-B, SEG-C, SEG-Y and SEG-D formats plus SEG-D rev 1&2). Compiled by SEG Technical Standards Committee. Society of Exploration Sheriff, R.E. & Geldart. L.P. (1982) Exploration Seismology Vol 1: History.Theory and DataAcquisition. Cambridge University Press, Sheriff, R.E. & Geldart, L.P. (1983) Exploration Seismology Vol 2: Data-Processing and Interpretation. Cambridge University Press, Waters, K.H. (1978) Re?ection Seismology — A Tool For Energy Re- Zoeppritz, K, 1919. Uber re?exion und durchgang seismischer wellen durch Unstetigkerls?aschen. Berlin, Uber Erdbeben- wellen VII B, Nachrichten der Koniglichen Gesellschaft der Wissensschaften zu Gottingen, math-phys. Kl. pp. 57–84.

    4.1 Introduction Seismic re?ection surveying is the most widely used and well-known geophysical technique.The current state of sophistication of the technique is largely a result of the enormous investment in its development made by the hydrocarbon industry, coupled with the development of advanced electronic and computing technology. Seismic sections can now be produced to reveal details of geo- logical structures on scales from the top tens of metres of drift to the whole lithosphere. Part of the spectacu- lar success of the method lies in the fact that the raw data are processed to produce a seismic section which is an image of the subsurface structure. This also provides a trap for the unwary, since the seismic section is similar to, but fundamentally different from, a depth section of the geology. Only by understanding how the re?ection method is used and seismic sections are created, can the geologist make informed interpretations. This chapter provides the essential knowledge and understanding to support interpretation of seismic re?ection data. It builds up systematically from the basics of seismic wave re- ?ection from rock layers, and refers back to relevant material in Chapters 2 and 3.

    4.2 Geometry of re?ected ray paths In seismic re?ection surveys seismic energy pulses are re?ected from subsurface interfaces and recorded at near-normal incidence at the surface. The travel times are measured and can be converted into estimates of depths to the interfaces. Re?ection surveys are most commonly carried out in areas of shallowly dipping sedimentary sequences. In such situations, velocity varies as a function of depth, due to the differing physical properties of the individual layers. Velocity may also vary horizontally, due to lateral lithological changes within the individual layers. As a ?rst approxi- mation, the horizontal variations of velocity may be Figure 4.1 shows a simple physical model of horizontally-layered ground with vertical re?ected ray paths from the various layer boundaries. This model assumes each layer to be characterized by an interval veloc- ity v , which may correspond to the uniform velocity i within a homogeneous geological unit or the average velocity over a depth interval containing more than one unit. If z is the thickness of such an interval and t is the ii one-way travel time of a ray through it, the interval velocity is given by

    z v=i it i The interval velocity may be averaged over several depth intervals to yield a time-average velocity or, simply, average velocityV .Thus the average velocity of the top n layers in Fig. 4.1 is given by

    nn Âz Âvt i ii V = i =1 = i =1 nn Ât Ât ii i =1 i =1

    or, if Z is the total thickness of the top n layers and T is nn the total one-way travel time through the n layers,

    v 1 v 2 v 3 v n–1 v n Fig. 4.1 Vertical re?ected ray paths in a horizontally-layered ground.

    ?ector lying at a depth z beneath a homogeneous top layer of velocity V. The equation for the travel time t of the re?ected ray from a shot point to a detector at a hori- zontal offset, or shot–detector separation, x is given by the ratio of the travel path length to the velocity 12 t = (x2 + 4z2) V (4.1) In a re?ection survey, re?ection time t is measured at an offset distance x.These values can be applied to equation (4.1), but still leave two unknown values which are re- lated to the subsurface structure, z and V. If many re?ec- tion times t are measured at different offsets x, there will be enough information to solve equation (4.1) for both these unknown values. The graph of travel time of re?ected rays plotted against offset distance (the time– distance curve) is a hyperbola whose axis of symmetry is Substituting x = 0 in equation (4.1), the travel time t 0 of a vertically re?ected ray is obtained:

    2z t = (4.2) 0 V (a) xx

    z V (b)t t x ?T t 0

    –x O + x x Fig. 4.2 (a) Section through a single horizontal layer showing the geometry of re?ected ray paths and (b) time–distance curve for re?ected rays from a horizontal re?ector. DT = normal moveout (NMO).

    This is the intercept on the time axis of the time–distance curve (see Fig. 4.2(b)). Equation (4.1) can be written

    4z2 x2 t 2 = + (4.3) V2 V2

    Thus x2 t 2 = t 2 + (4.4) 0 V2

    velocity is by considering the increase of re?ected travel time with offset distance, the moveout, as discussed Equation (4.3) can also be rearranged 12 12 È 2? 2 2z Ê x ^ È Ê x ^ ? Ë ¯ 0 Ë ¯ (4.5) V Î 2z ° Î Vt ° 0

    This form of the equation is useful since it indicates clearly that the travel time at any offset x will be the vertical travel time plus an additional amount which 0 This relationship can be reduced to an even simpler form with a little more rearrangement. Using the standard binomial expansion of equation (4.5) gives È24 1Ê x ^ 1Ê x ^ ? 0 Î 2 ËVt0 ¯ 8 ËVt0 ¯ °

    Remembering that t = 2z/V, the term x/Vt can be 00 written as x/2z. If x = z, the second term in this series becomes 1/8 of (1/2)4, i.e. 0.0078, which is less than a 1% change in the value of t. For small offset/depth ratios (i.e. x/z << 1), the normal case in re?ection surveying, this equation may be truncated after the ?rst term to obtain the approximation

    È 1Ê x ^2? x2 t ª t Í1 + . ª t + (4.6) 0 Î 2 ËVt ¯ ° 2V 2t0 0 0

    This is the most convenient form of the time–distance equation for re?ected rays and it is used extensively in the Moveout is de?ned as the difference between the travel times t and t of re?ected-ray arrivals recorded at 12 two offset distances x and x . Substituting t , x and t , x 1 2 11 22 in equation (4.6), and subtracting the resulting equations gives

    x2 – x2 t -t ª 2 1 2 1 2V 2t 0 Normal moveout (NMO) at an offset distance x is the difference in travel time DT between re?ected arrivals at x and at zero offset (see Fig. 4.2)

    x2 DT = t – t ª (4.7) x 0 2V 2t 0 Seismic Re?ection Surveying 45

    Note that NMO is a function of offset, velocity and re- ?ector depth z (since z = Vt /2).The concept of move- 0 out is fundamental to the recognition, correlation and enhancement of re?ection events, and to the calculation of velocities using re?ection data. It is used explicitly or implicitly at many stages in the processing and interpre- As an important example of its use, consider the T –DT method of velocity analysis. Rearranging the terms of equation (4.7) yields

    x V ª (4.8) 12 (2t DT ) 0

    Using this relationship, the velocity V above the re?ector can be computed from knowledge of the zero-offset re?ection time (t ) and the NMO (DT ) at a particular 0 offset x. In practice, such velocity values are obtained by computer analysis which produces a statistical estimate based upon many such calculations using large numbers of re?ected ray paths (see Section 4.7). Once the velocity has been derived, it can be used in conjunction with t to compute the depth z to the re?ector using 0 0

    4.2.2 Sequence of horizontal re?ectors In a multilayered ground, inclined rays re?ected from the nth interface undergo refraction at all higher inter- faces to produce a complex travel path (Fig. 4.3(a)). At offset distances that are small compared to re?ector depths, the travel-time curve is still essentially hyper- bolic but the homogeneous top layer velocity V in equa- tions (4.1) and (4.7) is replaced by the average velocityV or, to a closer approximation (Dix 1955), the root-mean- square velocity V of the layers overlying the re?ector. As r ms the offset increases, the departure of the actual travel- time curve from a hyperbola becomes more marked The root-mean-square velocity of the section of ground down to the nth interface is given by

    12 nn È? V = Âv2t Ât Î i =1 i =1 °

    where v is the interval velocity of the ith layer and t is the ii one-way travel time of the re?ected ray through the ith layer.

    (a) (b)

    v 1 v 2 zV v rms, n 3 v n–1 v n t x Actual curve

    Hyperbolic curve 2 2 x2 t =t + 02 V rms Fig. 4.3 (a)The complex travel path of a re?ected ray through a multilayered ground, showing refraction at layer boundaries. (b)The time–distance curve for re?ected rays following such a travel path. Note that the divergence from the hyperbolic travel-time curve for a r ms

    Thus at small offsets x (x << z), the total travel time t n of the ray re?ected from the nth interface at depth z is given to a close approximation by

    12 t =(x2+4z2) V cf.equation(4.1) n rms

    and the NMO for the nth re?ector is given by x2 DTn ª cf. equation (4.7) 2V 2 t rms,n 0

    The individual NMO value associated with each re?ec- tion event may therefore be used to derive a root-mean- Values of V down to different re?ectors can then r ms be used to compute interval velocities using the Dix formula. To compute the interval velocity v for the nth n interval

    12 ÈVr2ms,n tn -V n -1 tn -1 ? 2 rms, n Î t -t ° n n -1

    where V 2 , t and V , t are, respectively, the rms,n-1 n-1 rms,n n root-mean-square velocity and re?ected ray travel times to the (n – 1)th and nth re?ectors (Dix 1955).

    4.2.3 Dipping re?ector In the case of a dipping re?ector (Fig. 4.4(a)) the value of dip q enters the time–distance equation as an additional unknown. The equation is derived similarly to that for horizontal layers by considering the ray path length divided by the velocity:

    12 (x2+4z2+4xzsinq) t = cf. equation (4.1) V

    The equation still has the form of a hyperbola, as for the horizontal re?ector, but the axis of symmetry of the Proceeding as in the case of a horizontal re?ector, using a truncated binomial expansion, the following expres- sion is obtained:

    (x2+4xzsinq) t ª t + (4.9) 0 2V 2t 0

    Seismic Re?ection Surveying 47 (a) (b) xx Fig. 4.4 (a) Geometry of re?ected ray paths and (b) time–distance curve for re?ected rays from a dipping re?ector. DT = dip moveout. –x 0 +x x d z

    t ?T d t x t –x V ? difference in travel times t and t of rays re?ected from x -x the dipping interface to receivers at equal and opposite offsets x and -x DT = t – t d x -x

    Using the individual travel times de?ned by equation (4.9) DT = 2x sin q V d

    Rearranging terms, and for small angles of dip (when sin q ª q ) q ª V DT 2x d

    (a) Primary Double-path Near-surface Peg-leg multiple multiples multiple

    (b) Short-path multiples extend pulse length Long-path multiples generate discrete pulse

    Fig. 4.5 (a) Various types of multiple re?ection in a layered ground. (b)The difference between short-path and long-path multiples.

    recorded pulse. Such multiples are known as short-path multiples (or short-period reverberations) and these may be contrasted with long-path multiples whose additional path length is suf?ciently long that the multiple re?ec- tion is a distinct and separate event in the seismic record Misidenti?cation of a long-path multiple as a primary event, for example, would lead to serious interpretation error. The arrival times of multiple re?ections are pre- dictable, however, from the corresponding primary re- ?ection times. Multiples can therefore be suppressed by suitable data processing techniques to be described later (Section 4.8).

    4.3 The re?ection seismogram The graphical plot of the output of a single detector in a re?ection spread is a visual representation of the local pattern of vertical ground motion (on land) or pressure variation (at sea) over a short interval of time following the triggering of a nearby seismic source. This seismic trace represents the combined response of the layered ground and the recording system to a seismic pulse. Any display of a collection of one or more seismic traces is termed a seismogram. A collection of such traces repre- senting the responses of a series of detectors to the energy from one shot is termed a shot gather. A collection of the traces relating to the seismic response at one surface mid-point is termed a common mid-point gather (CMP gather). The collection of the seismic traces for each CMP and their transformation to a component of the image presented as a seismic section is the main task of seismic re?ection processing.

    4.3.1 The seismic trace At each layer boundary a proportion of the incident en- The proportion is determined by the contrast in acoustic impedances of the two layers, and for a vertically travel- ling ray, the re?ection coef?cient can be simply calcul- ated (see Section 3.6). Figure 4.6 shows the relationship of the geological layering, the variation in acoustic im- pedance and the re?ection coef?cients as a function of depth. The detector receives a series of re?ected pulses, scaled in amplitude according to the distance travelled and the re?ection coef?cients of the various layer boundaries.The pulses arrive at times determined by the depths to the boundaries and the velocities of propaga- Assuming that the pulse shape remains unchanged as it propagates through such a layered ground, the resultant seismic trace may be regarded as the convolution of the input pulse with a time series known as a re?ectivity func- tion composed of a series of spikes. Each spike has an am- plitude related to the re?ection coef?cient of a boundary and a travel time equivalent to the two-way re?ection time for that boundary. This time series represents the impulse response of the layered ground (i.e. the output for a spike input). The convolution model is illustrated schematically in Fig. 4.6. Since the pulse has a ?nite length, individual re?ections from closely-spaced boundaries are seen to overlap in time on the resultant seismogram.

    Seismic Re?ection Surveying 49 Depth Fig. 4.6 The convolutional model of the re?ection seismic trace, showing the trace as the convolved output of a re?ectivity function with an input pulse, and the relationship of the re?ectivity function to the physical properties of the geological layers.

    (a) Detectors Central shot Geological Acoustic Reflection section impedance coefficient log log Reflectivity function Time vvv vv vvv

    (b) Detectors End shot Input Seismic * pulse = trace

    Detectors Fig. 4.7 Shot–detector con?gurations used in multichannel seismic re?ection pro?ling. (a) Split spread, or straddle spread. (b) Single- ended or on-end spread.

    In practice, as the pulse propagates it lengthens due to the progressive loss of its higher frequency components by absorption. The basic re?ection seismic trace may then be regarded as the convolution of the re?ectivity function with a time-varying seismic pulse. The trace will be further complicated by the superposition of various types of noise such as multiple re?ections, direct and re- fracted body waves, surface waves (ground roll), air waves and coherent and incoherent noise unconnected with the seismic source. In consequence of these several effects, seismic traces generally have a complex appear- ance and re?ection events are often not recogniz- able without the application of suitable processing In seismic re?ection surveying, the seismic traces are recorded, and the purpose of seismic processing can be viewed as an attempt to reconstruct the various columns of Fig. 4.6, moving from right to left.This will involve: · removing noise · determining the input pulse and removing that to give the re?ectivity function · determining the velocity function to allow conversion from time to depth axis · determination of the acoustic impedances (or related properties) of the formations.

    particular shot. In shot gathers, the seismic traces are plotted side by side in their correct relative positions and the records are commonly displayed with their time axes arranged vertically in a draped fashion. In these seismic records, recognition of re?ection events and their corre- lation from trace to trace is much assisted if one half of the normal `wiggly-trace’ waveform is blocked out. Figure 4.8 shows a draped section with this mode of display, de- rived from a split-spread multichannel survey. A short time after the shot instant the ?rst arrival of seismic ener- gy reaches the innermost geophones (the central traces) and this energy passes out symmetrically through the two arms of the split spread.The ?rst arrivals are followed by a series of re?ection events revealed by their hyper- bolic moveout.

    4.3.3 The CMP gather Each seismic trace has three primary geometrical factors which determine its nature.Two of these are the shot po- sition and the receiver position. The third, and perhaps most critical, is the position of the subsurface re?ection point. Before seismic processing this position is un- known, but a good approximation can be made by as- suming this re?ection point lies vertically under the position on the surface mid-way between the shot and Older terminology is to call this point the depth point, but the former term is a description of what the position is, rather than what it is wished to represent, and is hence preferred. Collecting all the traces with a common mid- The seismic industry and the literature use the older term common depth point (CDP) interchangeably for The CMP gather lies at the heart of seismic processing for two main reasons: 1. The simple equations derived in Section 4.2 assume horizontal uniform layers. They can be applied with less error to a set of traces that have passed through the same geological structure. The simplest approximation to such a set of traces is the CMP gather. In the case of horizontal layers, re?ection events on each CMP gather are re?ected from a common depth point (CDP – see Fig. 4.9(a)). For these traces, the variation of travel time with offset, the moveout, will depend only on the veloc- ity of the subsurface layers, and hence the subsurface 2. The re?ected seismic energy is usually very weak. It is imperative to increase the signal-to-noise ratio of most Fig. 4.8 A draped seismic record of a shot gather from a split spread (courtesy Prakla-Seismos GmbH). Sets of re?ected arrivals from individual interfaces are recognizable by the characteristic hyperbolic alignment of seismic pulses.The late-arriving, high- amplitude, low-frequency events, de?ning a triangular-shaped central zone within which re?ected arrivals are masked, represent surface waves (ground roll).These latter waves are a typical type of coherent noise.

    Seismic Re?ection Surveying 51 Shot – detector (a) midpoint S S S S CMP D D D D 43211234

    CDP (b) S S S S CMP D D D D 43211234

    Fig. 4.9 Common mid-point (CMP) re?ection pro?ling. (a) A set of rays from different shots to detectors re?ected off a common depth point (CDP) on a horizontal re?ector. (b)The common depth point is not achieved in the case of a dipping re?ector.

    random and coherent noise. Combining all the traces in a CMP together will average out the noise, and increase the signal-to-noise ratio (SNR). This process is termed Strictly, the common mid-point principle breaks down in the presence of dip because the common depth point then no longer directly underlies the shot– detector mid-point and the re?ection point differs for rays travelling to different offsets (see Fig. 4.9(b)). Never- theless, the method is suf?ciently robust that CMP stacks almost invariably result in marked improvements In two-dimensional CMP surveying, known as CMP pro?ling, the re?ection points are all assumed to lie in three-dimensional surveying, the re?ection points are distributed across an area of any subsurface re?ector, and the CMP is de?ned as a limited area on the surface.

    across a series of closely-spaced survey lines or around a grid of lines. However, as discussed later in Section 4.10, three-dimensional surveys provide a much better means of mapping three-dimensional structures and, in areas of structural complexity, they may provide the only means Re?ection pro?ling is normally carried out along pro?le lines with the shot point and its associated spread of detectors being moved progressively along the line to build up lateral coverage of the underlying geological section. This progression is carried out in a stepwise fashion on land but continuously, by a ship under way, at The two most common shot–detector con?gurations in multichannel re?ection pro?ling surveys are the split 4.7), where the number of detectors in a spread may be several hundred. In split spreads, the detectors are dis- tributed on either side of a central shot point; in single- ended spreads, the shot point is located at one end of the detector spread. Surveys on land are commonly carried out with a split-spread geometry, but in marine re?ec- tion surveys single-ended spreads are the normal con- ?guration due to the constraint of having to tow equipment behind a ship. The marine source is towed close behind the ship, with the hydrophone streamer (which may be several kilometers long) trailing behind.

    4.4.1 Vertical and horizontal resolution Re?ection surveys are normally designed to provide a speci?ed depth of penetration and a particular degree of resolution of the subsurface geology in both the vertical and horizontal dimensions. The vertical resolution is a measure of the ability to recognize individual, closely- spaced re?ectors and is determined by the pulse length on the recorded seismic section. For a re?ected pulse represented by a simple wavelet, the maximum resolu- tion possible is between one-quarter and one-eighth of the dominant wavelength of the pulse (Sheriff & Gel- dart 1983). Thus, for a re?ection survey involving a sig- nal with a dominant frequency of 50 Hz propagating in sedimentary strata with a velocity of 2.0 km s-1, the dominant wavelength would be 40 m and the vertical This ?gure is worth noting since it serves as a reminder that the smallest geological structures imaged on seismic sections tend to be an order of magnitude larger than the Since deeper-travelling seismic waves tend to have a x

    0.5x Fig. 4.10 The horizontal sampling of a seismic re?ection survey is half the detector spacing.

    Source ? 4 Reflector Fresnel zone Fig. 4.11 Energy is returned to source from all points of a re?ector.The part of the re?ector from which energy is returned within half a wavelength of the initial re?ected arrival is known as the Fresnel zone.

    structively to build up the re?ected signal, and the part of the interface from which this energy is returned is known as the ?rst Fresnel zone (Fig. 4.11) or, simply, the Fresnel zone. Around the ?rst Fresnel zone are a series of annular zones from which the overall re?ected energy tends to interfere destructively and cancel out. The width of the Fresnel zone represents an absolute limit on the horizontal resolution of a re?ection survey since re- ?ectors separated by a distance smaller than this cannot be individually distinguished.The width w of the Fresnel zone is related to the dominant wavelength l of the source and the re?ector depth z by

    12 w = (2zl ) (for z >> l ) The size of the ?rst Fresnel zone increases as a function of re?ector depth. Also, as noted in Section 3.5, deeper- travelling re?ected energy tends to have a lower domi- nant frequency due to the effects of absorption. The lower dominant frequency is coupled with an increase in interval velocity, and both lead to an increase in the wavelength. For both these reasons the horizontal reso- lution, like the vertical resolution, reduces with increas- As a practical rule of thumb, the Fresnel zone width for the target horizons should be estimated, then the Seismic Re?ection Surveying 53

    geophone spacing ?xed at no more than one-quarter of that width. In this case the horizontal resolution will be limited only by the physics of the seismic wave, not by the survey design.

    4.4.2 Design of detector arrays Each detector in a conventional re?ection spread con- sists of an array (or group) of several geophones or hy- drophones arranged in a speci?c pattern and connected together in series or parallel to produce a single channel of output. The effective offset of an array is taken to be the distance from the shot to the centre of the array. Ar- rays of geophones provide a directional response and are used to enhance the near-vertically travelling re?ected pulses and to suppress several types of horizontally trav- elling coherent noise. Coherent noise is that which can be correlated from trace to trace as opposed to random noise (Fig. 4.12). To exemplify this, consider a Rayleigh surface wave (a vertically polarized wave travelling along the surface) and a vertically travelling compressional wave re?ected from a deep interface to pass simultane- ously through two geophones connected in series and spaced at half the wavelength of the Rayleigh wave. At any given instant, ground motions associated with the Rayleigh wave will be in opposite directions at the two geophones and the individual outputs of the geophones at any instant will therefore be equal and opposite and be cancelled by summing. However, ground motions asso- ciated with the re?ected compressional wave will be in phase at the two geophones and the summed outputs of the geophones will therefore be twice their individual The directional response of any linear array is gov- erned by the relationship between the apparent wave- length l of a wave in the direction of the array, the a The response is given by a response function R

    sin nb R= sin b where b = pDx l a R is a periodic function that is fully de?ned in the inter- aa Typical array response curves are shown in Fig. 4.13.

    1.0 Array response function R n=2 n=4 n=8 0 0 0.5 Detector spacing ?x Wavelength ?

    Arrays comprising areal rather than linear patterns of geophones may be used to suppress horizontal noise The initial stage of a re?ection survey involves ?eld trials in the survey area to determine the most suitable combination of source, offset recording range, array geometry and detector spacing (the horizontal distance between the centres of adjacent geophone arrays, often referred to as the group interval) to produce good seis- Source trials involve tests of the effect of varying, for example, the shot depth and charge size of an explosive source, or the number, chamber sizes and trigger delay times of individual guns in an air gun array.The de- tector array geometry needs to be designed to suppress the prevalent coherent noise events (mostly source- generated). On land, the local noise is investigated by means of a noise test in which shots are ?red into a spread of closely-spaced detectors (noise spread) consisting of in- dividual geophones, or arrays of geophones clustered to- gether to eliminate their directional response. A series of shots is ?red with the noise spread being moved progres- sively out to large offset distances. For this reason such a test is sometimes called a walk-away spread. The purpose of the noise test is to determine the characteristics of the coherent noise, in particular, the velocity across the spread and dominant frequency of the air waves (shot noise travelling through the air), surface waves (ground roll), direct and shallow refracted arrivals, that together tend to conceal the low-amplitude re?ections. A typical noise section derived from such a test is shown in Fig.

    1.0 Fig. 4.13 Response functions for different detector arrays. (After Al-Sadi 1980.)

    4.12(a). This clearly reveals a number of coherent noise events that need to be suppressed to enhance the SNR of re?ected arrivals. Such noise sections provide the neces- sary information for the optimal design of detector phone arrays. Figure 4.12(b) shows a time section ob- tained with suitable array geometry designed to suppress the local noise events and reveals the presence of re?ec- tion events that were totally concealed in the noise It is apparent from the above account that the use of suitably designed arrays can markedly improve the SNR of re?ection events on ?eld seismic recordings. Further improvements in SNR and survey resolution are achiev- able by various types of data processing discussed later in the chapter. Unfortunately, the noise characteristics tend to vary along any seismic line, due to near-surface geological variations and cultural effects.With the tech- nical ability of modern instrumentation to record many hundreds of separate channels of data, there is an increas- ing tendency to use smaller arrays in the ?eld, record more separate channels of data, then have the ability to experiment with different array types by combining recorded traces during processing. This allows more so- phisticated noise cancellation, at the cost of some increase in processing time.

    Each seismic trace then represents a unique sampling of some point on the re?ector. In common mid-point (CMP) pro?ling, which has become the standard method of two-dimensional multichannel seismic sur- veying, it is arranged that a set of traces recorded at dif- ferent offsets contains re?ections from a common depth The fold of the stacking refers to the number of traces in the CMP gather and may conventionally be 24, 30, 60 or, exceptionally, over 1000.The fold is alternatively ex- pressed as a percentage: single-fold = 100% coverage, six-fold = 600% coverage and so on.The fold of a CMP pro?le is determined by the quantity N/2n, where N is the number of geophone arrays along a spread and n is the number of geophone array spacings by which the spread is moved forward between shots (the move-up rate). Thus with a 96-channel spread (N = 96) and a move-up rate of 8 array spacings per shot interval (n = 8), the coverage would be 96/16 = 6-fold. A ?eld procedure for the routine collection of six-fold CMP coverage using a single-ended 12-channel spread con?guration progressively moved forward along a The theoretical improvement in SNR brought about by stacking n traces containing a mixture of coherent in- Stacking also attenuates long-path multiples. They have travelled in nearer-surface, lower velocity layers and have a signi?cantly different moveout from the primary re- ?ections. When the traces are stacked with the correct velocity function, the multiples are not in phase and do not sum. The stacked trace is the equivalent of a trace recorded with a vertical ray path, and is often referred to as a zero-offset trace.

    4.4.4 Display of seismic re?ection data Pro?ling data from two-dimensional surveys are con- ventionally displayed as seismic sections in which the in- dividual stacked zero-offset traces are plotted side by side, in close proximity, with their time axes arranged verti- cally. Re?ection events may then be traced across the section by correlating pulses from trace to trace and in this way the distribution of subsurface re?ectors beneath the survey line may be mapped. However, whilst it is tempting to envisage seismic sections as straightforward images of geological cross-sections it must not be forgot- ten that the vertical dimension of the sections is time, not depth.

    Seismic Re?ection Surveying 57 DS 21 Path 1 D 4S 2 Path 2 D 6S 3

    Path 3 D 8S 4 Path 4 D 10S 5 Path 5 D 12S 6 Path 6 Common depth (reflection) point

    Fig. 4.14 A ?eld procedure for obtaining six-fold CDP coverage with a single-ended 12-channel detector spread moved progressively along the survey line.

    4.5 Time corrections applied to seismic traces Two main types of correction need to be applied to re- ?ection times on individual seismic traces in order that the resultant seismic sections give a true representation of geological structure. These are the static and dynamic corrections, so-called because the former is a ?xed time correction applied to an entire trace whereas the latter varies as a function of re?ection time.

    (a) (b) D 3 Surface D 1 D 2Datum S

    V w r e lya d h B s f at ere ao e we S 3 S 1 S 2 V 1

    ttt 12 12 12 1 Seismic Re?ection Surveying 59

    D SD SD 1 22 33 Datum

    V 1 SD 11 SD 22 SD 33 t SD 11 SD 22 SD 33 ttt 23 23 23

    Fig. 4.15 Static corrections. (a) Seismograms showing time differences between re?ection events on adjacent seismograms due to the different elevations of shots and detectors and the presence of a weathered layer. (b)The same seismograms after the application of elevation and weathering corrections, showing good alignment of the re?ection events. (After O’Brien, 1974.)

    to the shot hole to measure the vertical time (VT ) or uphole time, from which the velocity of the surface layer above The complex variations in velocity and thickness within the weathered layer can never be precisely de- ?ned. The best estimate of the static correction derived It always contains errors, or residuals, which have the effect of diminishing the SNR of CMP stacks and reducing the coherence of re?ection events on time sections. These residuals can be investigated using so- This purely empirical approach assumes that the weath- ered layer and surface relief are the only cause of irregu- larities in the travel times of rays re?ected from a shallow interface. It then operates by searching through all the data traces for systematic residual effects associated with individual shot and detector locations and applying these as corrections to the individual traces before the CMP stack. Figure 4.16 shows the marked improvement in SNR and re?ection coherence achievable by the appli- cation of these automatically computed residual static In marine re?ection surveys the situation is much simpler since the shot and receivers are situated in a The static correction is commonly restricted to a con- version of travel times to mean sea-level datum, without removing the overall effect of the water layer. Travel times are increased by (d + d )v , where d and d are s hw s h the depths below mean sea-level of the source and hydrophone array and v is the seismic velocity of sea w water. The effect of marine tidal height is often signi?- cant, especially in coastal waters, and demands a time- variant static correction. Tidal height data are usually readily available and the only complexity to the correc- tion is their time-variant nature.

    computer analysis of moveout in the groups of traces from a common mid-point (CMP gathers). Prior to this velocity analysis, static corrections must be applied to the individual traces to remove the effect of the low- velocity surface layer and to reduce travel times to a common height datum.The method is exempli?ed with reference to Fig. 4.17 which illustrates a set of statically corrected traces containing a re?ection event with a zero-offset travel time of t . Dynamic corrections are cal- 0 culated for a range of velocity values and the dynamically corrected traces are stacked. The stacking velocity V is st de?ned as that velocity value which produces the maxi- mum amplitude of the re?ection event in the stack of traces.This clearly represents the condition of successful removal of NMO. Since the stacking velocity is that which removes NMO, it is given by the equation x2 t 2 = t 2 + (cf. equation (4.4)) 0 V2 st Fig. 4.16 Major improvement to a seismic section resulting from residual (Courtesy Prakla Seismos GmbH.)

    Seismic Re?ection Surveying 61 Offset Velocity DDDDDDx VVV 123456 123

    Fig. 4.17 A set of re?ection events in a t 0 CMP gather is corrected for NMO using a range of velocity values.The stacking velocity is that which produces peak cross-power from the stacked events; that is, the velocity that most successfully removes the NMO. In the case illustrated, V represents the stacking velocity. (After 2 Taner & Koehler 1969.) Reflection time Fig. 4.18 The velocity spectrum is used to determine the stacking velocity as a function of re?ection time.The cross-power function (semblance) is calculated over a large number of narrow time windows down the seismic trace, and for a range of possible velocities for each time window.The velocity spectrum is typically displayed alongside the relevant CMP gather as shown. Peaks in the contoured semblance values correspond to appropriate velocities for that travel time, where a re?ection phase occurs in the CMP gather.

    t 0 V 3 Cross-power V 2Peak power defines correct stacking velocity V 1

    stacked wavelet. A velocity function de?ning the in- crease of velocity with depth for that CMP is derived by picking the location of the peaks on the velocity spec- Velocity functions are derived at regular intervals along a CMP pro?le to provide stacking velocity values for use in the dynamic correction of each individual trace.

    Fig. 4.19 Filter panels showing the frequency content of a panel of re?ection records by passing them through a series of narrow-band frequencies.This plot allows the geophysicist to assess the frequency band that maximises the signal-to-noise ratio. Note that this may vary down the traces due to frequency-dependent absorption. (From Hatton et al. 1986, p. 88)

    main types of waveform manipulation are frequency ?l- tering and inverse ?ltering (deconvolution). Frequency ?ltering can improve the SNR but potentially damages the vertical resolution, while deconvolution improves the resolution, but at the expense of a decrease in the SNR. As with many aspects of seismic processing, com- promises must be struck in each process to produce the optimum overall result.

    4.8.1 Frequency ?ltering Any coherent or incoherent noise event whose domi- nant frequency is different from that of re?ected arrivals may be suppressed by frequency ?ltering (see Chapter 2). Thus, for example, ground roll in land surveys and several types of ship-generated noise in marine seismic surveying can often be signi?cantly attenuated by low- cut ?ltering. Similarly, wind noise may be reduced by high-cut ?ltering. Frequency ?ltering may be carried out at several stages in the processing sequence. Nor- mally, shot records would be ?ltered at a very early stage in the processing to remove obvious noise. Later applica- tions of ?lters are used to remove artefacts produced by other processing stages. The ?nal application of ?lters is to produce the sections to be used by the seismic inter- preters, and here the choice of ?lters is made to produce the optimum visual display.

    Since the dominant frequency of re?ected arrivals decreases with increasing length of travel path, due to the selective absorption of the higher frequencies, the char- acteristics of frequency ?lters are normally varied as a function of re?ection time. For example, the ?rst second of a 3 s seismic trace might typically be band-pass ?ltered between limits of 15 and 75 Hz, whereas the frequency limits for the third second might be 10 and 45 Hz. The choice of frequency bands is made by inspection of ?lter panels (Fig. 4.19). As the frequency characteristics of re?ected arrivals are also in?uenced by the prevailing geology, the appropriate time-variant frequency ?lter- ing may also vary as a function of distance along a seismic pro?le. The ?ltering may be carried out by computer in the time domain or the frequency domain (see Chapter 2).

    processing, each designed to remove some speci?c ad- verse effect of ?ltering in the ground along the transmis- Deconvolution is the analytical process of removing the effect of some previous ?ltering operation (convolu- tion). Inverse ?lters are designed to deconvolve seismic traces by removing the adverse ?ltering effects associated with the propagation of seismic pulses through a layered ground or through a recording system. In general, such effects lengthen the seismic pulse; for example, by the generation of multiple wave trains and by progressive ab- sorption of the higher frequencies. Mutual interference of extended re?ection wave trains from individual inter- faces seriously degrades seismic records since onsets of re?ections from deeper interfaces are totally or partially concealed by the wave trains of re?ections from shal- Examples of inverse ?ltering to remove particular ?ltering effects include: · dereverberation to remove ringing associated with · deghosting to remove the short-path multiple asso- ciated with energy travelling upwards from the source and re?ected back from the base of the weathered layer or the surface; and · whitening to equalize the amplitude of all frequency components within the recorded frequency band (see All these deconvolution operations have the effect of shortening the pulse length on processed seismic sec- Consider a composite waveform w resulting from an k initial spike source extended by the presence of short- path multiples near source such as, especially, water layer reverberations. The resultant seismic trace x will be k given by the convolution of the re?ectivity function r k with the composite input waveform w as shown k schematically in Fig. 4.6 (neglecting the effects of attenuation and absorption)

    xk = rk * wk (plus noise) Re?ected waveforms from closely-spaced re?ectors will overlap in time on the seismic trace and, hence, will in- terfere. Deeper re?ections may thus be concealed by the reverberation wave train associated with re?ections from shallower interfaces, so that only by the elimination of Note that short-path multiples have effectively the same normal moveout as the related primary re?ection and are Seismic Re?ection Surveying 63

    therefore not suppressed by CDP stacking, and they have similar frequency content to the primary re?ection so Deconvolution has the general aim, not fully realiz- able, of compressing every occurrence of a composite waveform w on a seismic trace into a spike output, in k order to reproduce the re?ectivity function r that would k fully de?ne the subsurface layering.This is equivalent to the elimination of the multiple wave train.The required deconvolution operator is an inverse ?lter i which, k when convolved with the composite waveform w , k yields a spike function d k

    ik * w = d kk Convolution of the same operator with the entire seismic trace yields the re?ectivity function

    2. that the composite waveform w for an impulsive k source is minimum delay (i.e. that its contained energy is concentrated at the front end of the pulse; see From assumption (1) it follows that the autocorrela- tion function of the seismic trace represents the autocor- relation function of the composite waveform w . From k assumption (2) it follows that the autocorrelation func- tion can be used to de?ne the shape of the waveform, the

    * Input waveform Filter operator

    = Filtered output Desired output (a) ? (?) xx necessary phase information coming from the Such an approach allows prediction of the shape of the composite waveform for use in Wiener ?ltering. A par- ticular case of Wiener ?ltering in seismic deconvolution This is the basis of spiking deconvolution, also known as whitening deconvolution because a spike has the amplitude spectrum of white noise (i.e. all frequency components A wide variety of deconvolution operators can be de- signed for inverse ?ltering of real seismic data, facilitat- ing the suppression of multiples (dereverberation and deghosting) and the compression of re?ected pulses.The presence of short-period reverberation in a seismogram is revealed by an autocorrelation function with a series of decaying waveforms (Fig. 4.21(a)). Long-period rever- berations appear in the autocorrelation function as a series of separate side lobes (Fig. 4.21(b)), the lobes occurring at lag values for which the primary re?ection aligns with a multiple re?ection.Thus the spacing of the side lobes represents the periodicity of the reverberation pattern.The ?rst multiple is phase-reversed with respect to the primary re?ection, due to re?ection at the ground surface or the base of the weathered layer. Thus the ?rst side lobe has a negative peak resulting from cross- correlation of the out-of-phase signals.The second mul- tiple undergoes a further phase reversal so that it is in phase with the primary re?ection and therefore gives rise 4.21(b)). Autocorrelation functions such as those shown in Fig. 4.21 form the basis of predictive deconvolution operators for removing reverberation events from seismograms.

    ? (b) ? (?) xx

    ? Fig. 4.21 Autocorrelation functions of (a) A gradually decaying function (b) A function with separate side lobes indicative of long-period reverberation.

    Fig. 4.22 Removal of reverberations by predictive deconvolution. (a) Seismic record dominated by strong reverberations. (b) Same section after spiking deconvolution. (Courtesy Prakla Seismos GmbH.)

    Practically achievable inverse ?lters are always approximations to the ideal ?lter that would produce a re?ectivity function from a seismic trace: ?rstly, the ideal ?lter operator would have to be in?nitely long; second- ly, predictive deconvolution makes assumptions about the statistical nature of the seismic time series that are only approximately true. Nevertheless, dramatic im- provements to seismic sections, in the way of multiple suppression and associated enhancement of vertical resolution, are routinely achieved by predictive decon- volution. An example of the effectiveness of predictive deconvolution in improving the quality of a seismic section is shown in Fig. 4.22. Deconvolution may be carried out on individual seismic traces before stacking (deconvolution before stacking: DBS) or on CMP stacked traces (deconvolution after stacking: DAS), and is com- monly employed at both these stages of data processing.

    Seismic Re?ection Surveying 65 4.8.3 Velocity ?ltering The use of velocity ?ltering (also known as fan ?ltering or pie slice ?ltering) is to remove coherent noise events from seismic records on the basis of the particular angles at which the events dip (March & Bailey 1983). The angle of dip of an event is determined from the apparent velocity with which it propagates across a spread of A seismic pulse travelling with velocity v at an angle a to the vertical will propagate across the spread with an apparent velocity v = v/sin a (Fig. 4.23). Along the a spread direction, each individual sinusoidal component of the pulse will have an apparent wavenumber k related a to its individual frequency f, where

    Hence, a plot of frequency f against apparent wavenumber k for the pulse will yield a straight-line a curve with a gradient of v (Fig. 4.24). Any seismic event a propagating across a surface spread will be characterized by an f–k curve radiating from the origin at a particular gradient determined by the apparent velocity with which the event passes across the spread. The overall set of curves for a typical shot gather containing re?ected 4.25. Events that appear to travel across the spread away from the source will plot in the positive wavenumber ?eld; events travelling towards the source, such as backscattered rays, will plot in the negative wavenumber It is apparent that different types of seismic event fall within different zones of the f–k plot and this fact provides a means of ?ltering to suppress unwanted events on the basis of their apparent velocity.The normal means

    v/sin a Surface a v Wavefront Fig. 4.23 A wave travelling at an angle a to the vertical will pass across an in-line spread of surface detectors at a velocity of v/sin a.

    Reflected events (signal) f Back-scattered noise by which this is achieved, known as f–k ?ltering, is to enact a two-dimensional Fourier transformation of the seismic data from the t–x domain to the f–k domain, then to ?lter the f–k plot by removing a wedge-shaped zone or zones containing the unwanted noise events (March & Bailey 1983), and ?nally to transform back into the An important application of velocity ?ltering is Frequency ( f ) Seismic event of velocity v (Gradient = v ) a Apparent wavenumber k a

    Fig. 4.24 An f–k plot for a seismic pulse passing across a surface spread of detectors.

    the removal of ground roll from shot gathers. This leads to marked improvement in the subsequent stacking process, facilitating better estimation of stacking veloci- ties and better suppression of multiples.Velocity ?ltering can also be applied to portions of seismic record sections, rather than individual shot gathers, in order to suppress coherent noise events evident because of their anom- alous dip, such as diffraction patterns. An example of It may be noted that individual detector arrays operate selectively on seismic arrivals according to their apparent velocity across the array (Section 4.4.2), and therefore function as simple velocity ?lters at the data acquisition stage.

    4.9 Migration of re?ection data On seismic sections such as that illustrated in Fig. 4.22 each re?ection event is mapped directly beneath the mid-point of the appropriate CMP gather. However, the re?ection point is located beneath the mid-point only if the re?ector is horizontal. In the presence of a component of dip along the survey line the actual re?ec- tion point is displaced in the up-dip direction; in the presence of a component of dip across the survey line (cross-dip) the re?ection point is displaced out of the plane of the section. Migration is the process of recon- structing a seismic section so that re?ection events are repositioned under their correct surface location and at a corrected vertical re?ection time. Migration also improves the resolution of seismic sections by focusing energy spread over a Fresnel zone and by collapsing diffraction patterns produced by point re?ectors and faulted beds. In time migration, the migrated seismic sections still have time as the vertical dimension. In depth migration, the migrated re?ection times are con- verted into re?ector depths using appropriate velocity Two-dimensional survey data provide no information on cross-dip and, hence, in the migration of two- dimensional data the migrated re?ection points are con- strained to lie within the plane of the section. In the presence of cross-dip, this two-dimensional migration is clearly an imperfect process. Its inability to deal with effects of cross-dip mean that, even when the seismic line is along the geological strike, migration will be imperfect since the true re?ection points are themselves out of the The conversion of re?ection times recorded on non- Seismic Re?ection Surveying 67

    Fig. 4.26 The effect of f–k ?ltering of a seismic section. (a) Stacked section showing steeply-dipping coherent noise events, especially (b)The same section after rejection of noise by f–k ?ltering (Courtesy Prakla-Seismos GmbH).

    Seismic Re?ection Surveying 69 (a) 0 1 2 3 km (b) 0 1 2 3 km 0 0

    1 Depth (km) 2 Reflection time (s) 1 2 3 3

    Fig. 4.27 (a) A structural model of the subsurface and (b) the resultant re?ection events that would be observed in a non-migrated seismic section, containing numerous diffraction events. (After Sheriff 1978.)

    (a) A B Distance

    W XZ Depth Y (b) A B Distance

    t AW t BX t BZ t BY Time eral, if a is the dip of the record surface and a is the true st dip of the re?ector, sin a = tan a . Hence the maximum ts dip of a record surface is 45° and represents the case of horizontal re?ection paths from a vertical re?ector.This wavefront common-envelope method of migration can be Fig. 4.28 (a) A sharp synclinal feature in a re?ecting interface, and (b) the resultant `bow-tie’ shape of the re?ection event on the non-migrated seismic section.

    velocity–depth relationship and this is used to construct the wavefront segments passing through each re?ection An alternative approach to migration is to assume that any continuous re?ector is composed of a series of closely-spaced point re?ectors, each of which is a source of diffractions, and that the continuity of any re?ection event results from the constructive and destructive inter- ference of these individual diffraction events.A set of dif- fracted arrivals from a single point re?ector embedded in a uniform-velocity medium is shown in Fig. 4.31. The two-way re?ection times to different surface locations de?ne a hyperbola. If arcs of circles (wavefront segments) are drawn through each re?ection event, they intersect at the actual point of diffraction (Fig. 4.31). In the case of a variable velocity above the point re?ector the diffraction event will not be a hyperbola but a curve of similar con- vex shape. No re?ection event on a seismic section can have a greater convexity than a diffraction event, hence the latter is referred to as a curve of maximum convexity. In diffraction migration all dipping re?ection events are as- sumed to be tangential to some curve of maximum con-

    Source–detector Actual reflection Locus of all point reflection points with equal Display position travel times on seismic section Fig. 4.29 For a given re?ection time, the re?ection point may be anywhere on the arc of a circle centred on the source–detector position. On a non-migrated seismic section the point is mapped to be immediately below the source–detector.

    vexity. By the use of a wavefront chart appropriate to the prevailing velocity–depth relationship, wavefront seg- ments can be drawn through dipping re?ection events on seismic sections and the events migrated back to their diffraction points (Fig. 4.31). Events so migrated will, All modern approaches to migration use the seismic wave equation which is a partial differential equation de- scribing the motion of waves within a medium that have been generated by a wave source. The migration prob- lem can be considered in terms of wave propagation through the ground in the following way. For any re?ec- tion event, the form of the seismic wave?eld at the surface can be reconstructed from the travel times of For the purpose of migration it is required to reconstruct the form of the wave?eld within the ground, in the vicinity of a re?ecting interface.This reconstruction can be achieved by solution of the wave equation, effectively Propagation of the wave?eld of a re?ection event half- way back to its origin time should place the wave on the re?ecting interface, hence, the form of the wave?eld at Migration using the wave equation is known as wave equation migration (Robinson & Treitel 2000). There are several approaches to the problem of solving the wave equation and these give rise to speci?c types of wave equation migration such as ?nite difference migration, in which the wave equation is approximated by a ?nite dif- ference equation suitable for solution by computer, and frequency-domain migration, in which the wave equation is solved by means of Fourier transformations, the neces- sary spatial transformations to achieve migration being enacted in the frequency domain and recovered by an Migration by computer can also be carried out by

    Reflector surface Record Fig. 4.30 A planar-dipping re?ector surface surface and its associated record surface derived from a non-migrated seismic ?? t s section.

    Seismic Re?ection Surveying 71 (a) (b) Distance 1234567 1234567

    Point reflector Reflection time Curve of maximum convexity (c)

    Diffraction migrated position of event Wavefront Curve of Reflection event on maximum seismic section convexity

    Fig. 4.31 Principles of diffraction migration. (a) Re?ection paths from a point re?ector. (b) Migration of individual re?ection events back to position of point re?ector. (c) Use of wavefront chart and curve of maximum convexity to migrate a speci?c re?ection event; the event is tangential to the appropriate curve of maximum convexity, and the migrated position of the event is at the intersection of the wavefront with the apex of the curve.

    direct modelling of ray paths through hypothetical mod- els of the ground, the geometry of the re?ecting inter- faces being adjusted iteratively to remove discrepancies Particularly in the case of seismic surveys over highly complex subsurface structures, for example those en- countered in the vicinity of salt domes and salt walls, this ray trace migration method may be the only method capa- In order to migrate a seismic section accurately it would be necessary to de?ne fully the velocity ?eld of the ground; that is, to specify the value of velocity at all points. In practice, for the purposes of migration, an es- timate of the velocity ?eld is made from prior analysis of the non-migrated seismic section, together with infor- mation from borehole logs where available. In spite of this approximation, migration almost invariably leads to major improvement in the seismic imaging of re?ector Migration of seismic pro?le data is normally carried out on CMP stacks, thus reducing the number of traces to be migrated by a factor equal to the fold of the survey and thereby reducing the computing time and associated costs. Migration of stacked traces is based on the assump- tion that the stacks closely resemble the form of individ- ual traces recorded at zero offset and containing only normal-incidence re?ection events. This assumption is clearly invalid in the case of recordings over a wide range of offsets in areas of structural complexity. A better approach is to migrate the individual seismic traces (assembled into a series of pro?les containing all traces with a common offset), then to assemble the migrated traces into CMP gathers and stacks. Such an approach is not necessarily cost-effective in the case of high-fold CMP surveys, and a compromise is to migrate subsets of CMP stacks recorded over a narrow range of offset dis- tances, and then produce a full CMP stack by summing the migrated partial stacks after correction for normal moveout. Procedures involving migration before ?nal stacking involve extra cost but can lead to signi?cant improvements in the migrated sections and to more reliable stacking velocities.

    Any system of migration represents an approximate solution to the problem of mapping re?ecting surfaces into their correct spatial positions and the various meth- ods have different performances with real data. For example, the diffraction method performs well in the presence of steep re?ector dips but is poor in the pres- ence of a low SNR. The best all round performance is given by frequency-domain migration. Examples of the migration of seismic sections are illustrated in Figs 4.32 and 4.33. Note in particular the clari?cation of structur- al detail, including the removal of bow-tie effects, and the repositioning of structural features in the migrated sections. Clearly, when planning to test hydrocarbon Fig. 4.32 (a) A non-migrated seismic section. (b)The same seismic section after wave equation migration. (Courtesy Prakla-Seismos GmbH.)

    prospects in areas of structural complexity (as on the ?ank of a salt dome) it is important that drilling locations are based on interpretation of migrated rather than non-migrated seismic sections.

    Fig. 4.33 (a) A non-migrated seismic section. (b)The same seismic section after diffraction migration. (Courtesy Prakla-Seismos GmbH.)

    stricted to rays that have travelled in a single vertical plane. In a three-dimensional survey, the disposition of shots and receivers is such that groups of recorded ar- rivals can be assembled that represent rays re?ected from an area of each re?ecting interface. Three-dimensional surveying therefore samples a volume of the subsurface rather than an area contained in a vertical plane, as in In three-dimensional surveying the common mid- point principle applies similarly, but each CMP gather involves an areal rather than a linear distribution of shot points and detector locations (Fig. 4.34). Thus, for ex- ample, a 20-fold coverage is obtained in a crossed-array three-dimensional survey if re?ected ray paths from ?ve shots along different shot lines to four detectors along different recording lines all have a common re?ection On land, three-dimensional data are normally col- lected using the crossed-array method in which shots and Seismic Re?ection Surveying 73

    Shot lines Recording lines CDP Fig. 4.34 Re?ected ray paths de?ning a Reflector common depth point from an areal distribution of shot points and detector locations in a three-dimensional survey.

    Shot line Recording line Subsurface coverage Fig. 4.35 The areal coverage derived from a single pair of crossing lines in a three-dimensional survey. Each dot represents the mid- point between a shot and a detector.

    Seismic Re?ection Surveying 75 Source 1 * Hydrophone streamer

    * Shot point positions Receiver positions Source –receiver mid-points* Source 2 Fig. 4.36 The dual source array method of collecting three-dimensional seismic data at sea. Alternate ?ring of sources 1 and 2 into the hydrophone streamer produces two parallel sets of source–detector mid-points.

    Fig. 4.37 The two-pass method of three-dimensional migration for the case of a point re?ector.The apices of diffraction hyperbolas in one line direction may be used to construct a diffraction hyperbola in the orthogonal line direction.The apex of the latter hyperbola de?nes the position of the point re?ector.

    the diffraction hyperbola recorded in a two-dimensional survey representing a vertical slice through this hyper- boloid. In a three-dimensional survey, re?ections are recorded from a surface area of the hyperboloid and three-dimensional migration involves summing ampli- tudes over the surface area to de?ne the apex of the hyperboloid.

    hot lines Recording lines Random section Sect on along record ng line

    Fig. 4.38 The re?ect on da a vo ume ob ned from a three- dimensional seismic survey By ak ng data volume, it is possib e genera azimuthal direction; by areal distribution of re?ec on even ng hor zon l slices through this sections in any es (time slices), the tudied at any two- way re?ection time.

    dimensional surveys s carr out computer work sta- tions using software rout nes that ble seismic sections and time slices to d sp ayed equired. Automatic event picking and contour are a o facilitated (Brown On high-quality modern se sm c data it is quite com- mon to image the –water con ct within a hydro- carbon reservoir 39) he bright spot, a particularly strong re?ect on caused by the high re?ec- tion coef?cient at the S

    Time slice Section along shot line i l t (F be ak i o i to i ti

    il t i i t i l i i l ed i t i t ng , es s i , e t ve

    can as or i t t is al en l i a r ca c c e at a r s ta t i i mi sl b

    ll i i 4.11 Three component (3C) seismic re?ection surveys All the previous discussion has only considered seismic recording using vertical geophones. These only record one component of the total seismic wave motion.Verti- cal geophones are chosen in preference since they are most sensitive to vertically travelling P-waves. The actual ground motion consists of movement in all direc- 76 Chapter 4

    Fig. 4.39 Seismic section from a 3D data volume showing the horizontal re?ector produced by the oil–water contact.This is clearly distinguishable from the re?ections from geological formations due to its strictly horizontal nature. Example from the Fulmar ?eld, UK North Sea. (From Jack 1997.)

    tions. This can be measured fully by having three geo- phones at each location, oriented mutually at right angles, and each recording one component. Thus three components of the ground motion are recorded, giving the method its name. Often these are labelled as having their sensitive axes oriented to vertical, north–south and east–west, though any set of orthogonal components is suf?cient. In this case the true ground motion is fully The three component (3C) technique requires three times as many recording sensors, and more stages of data analysis than vertical component recording.With devel- oping technology, the additional sophistication of the ?eld equipment (Fig. 4.40) and the availability of large computing power for the data analysis have made 3C recording practicable. In fact, 3C data recording is becoming increasingly common, and is now a routine These are the ability to identify S-waves in addition to P- waves in the same data, and the ability to perform more sophisticated ?ltering to identify and remove unwanted wave energy, whether from surface waves, or noise sources. Naturally the improved ?ltering contributes substantially to the ability to detect the separate P- and S-waves. S-waves are generated at any interface where a P-wave is obliquely incident (see Section 3.6.2). Thus, any seismic data will always contain energy from both P- and S-waves. With appropriate processing, principally exploiting the different particle motions and velocities of the two waves, the P-wave and S-wave energy can be separated and analysed.

    Knowledge of the behaviour of both body waves pro- vides important additional information. In a lithi?ed rock formation, such as an oil reservoir, the P-wave is transmitted through both the rock matrix and the ?uids in the pore spaces. The behaviour of the P-wave is thus determined by the average of the rock matrix and pore ?uid properties, weighted with respect to the The S-wave on the other hand is only transmitted through the rock matrix, since the shear wave cannot propagate through a ?uid. Comparison of the P-wave and S-wave velocities of the same formation thus can give information about the porosity of the formation and the nature of the ?uids ?lling the pore spaces. The relationships can be complex, but the presence of hy- drocarbons, especially if accompanied by gas, can be identi?ed directly from the seismic data in favourable circumstances. Derivation of measures which reliably predict the presence of hydrocarbons, direct hydrocarbon indicators (DHIs), is an important part of modern seismic processing (Yilmaz 1987, 2001), though the details of The ability to detect these features is an enormous advantage to the hydrocarbon industry and has had a marked effect on the success rate of exploration bore- holes in locating oil or gas reservoirs. Since the cost of drilling a borehole can often reach or exceed $10 m, the additional effort in seismic data acquisition and process- ing is very cost-effective.

    Seismic Re?ection Surveying 77 4.12 4D seismic surveys Once an oil?eld is in production, the oil and/or gas is extracted and its place in the pore spaces of the reservoir rock is taken by in?owing groundwater. Since the pore ?uids are changing, the seismic response of the forma- tions also changes. Even in an extensively developed ?eld with many wells, there are large intervals between the wells, of the order of 1 km. It is impossible from mon- itoring the well-?ow to be sure how much of the hydro- carbon is being extracted from any particular part of the reservoir. Often oil reservoirs are cut by numerous faults and some of them may isolate a volume of the reservoir so that the hydrocarbons cannot ?ow to the nearby wells. If the location of such isolated `pools’ can be found, additional wells can be drilled to extract these pools and hence increase the overall hydrocarbon recov- It is apparent that if the location of such features as the oil–water contact and gas accumulations can be mapped with a seismic survey, then repeated surveys at time intervals during the production of the ?eld offer the prospect of monitoring the extraction of hydrocarbons, and contribute to the management of the production phase of the ?eld operation. This is the rationale for 4D seismic surveys, which essentially consist of the repeated shooting of 3D (and often 3C) surveys over a producing ?eld at regular intervals. The fourth dimension is, of The practical implementation of 4D surveying is far from simple ( Jack 1997). The essential measurements made by a seismic survey are the values of amplitudes of seismic waves at speci?c locations and times after a seis- mic source has been ?red. Any factor which affects the location, amplitude or timing of seismic waves must be allowed for when comparing two sets of data recorded in different surveys. Obvious effects would be different geophones in different locations, for each survey. Other effects are much more subtle. The seasonal change in level of the water table may be enough to affect the trav- el time of seismic waves in the near-surface such that all deep re?ections will be systematically mistimed between two surveys in different seasons. As an oil?eld develops, the increased plant (pumps, drill-rigs, vehicles) changes In the processing of the raw data to make the ?nal seismic sections for comparison many different mathematical operations change the amplitudes of the data. Each of these must be rigorously checked and identical process- ing must be carried out for each separate dataset.

    Fig. 4.41 Repeat surveys showing the effect of gas being pumped into a formation for storage. (a) Before gas injection; (b) after gas injection; (c) difference section composed by subtracting (b) from (a). (From Jack 1997.) The primary properties of the reservoir which change with time as hydrocarbon extraction proceeds are the pore ?uid pressure, the nature of the pore ?uids, and the temperature. Each of these may have an effect on the seismic response. Changes in ?uid pressure will affect the state of stress in the rock matrix combined with temper- ature, will directly affect factors such as the exsolution of gas from hydrocarbon ?uids. That these features can be observed in seismic data has been tested directly by large- scale experiments in producing ?elds. In some cases gas has been directly pumped into permeable formations to displace pore water, and repeat seismic surveys conduct- ed to monitor the effect (Fig. 4.41). There are also now well-documented case studies of clear location of the 4.42). In this case pumping of steam into a reservoir has a complex effect of liberating gas dissolved in oil, con- densing to form water, and also replacing the oil and gas by uncondensed steam.The ?gure shows the observable seismic effects of this action over 31 months. The data can be modelled to show that the seismic monitoring is allowing real-time study of the ?uid ?ow in the reservoir ( Jack 1997).This ability to monitor producing reservoirs has major importance in allowing sophisticated control The economic importance of 4D seismic surveying to the oil industry is apparent. Increasing the oil recovery from a producing oil?eld increases the ?nancial return on the huge investment needed to establish a new ?eld and its infrastructure. Relative to this, a 4D seismic survey at perhaps $30 m represents only a mar- ginal cost. Plans are actively being developed to install permanent seismic recording instrumentation over oil- ?elds to facilitate repeat surveys. If all the recording equipment is permanently installed, although this is a large initial expense, much of the dif?culty in recording later directly comparable datasets is removed, and only a seismic source is needed.The future prospect is of hydro-

    carbon ?elds where 4D seismic surveys are routinely used for the management of the production from the ?eld. It can be argued that there is more hydrocarbon re- source to be recovered by careful monitoring of known ?elds, than by exploration for new ?elds.

    4.13 Vertical seismic pro?ling Vertical seismic pro?ling (VSP) is a form of seismic re- ?ection surveying that utilizes boreholes. Shots are nor- mally ?red at surface, at the wellhead or offset laterally from it, and recorded at different depths within the bore- hole using special detectors clamped to the borehole wall. Alternatively, small shots may be ?red at different depths within the borehole and recorded at surface using conventional geophones, but in the following account the former con?guration is assumed throughout. Typi- cally, for a borehole 1 km or more deep, seismic data are recorded at more than 100 different levels down the borehole. If the surface shot location lies at the wellhead vertically above the borehole detector locations, so that the recorded rays have travelled along vertical ray paths, the method is known as zero-offsetVSP. If the surface shot locations are offset laterally, so that the recorded rays have travelled along inclined ray paths, the method is known VSP has several major applications in seismic explo- ration (Cassell 1984). Perhaps most importantly, re?ec- tion events recorded on seismic sections obtained at surface from conventional re?ection surveys can be traced byVSP to their point of origin in the subsurface, thus calibrating the seismic sections geologically. Ambi- guity as to whether particular events observed on con- ventional seismic sections represent primary or multiple re?ections can be removed by direct comparison of the sections withVSP data.The re?ection properties of par- ticular horizons identi?ed in the borehole section can be investigated directly using VSP and it can therefore be determined, for example, whether or not an horizon re- Uncertainty in interpreting subsurface geology using conventional seismic data is in part due to the surface location of shot points and detectors. VSP recording in a borehole enables the detector to be located in the immediate vicinity of the target zone, thus shortening the overall path length of re?ected rays, reducing the ef- fects of attenuation, and reducing the dimensions of the Fresnel zone (Section 4.4.1). By these various means, the overall accuracy of a seismic interpretation may be Seismic Re?ection Surveying 79

    Fig. 4.44 A synthetic zero-offset VSP record section for the velocity–depth model shown.The individual traces are recorded DS1, DS2 and DS3 are downgoing waves with multiple re?ections between the surface and interfaces 1, 2 and 3 respectively. U1, U2 and U3 are primary re?ections from the three interfaces; US3 is a re?ection from the third interface with multiple re?ection in the top layer. (From Cassell 1984.)

    ing and upgoing events to produce aVSP section retain- ing only upgoing, re?ected arrivals.The opposite dip of the two types of event in the original VSP section enables this separation to be carried out by f–k ?ltering (see Sec- tion 4.8.3). Figure 4.45(a) illustrates a synthetic VSP sec- tion after removal of downgoing events. The removal of the stronger downgoing events has enabled representa- tion of the upgoing events at enhanced amplitude, and weak multiple re?ection events are now revealed. Note that these terminate at the same depth as the relevant primary event, and therefore do not extend to the point of intersection with the direct downgoing event. It is now possible to apply a time correction to each trace in the VSP section, based on the travel time of the downgo- ing direct event, in order to predict the form of seismic trace that would be obtained at surface (Fig. 4.45(b)). By stacking these traces within a time corridor that avoids the multiple events, it is possible to produce a stacked trace containing only primary re?ection events. Com- parison of this stacked trace with a conventional seismic section from the vicinity of the borehole (Fig. 4.46) en- ables the geological content of the latter to be identi?ed reliably.

    Seismic Re?ection Surveying 81 Fig. 4.45 (a) Synthetic VSP section of Fig. 4.44 with downgoing waves removed by ?ltering. (b) Each trace has been time shifted by the relevant uphole time to simulate a surface recording. (c) Stacked seismogram produced by stacking in the shaded corridor zone of part (b) to avoid multiple events. (From Cassell 1984.)

    both structural and stratigraphic analysis may be carried out, and in the following sections examples are taken from both two- and three-dimensional survey applications.

    4.45(c)) reproduced eight times and spliced into a conventional seismic section based on surface pro?ling data from the vicinity of the borehole site. Comparison of the VSP stack with the surface recorded data enables the primary events in the seismic section to be reliably distinguished from multiple events. (From Cassell 1984.)

    closed loop of survey lines reveals any errors in the iden- ti?cation or correlation of a re?ection event across the Reprocessing of data, or migration, may be employed to help resolve uncertainties of interpretation, but addi- tional seismic lines are often needed to resolve problems associated with an initial phase of interpretation. It is common for several rounds of seismic exploration to be necessary before a prospective structure is suf?ciently well de?ned to locate the optimal position of an explo- Structural interpretation of three-dimensional data is able to take advantage of the areal coverage of re?ection points, the improved resolution associated with three- dimensional migration and the improved methods of data access, analysis and display provided by dedicated seismic work stations. Examples of the display of geolog- ical structures using three-dimensional data volumes are illustrated in Plates 4.1 and 4.2. Interpretation of three- dimensional data is often crucial to the successful devel- An example is the North Cormorant oil?eld in the UK Sector of the North Sea, where three-dimensional seis- mics enabled the mapping of far more fault structures than had been possible using pre-existing two- dimensional data, and revealed a set of NW–SE trending faults that had previously been unsuspected.

    Seismic Re?ection Surveying 83 Fig. 4.47 Time-structure map of re?ector at the base of the Lower Cretaceous in the Moray Firth off northeast Scotland, UK. Contour values represent two-way travel times of re?ection event in milliseconds. (Courtesy British Geological Survey, Edinburgh, UK.)

    Upper boundary Erosional Toplap Lower boundary

    Onlap Downlap Concordant Concordant Fig. 4.48 Different types of geological boundary de?ning seismic sequences. (After Sheriff 1980.)

    for example, parallel re?ections characterize some shallow-water shelf environments whilst the deeper- water shelf edge and slope environments are often marked by the development of major sigmoidal or oblique cross-bedded units. The ability to identify par- ticular sedimentary environments and predict lithofacies from analysis of seismic sections can be of great value to exploration programmes, providing a pointer to the Thus, organic-rich basinal muds represent potential source rocks; discrete sand bodies developed in shelf 3 30’W 3 00’W 500 Scotland 800 700 300 400 500 Moray Firth 900

    800 700 300 700 600 58 00’N 500 200 300 200 Sealed outcrops Faults

    little or no geological control often enables correlation of locally recognized depositional sequences with the worldwide pattern of sea-level changes (Payton 1977). It also facilitates identi?cation of the major progradational sedimentary sequences which offer the main potential for hydrocarbon generation and accumulation. Strati- graphic analysis therefore greatly enhances the chances of successfully locating hydrocarbon traps in sedimen- Hydrocarbon accumulations are sometimes revealed directly on true-amplitude seismic sections (see below) by localized zones of anomalously strong re?ections known as bright spots. These high-amplitude re?ection events (Fig. 4.51) are attributable to the large re?ection coef?cients at the top and bottom of gas zones (typically,

    Parallel Subparallel Divergent

    Sigmoidal Oblique Hummocky

    Fig. 4.49 Various internal bedforms that give rise to different seismic facies within sedimentary sequences identi?ed on seismic sections. (After Sheriff 1980.) gas-?lled sands) within a hydrocarbon reservoir. In the absence of bright spots, ?uid interfaces may nevertheless be directly recognizable by ?at spots which are horizontal or near-horizontal re?ection events discordant to the local geological dip (see also Sections 4.10 and 4.11).

    4.14.3 Seismic modelling Re?ection amplitudes may be normalized prior to their presentation on seismic sections so that original distinc- tions between weak and strong re?ections are sup- pressed. This practice tends to increase the continuity of re?ection events across a section and therefore aids their identi?cation and structural mapping. However, much valuable geological information is contained in the true amplitude of a re?ection event, which can be Any lateral variation of re?ection amplitude is due to lateral change in the lithology of a rock layer or in its pore ?uid content. Thus, whilst the production of normalized-amplitude sections may assist structural mapping of re?ectors, it suppresses information that is vital to a full stratigraphic interpretation of the data.With increasing interest centring on stratigraphic interpreta- tion, true-amplitude seismic sections are becoming In addition to amplitude, the shape and polarity of a re?ection event also contain important geological infor- mation (Meckel & Nath 1977). Analysis of the signi?- cance of lateral changes of shape, polarity and amplitude

    Dark grey marls, black organic-rich mudstones Siltstones, shales, reef limestones Calcareous sandstones, oolites, bioclastic limestones Sandstones, mudstones, dolomitic mudstones, evaporites Typical lithologies Very thin and continuous units Thin to intermediate tabular bodies with lensoid reef limestones Intermediate continuous to lensoid bodies Irregular to discontinuous units Bed geometry 25–50 150–450 100–50 50–25 Thickness (m) Basinal Outer shelf Inner shelf Coastal Environment Reservoir

    Seismic Re?ection Surveying 85 Fig. 4.51 Part of a true-amplitude seismic section containing a seismic bright spot associated with a local hydrocarbon accumulation. (From Sheriff 1980, after Schramm et al. 1977.)

    observed in true-amplitude seismic sections is carried out by seismic modelling, often referred to in this context as stratigraphic modelling. Seismic modelling involves the production of synthetic seismograms for layered sequences to investigate the effects of varying the model Synthetic seismograms and synthetic seismic sections can be compared with observed data, and models can be manipulated in order to simulate the observed data. By this means, valuable insights can be obtained into the subsurface geology responsible for a particular seismic section. The standard type of synthetic seismogram represents the seismic response to vertical propagation of an assumed source wavelet through a model of the subsurface composed of a series of horizontal layers of differing acoustic impedance. Each layer boundary re?ects some energy back to the surface, the amplitude and polarity of the re?ection being determined by the acoustic impedance contrast. The synthetic seismogram comprises the sum of the individual re?ections in their correct travel-time relationships In its simplest form, a synthetic seismogram x(t) may be considered as the convolution of the assumed source function s(t) with a re?ectivity function r(t) representing the acoustic impedance contrasts in the layered model:

    x(t) = s(t) * r(t) However, ?ltering effects along the downgoing and upgoing ray paths and the overall response of the record- ing system need to be taken into account. Multiples may or may not be incorporated into the synthetic The acoustic impedance values necessary to compute the re?ectivity function may be derived directly from sonic log data (as described in Section 11.8).This is nor- mally achieved assuming density to be constant through- out the model, but it may be important to derive estimates of layer densities in order to compute more Synthetic seismograms can be derived for more com- Particular stratigraphic features that have been investi- gated by seismic modelling, to determine the nature of their representation on seismic sections, include thin layers, discontinuous layers, wedge-shaped layers, transi- tional layer boundaries, variable porosity and type of pore ?uid. Figure 4.53 illustrates synthetic seismograms computed across a section of stratigraphic change.These show how the varying pattern of interference between re?ection events expresses itself in lateral changes of pulse shape and peak amplitude.

    Synthetic seismogram Geological Acoustic Reflection section impedance coefficient

    1 1 2 2 3 3

    4 4 5 5 waveforms of seismic traces are ?lled in black. This has the desirable effect of merging the shaded areas from trace to trace to form continuous black lines across the section.These black lines guide the eye of the interpreter to correlate features across the section, and hence make a structural interpretation. The undesirable effect of this display is that the precise amplitude and shape of the waveform, which has been the subject of so much effort during data acquisition and processing, is lost. The amplitude of a normally re?ected wave is directly related to the re?ection coef?cient at the interface, and hence the physical properties (density and velocity) of the for- mations. Thus, variations in amplitude along a re?ector should indicate changes in the properties of the These properties can be viewed by presenting an image of the seismic section where the amplitude of the seismic wave is displayed as a colour scale. Changes of amplitude along a continuous re?ector will then be em- phasized by the colour change, rather than hidden in a broad black line. Such amplitude changes may be related to changes in the pore ?uid in the rocks, and in favourable circumstances can be direct hydrocarbon indicators (DHIs). Amplitude is merely the simplest ex- ample of a property (attribute) of the seismic wave which can be examined for its geological signi?cance. Others include the seismic wave phase and the frequency con- tent. From the waveform amplitudes the acoustic impedance of each formation can be estimated, and if On a yet more detailed level, the amplitude variation of re?ected wavelets with source–receiver offset (AVO) within each CMP gather can be analysed. This AVO effect can be particularly diagnostic in distinguishing be- tween amplitude effects due to rock matrix variation and those due to pore ?uids. An excellent review of this complex subject is given in Castagna and Bachus (1993).

    Seismic Re?ection Surveying 87 (a) 0 1000 2000 3000 m 1 10 20 30 SP no.

    (b) Fig. 4.53 A set of synthetic seismograms simulating a seismic section across a zone of irregular sandstone geometry. (From Neidell & Poggiagliolmi 1977.)

    seismic surveying, single-channel pro?ling typically utilizes an oceanographic recorder in which a stylus repeatedly sweeps across the surface of an electrically- conducting recording paper that is continuously moving forward at a slow speed past a strip electrode in contact with the paper. A mark is burnt into the paper whenever an electrical signal is fed to the stylus and passes through the paper to the strip electrode. The seismic/acoustic source is triggered at the commencement of a stylus sweep and all seismic pulses returned during the sweep interval are recorded as a series of dark bands on the

    Hydrophone array Vessel under way Acoustic source

    Sea bed Sand layer Buried Bedrock channel

    Fig. 4.54 The survey set-up for single-channel seismic re?ection pro?ling.

    Peaks clipped recording paper (Fig. 4.55). The triggering rate and sweep speed are variable over a wide range. For a shallow penetration survey the source may be triggered every 500 ms and the recording interval may be 0–250 ms, whereas for a deep penetration survey in deep water the source may be triggered every 8 s and the recording The analogue recording systems used in single- channel pro?ling are relatively cheap to operate. There are no processing costs and seismic records are produced in real time by the continuous chart recording of band- pass ?ltered and ampli?ed signals, sometimes with time variable gain (TVG). When careful consideration is given to source and hydrophone array design and deployment, good basic re?ection records may be ob- tained from a single-channel system, but they cannot compare in quality with the type of seismic record pro- Moreover, single-channel recordings cannot provide ve- locity information so that the conversion of re?ection times into re?ector depths has to utilize independent es- timates of seismic velocity. Nonetheless, single-channel pro?ling often provides good imaging of subsurface ge- ology and permits estimates of re?ector depth and geometry that are suf?ciently accurate for many The record sections suffer from the presence of multiple re?ections, especially multiples of the sea bed re?ection, which may obliterate primary re?ection events in the later parts of the records. Multiples are a particular problem when surveying in very shallow

    Threshold level Signal amplitude + Positive values recorded

    Time 0 – Negative values cut off Pattern of marks on chart recording paper

    water, since they then occur at a short time interval after the primary events (Fig. 4.56). Record sections are often dif?cult to interpret in areas of complex re?ector geom- etry because of the presence of bow-tie effects, diffrac- tion events and other features of non-migrated seismic sections.

    4.15.1 Shallow marine seismic sources As discussed in Chapter 3 there are a variety of marine seismic/acoustic sources, operating at differing energy levels and characterized by different dominant frequen- cies. Consequently, by selection of a suitable source, single-channel pro?ling can be applied to a wide range of offshore investigations from high-resolution surveys of near-surface sedimentary layers to surveys of deep geological structure. In general, there is a trade-off between depth of penetration and degree of vertical resolution, since the higher energy sources required to transmit signals to greater depths are characterized by lower dominant frequencies and longer pulse lengths that adversely affect the resolution of the resultant Pingers are low-energy (typically about 5 J), tunable sources that can be operated within the frequency range

    0.1 h 0.2 d 0.3 0.4 0.5 S 0 Seismic Re?ection Surveying 89

    from 3 to 12 kHz. The piezoelectric transducers used to generate the pinger signal also serve as receivers for re?ected acoustic energy and, hence, a separate hydrophone streamer is not required in pinger survey- ing. Vertical resolution can be as good as 10–20 cm but depth penetration is limited to a few tens of metres in muddy sediments or several metres in coarse sediments, with virtually no penetration into solid rock. Pinger sur- veys are commonly used in offshore engineering site investigation and are of particular value in submarine pipeline route surveys. Repeated pinger surveying along a pipeline route enables monitoring of local sediment movement and facilitates location of the pipeline where it has become buried under recent sediments. A typical Boomer sources provide a higher energy output (typically 300–500 J) and operate at lower dominant frequencies (1–5 kHz) than pingers. They therefore provide greater penetration (up to 100 m in bedrock) with good resolution (0.5–1 m). Boomer surveys are useful for mapping thick sedimentary sequences, in connection with channel dredging or sand and gravel extraction, or for high-resolution surveys of shallow geological structures. A boomer record section is illus- trated in Fig. 4.58.

    D SB RH SBM1 RHM1 SBM2 2 km Fig. 4.56 Air gun record from the Gulf of Patras, Greece, showing Holocene hemipelagic (h) and deltaic (d) sediments overlying an irregular erosion surface (rockhead, RH) cut into tectonized Mesozoic andTertiary rocks of the Hellenide (Alpine) orogenic belt. SB = sea bed re?ection; SBM1 and SBM2 = ?rst and second multiples of sea bed re?ection; RHM1 = ?rst multiple of rockhead re?ection.

    0.1 0.2 0.3 0.4 0.5 0.6 S 0 2 km

    Fig.4.57 PingerrecordfromthenorthernAegeanSea,Greece,acrossazoneofactivegrowthfaultsextendinguptotheseabed.Thesea ?oor is underlain by a layered sequence of Holocene muds and silts that can be traced to a depth of about 50 m. Note the diffraction patterns associated with the edges of the individual fault blocks.

    Sparker sources can be operated over a wide range of energy levels (300–30 000 J), though the production of spark discharges of several thousand joules every few seconds requires a large power supply and a large bank of capacitors. Sparker surveying therefore represents a versatile tool for a wide range of applications, from shal- low penetration surveys (100 m) with moderate resolu- tion (2 m) to deep penetration surveys (>1 km) where resolution is not important. However, sparker surveying cannot match the resolution of precision boomer surveying, and sparkers do not offer as good a source By suitable selection of chamber size and rate of release of compressed air, air gun sources can be tailored to high resolution or deep penetration pro?ling applica- tions and therefore represent the most versatile source for single-channel pro?ling. The re?ection record shown in Fig. 4.56 was obtained in a shallow water area with a small air gun (40 in3).

    (a) (b) Sea floor 10 m 200 m Bedded marine sediments Bedrock Seismic Re?ection Surveying 91

    Bedrock Talus Sea bed multiple Fig. 4.58 (a) Precision boomer record from a coastal area of the Irish Sea, UK, and (b) line drawing interpretation showing Holocene sediments up to 10 m thick banked against a reef of Lower Palaeozoic rocks. (Courtesy C.R. Price.)

    Fig. 4.60 Sonograph obtained from a dual scan survey of a pipeline route across an area of linear sand waves in the southern North Sea. The inner edges of the two swathes de?ne the bathymetry beneath the survey vessel. (Scanning range: 100 m).

    and the resulting pattern of returned acoustic energy is known as a sonograph. The oblique insoni?cation pro- duces scale distortion resulting from the varying path 4.59(b)). This distortion can be automatically corrected prior to display so that the sonograph provides an iso- metric plan view of sea bed features. A sonograph is Although not strictly a seismic surveying tool, side- scan sonar provides valuable information on, for exam- ple, the con?guration and orientation of sedimentary bedforms or on the pattern of rock outcrops.This infor- mation is often very useful in complementing the subsurface information derived from shallow seismic re?ection surveys. Sidescan sonar is also useful for locat- ing artefacts on the sea ?oor such as wrecks, cables or pipes. As with sub-bottom pro?ling systems, results in deep water are much improved by the use of deep-tow systems.

    4.16 Applications of seismic re?ection surveying The 1980s and 1990s saw major developments in re?ec- tion seismic surveying. Over that period, the general quality of seismic record sections improved markedly due to the move to digital data acquisition systems and At the same time, the range of applications of the method increased considerably. Previously, re?ection surveying was concerned almost exclusively with the search for hydrocarbons and coal, down to depths of a few kilome- tres. Now, the method is being used increasingly for studies of the entire continental crust and the uppermost mantle to depths of several tens of kilometres. At the other end of the spectrum of target depths the method is increasingly applied for high-resolution onshore mapping of shallow geology to depths of a few tens or hundreds of metres.

    The search for hydrocarbons, onshore and offshore, nevertheless remains by far the largest single application of re?ection surveying. This re?ects the particular strength of the method in producing well-resolved images of sedimentary sequences down to a depth of several kilometres. The method is used at all stages of an exploration programme for hydrocarbons, from the early reconnaissance stage through to the detailed map- ping of speci?c structural targets in preparation for ex- ploration drilling, and on into the ?eld development stage when the overall reservoir geometry requires fur- Because of its relatively high cost, three-dimensional seismic surveying still does not ?nd routine application in hydrocarbon exploration programmes. However, whereas it was originally used only at the ?eld develop- ment stage, it now ?nds widespread application also at the exploration stage in some oil?elds. Vertical seismic pro?ling is another important technique that is being applied increasingly at the stage of oil?eld development because of its ability to reveal subsurface detail that is In the quest for ever more detailed subsurface informa- tion, three component (3C) surveys are becoming more common. The value of repeated surveys during oil?eld production is now established and `time lapse’ or 4D The initial round of seismic exploration for hydrocar- bons normally involves speculative surveys along widely-spaced pro?le lines covering large areas. In this way the major structural or stratigraphic elements of the regional geology are delineated, so enabling the plan- ning of detailed, follow-up re?ection surveys in more Where good geological mapping of known sedimentary sequences exists, the need for expenditure on initial speculative seismic surveys is often much reduced and effort can be concentrated from an early stage on the Detailed re?ection surveys involve closely-spaced pro?le lines and a high density of pro?le intersection points in order that re?ection events can be traced reli- ably from pro?le to pro?le and used to de?ne the pre- vailing structure. Initial seismic interpretation is likely to in-volve structural mapping, using time-structure and/or isochron maps (Section 4.14.1) in the search for the structural closures that may contain oil or gas. Any closures that are identi?ed may need further delineation by a second round of detailed seismic surveying before the geophysicist is suf?ciently con?dent to select the lo- Seismic Re?ection Surveying 93

    Fig. 4.61 Interpreted seismic section across the NorthViking gas ?eld, North Sea. (Courtesy Conoco UK Ltd.)

    Seismic Re?ection Surveying 95 Fig. 4.62 (a) Seismic section (courtesy Shell UK Ltd) and (b) line interpretation across the Brent oil?eld, North Sea. G = gas; O = oil;W = water.

    produce seismic sections of shallow subsurface geology at reasonable cost. High-resolution re?ection seismolo- gy is particularly well suited to the investigation of Quaternary sedimentary sequences (Fig. 4.56) and for the detailed mapping of concealed bedrock surfaces of irregular geometry (Fig. 4.64).The contrast between the crustal (Fig. 4.63) and near-surface sections (Fig. 4.64) neatly emphasizes the scalability of the seismic re?ec- tion method. In both these applications it is also the geophysical method with the highest resolution, both vertically and horizontally.

    Seismic Re?ection Surveying 97 Fig. 4.64 A near-surface seismic re?ection section showing Mesozoic sediments (re?ectorsT1–T3 and B) with an angular unconformity (U) against Lower Palaeozoic rocks. (From Ali & Hill 1991.)

    Problems 1. A seismic wave is incident normally on a re?ector with a re?ection coef?cient R of 0.01. What proportion of the incident energy is 2. What is the root-mean-square velocity in re?ection surveying, and how is it related to 3. A zero-offset re?ection event at 1.000 s has a normal moveout (NMO) of 0.005 s at 200 m 4. (a) Calculate the approximate dimensions of the Fresnel zone in the following two cases: (i) Re?ection pro?ling is used to investigate The dominant frequency of the re?ected pulse is found to be 10 Hz. Using a typical average (ii) A high-resolution re?ection survey is used to map rockhead beneath a Quaternary sediment cover about 100 m thick using a high-frequency source. The dominant frequency of the re?ected pulse is found to be 150 Hz. Use a sediment (b) Discuss the importance of the above Fresnel zone dimensions as indications of the inherent limits on horizontal resolution achievable in (c) Use the frequency and velocity information to calculate the vertical resolution of the two surveys above and again discuss the general importance of the results obtained to the verti- cal resolution that is achievable in re?ection seismics.

    Further reading Ali, J.W. & Hill, I.A. (1991) Re?ection seismics for shallow Bally, A.W. (ed.) (1983) Seismic Expression of Structural Styles (a picture and work atlas): Vol 1 — The layered Earth; Vol 2 — Tectonics of extensional provinces; Vol 3 — Tectonics of compressional provinces / Strike-slip tectonics. AAPG Studies in Geology No. 15, Bally, A.W. (ed.) (1987) Atlas of Seismic Stratigraphy (3 vols). AAPG Studies in Geology No. 27, American Association of Petroleum Barazangi, M. & Brown, L. (eds) (1986) Re?ection Seismology: Berg, O.R. & Woolverton, D.G. (eds) (1985) Seismic Stratigraphy II: An Integrated Approach to Hydrocarbon Exploration. AAPG Memoir 39, American Association of Petroleum Geologists, AAPG Memoir 42, American Association of Petroleum Camina, A.R. & Janacek, G.J. (1984) Mathematics for Seismic Data Cassell, B. (1984) Vertical seismic pro?les — an introduction. First Castagna, J.P. & Bachus, M.M. (1993) Offset-Dependent Re?ectivity: McGraw Hill, NewYork.

    Dobrin, M.B. & Savit, C.H. (1988) Introduction to Geophysical Hatton, L., Worthington, M.H. & Makin, J. (1986) Seismic Data Hubral, P. & Krey, T. (1980) Interval Velocities from Seismic Re?ection Jack, I. (1997) Time Lapse Seismic in Reservoir Management. Society of Exploration Geophysicists, Short Course Notes, Society of Kleyn, A.H. (1983) Seismic Re?ection Interpretation. Applied Science McQuillin, R., Bacon, M. & Barclay, W. (1979) An Introduction to Payton, C.E. (ed.) (1977) Seismic Stratigraphy — Application to Hydro- carbon Exploration. AAPG Memoir 26, American Association of Robinson, E.A. (1983) Migration of Geophysical Data. IHRDC, Robinson, E.A. (1983) Seismic Velocity Analysis and the Convolu- Sengbush, R.L. (1983) Seismic Exploration Methods. IHRDC, Sheriff, R.E. (1982) Structural Interpretation of Seismic Data. AAPG Sheriff, R.E. & Geldart, L.P. (1983) Exploration Seismology, Vol. 2: Data-Processing and Interpretation. Cambridge University Press, Waters, K.H. (1978) Re?ection Seismology — A Tool For Energy Ziolkowski, A. (1983) Deconvolution. IHRDC, Boston.

    5.1 Introduction The seismic refraction surveying method uses seismic energy that returns to the surface after travelling through the ground along refracted ray paths. As brie?y discussed in Chapter 3, the ?rst arrival of seismic energy at a detec- tor offset from a seismic source always represents either a direct ray or a refracted ray.This fact allows simple refrac- tion surveys to be performed in which attention is con- centrated solely on the ?rst arrival (or onset) of seismic energy, and time–distance plots of these ?rst arrivals are interpreted to derive information on the depth to refracting interfaces. As is seen later in the chapter, this simple approach does not always yield a full or accurate picture of the subsurface. In such circumstances more complex interpretations may be applied. The method is normally used to locate refracting interfaces (refractors) separating layers of different seismic velocity, but the method is also applicable in cases where velocity varies Refraction seismograms may also contain re?ection events as subsequent arrivals, though generally no special attempt is made to enhance re?ected arrivals in refrac- tion surveys. Nevertheless, the relatively high re?ection coef?cients associated with rays incident on an interface at angles near to the critical angle often lead to strong wide-angle re?ections which are quite commonly detected at the greater recording ranges that characterize large- scale refraction surveys. These wide-angle re?ections often provide valuable additional information on sub- surface structure such as, for example, indicating the presence of a low-velocity layer which would not be The vast majority of refraction surveying is carried out along pro?le lines which are arranged to be suf?ciently long to ensure that refracted arrivals from target layers are recorded as ?rst arrivals for at least half the length of the line. Refraction pro?les typically need to be between ?ve and ten times as long as the required depth of investi- gation. A consequence of this requirement is that large seismic sources are needed for the detection of deep re- fractors in order that suf?cient energy is transmitted over the long range necessary for the recording of deep re- fracted phases as ?rst arrivals.The pro?le length required in any particular survey depends upon the distribution of velocities with depth at that location.The requirement in refraction surveying for an increase in pro?le length with increase in the depth of investigation contrasts with the situation in conventional re?ection surveying, where near-normal incidence re?ections from deep interfaces Refraction seismology is applied to a very wide range of scienti?c and technical problems, from engineering site investigation surveys to large-scale experiments designed to study the structure of the entire crust or lithosphere. Refraction measurements can provide valu- able velocity information for use in the interpretation of re?ection surveys, and refracted arrivals recorded during land re?ection surveys are used to map the weathered layer, as discussed in Chapter 4.This wide variety of ap- plications leads to an equally wide variety of ?eld survey In many geological situations, subsurface refractors may approximate planar surfaces over the linear extent of a refraction line. In such cases the observed travel-time plots are commonly assumed to be derived from a set of planar layers and are analysed to determine depths to, and dips of, individual planar refractors.The geometry of re- fracted ray paths through planar layer models of the sub- surface is considered ?rst, after which consideration is given to methods of dealing with refraction at irregular (non-planar) interfaces.

    AxD Direct ray z Fig. 5.1 Successive positions of the expanding wavefronts for direct and ?v 1 refracted waves through a two-layer model. Only the wavefront of the ?rst B C arrival phase is shown. Individual ray paths Refracted ray v > v from source A to detector D are drawn as 21 solid lines.

    Wavefront geometries considered below are that the subsurface is composed of a series of layers, separated by planar and possibly dipping interfaces. Also, within each layer seis- mic velocities are constant, and the velocities increase with layer depth. Finally, the ray paths are restricted to a vertical plane containing the pro?le line (i.e. there is no component of cross-dip).

    5.2.1 Two-layer case with horizontal interface Figure 5.1 illustrates progressive positions of the wave- front from a seismic source at A associated with energy travelling directly through an upper layer and energy critically refracted in a lower layer. Direct and refracted ray paths to a detector at D, a distance x from the source, are also shown.The layer velocities are v and v (>v ) and 121 The direct ray travels horizontally through the top of the upper layer from A to D at velocity v . The re- 1 fracted ray travels down to the interface and back up to the surface at velocity v along slant paths AB and CD 1 that are inclined at the critical angle q, and travels along the interface between B and C at the higher velocity v . The total travel time along the refracted ray path 2 ABCD is t=t +t +t AB BC CD z (x – 2z tan q ) z =++ v cosq v v cosq 121

    Noting that sin q = v /v (Snell’s Law) and cos q = 12 (1 – v2/v2)1/2, the travel-time equation may be ex- 12 pressed in a number of different forms, a useful general form being x 2z cosq t = + (5.1) vv 21 t Refracted arrivals slope 1/v 2 t i Direct arrivals slope 1/v 1 xx x crit cros

    Fig. 5.2 Travel-time curves for the direct wave and the head wave from a single horizontal refractor.

    Alternatively 12 x 2z(v2-v2) t = + 2 1 (5.2) v vv 2 12

    or x t = + t (5.3) i v 2

    where, plotting t against x (Fig. 5.2), t is the intercept i on the time axis of a travel-time plot or time–distance plot having a gradient of 1/v . The intercept time t , 2i is given by

    Solving for refractor depth tvv z= i12 12 2(v2-v2) 21

    A useful way to consider the equations (5.1) to (5.3) is to note that the total travel time is the time that would have been taken to travel the total range x at the refractor velocity v (that is x/v ), plus an additional time to allow 22 for the time it takes the wave to travel down to the refrac- tor from the source, and back up to the receiver. The concept of regarding the observed time as a refractor travel-time plus delay times at the source and receiver is Values of the best-?tting plane layered model para- meters, v , v and z, can be determined by analysis of 12 the travel-time curves of direct and refracted arrivals: · v and v can be derived from the reciprocal of the 12 gradient of the relevant travel-time segment, see Fig. 5.2 · the refractor depth, z, can be determined from the i At the crossover distance x the travel times of direct cros and refracted rays are equal

    12 x x 2z(v2-v2) cros = cros + 2 1 v v vv 1 2 12

    Thus, solving for x cros 12 È v 2 + v1 ? x = 2z (5.4) 21

    From this equation it may be seen that the crossover distance is always greater than twice the depth to the refractor. Also the crossover distance equation (5.4) provides an alternative method of calculating z.

    5.2.2 Three-layer case with horizontal interface The geometry of the ray path in the case of critical refrac- tion at the second interface is shown in Fig. 5.3.The seis- mic velocities of the three layers are v , v (>v ) and v 1213 (>v ).The angle of incidence of the ray on the upper inter- 2 13 23 12 By analogy with equation (5.1) for the two-layer case, the travel time along the refracted ray path ABCDEF to Seismic Refraction Surveying 101

    x AF ? 13 z 1 v 1 B? E 23

    z 2v >v 21 CD v >v 32 Fig. 5.3 Ray path for a wave refracted through the bottom layer of a three-layer model.

    an offset distance x, involving critical refraction at the second interface, can be written in the form

    x 2z cosq 2z cosq t = + 1 13 + 2 23 (5.5) vvv 312

    where q = sin -1(v v ); q = sin -1(v v ) 13 1 3 23 2 3

    and the notation subscripts for the angles relate directly to the velocities of the layers through which the ray travels at that angle (q is the angle of the ray in layer 1 13 Equation (5.5) can also be written

    x t = + t + t (5.6) 12 v 3

    where t and t are the times taken by the ray to travel 12 The interpretation of travel-time curves for a three- layer case starts with the initial interpretation of the top two layers. Having used the travel-time curve for rays critically refracted at the upper interface to derive z and 1 v , the travel-time curve for rays critically refracted at 2 the second interface can be used to derive z and v using 23 equations (5.5) and (5.6) or equations derived from them.

    t 1 Slope 1/v Slope 1/v 2 Slope 1/v 3 2 +t 1 t x Fig. 5.4 Travel-time curves for the direct wave and the head waves from two horizontal refractors.

    5.2.3 Multilayer case with horizontal interfaces In general the travel time t of a ray critically refracted n along the top surface of the nth layer is given by x n-1 2z cosq tn = + Â i in (5.7) vv n i =1 i

    where q = sin -1(v v ) in i n

    Equation (5.7) can be used progressively to compute layer thicknesses in a sequence of horizontal strata repre- sented by travel-time curves of refracted arrivals. In prac- tice as the number of layers increases it becomes more dif?cult to identify each of the individual straight-line segments of the travel-time plot. Additionally, with in- creasing numbers of layers, there is less likelihood that each layer will be bounded by strictly planar horizontal It would be unusual to make an interpretation using this method for more than four layers.

    5.2.4 Dipping-layer case with planar interfaces In the case of a dipping refractor (Fig. 5.5(a)) the value of dip enters the travel-time equations as an additional un- known.The reciprocal of the gradient of the travel-time curve no longer represents the refractor velocity but a quantity known as the apparent velocity which is higher than the refractor velocity when recording along a pro- ?le line in the updip direction from the shot point and The conventional method of dealing with the possible presence of refractor dip is to reverse the refraction ex- periment by ?ring at each end of the pro?le line and In the presence of a component of refractor dip along the pro?le direction, the forward and reverse travel time plots for refracted rays will differ in their gradients and The general form of the equation for the travel-time t n of a ray critically refracted in the nth dipping refractor (Fig. 5.6; Johnson 1976) is given by x sin b n-1 h (cosa + cos b ) t= 1+Âi i i n (5.8) vv 1 i =1 i

    where h is the vertical thickness of the ith layer beneath i the shot, v is the velocity of the ray in the ith layer, a is ii the angle with respect to the vertical made by the down- going ray in the ith layer, b is the angle with respect to the i vertical made by the upgoing ray in the ith layer, and x is Equation (5.8) is comparable with equation (5.7), the only differences being the replacement of q by angles a and b that include a dip term. In the case of shooting downdip, for example (see Fig. 5.6), a = q – g and i in i b = q + g , where g is the dip of the ith layer and q = i in i i in sin-1(v /v ) as before. Note that h is the vertical thick- 1n ness rather than the perpendicular or true thickness of a As an example of the use of equation (5.8) in inter- preting travel-time curves, consider the two-layer case Shooting downdip, along the forward pro?le xsinb h(cosa+cosb) t= 1+1 2 vv 11 x sin(q + g ) h cos(q – g ) = 12 1 + 1 12 1 vv 11 h cos(q + g ) + 1 12 1 v 1

    Seismic Refraction Surveying 103 (a) AD z v h? 1 h’z’ ?

    B C v >v 21 ? (b) t t DAReciprocal time t AD S ope 1 v l / Slope 1/v 2d 2u t’ i

    t i Fig. 5.5 (a) Ray-path geometry and (b) travel-time curves for head wave arrivals from a dipping refractor in the forward and reverse directions along a refraction pro?le line. x Slope 1/v 1 Slope 1/v 1 Source Detector x

    h 1 h 2 Fig. 5.6 Geometry of the refracted ray path through a multilayer, dipping model. (After Johnson 1976.) ? v1 1

    and from the reverse direction 1 v = sin (q – g ) v (5.12) 2u 12 1 1

    Hence q + g = sin -1(v v ) 12 1 1 2d q – g = sin -1(v v ) 12 1 1 2u

    Solving for q and g yields 1 q = [sin -1(v v ) + sin -1(v v )] 12 1 2d 1 2u 2 1 g = [sin -1(v v ) – sin -1(v v )] 1 1 2d 1 2u 2 Knowing v , from the gradient of the direct ray travel- 1 time curve, and q , the true refractor velocity may be 12 derived using Snell’s Law v = v sin q 2 1 12

    The perpendicular distances z and z¢ to the interface under the two ends of the pro?le are obtained from the intercept times t and t ¢ of the travel-time curves ii obtained in the forward and reverse directions t = 2z cosq v i 12 1 \ z = v t 2cosq 1 i 12

    and similarly z¢ = v t¢ 2cosq 1 i 12 By using the computed refractor dip g , the respective 1 perpendicular depths z and z¢ can be converted into vertical depths h and h¢ using h = z cosg 1

    and h¢ = z¢ cosg 1 Note that the travel time of a seismic phase from one end of a refraction pro?le line to the other (i.e. from shot point to shot point) should be the same whether mea- sured in the forward or the reverse direction. Referring AD DA Establishing that there is satisfactory agreement between t

    t i2 t i1 x z 1 zv 21 A ?z

    B v >v 21 Fig. 5.7 Offset segments of the travel-time curve for refracted arrivals from opposite sides of a fault.

    these reciprocal times (or end-to-end times) is a useful means of checking that travel-time curves have been drawn correctly through a set of refracted ray arrival times derived from a reversed pro?le.

    5.2.5 Faulted planar interfaces The effect of a fault displacing a planar refractor is to off- set the segments of the travel-time plot on opposite sides of the fault (see Fig. 5.7). There are thus two intercept times t and t , one associated with each of the travel- i1 i2 time curve segments, and the difference between these For example, in the case of the faulted horizontal refrac- tor shown in Fig. 5.7 the throw of the fault Dz is given by Dz cosq DT ª v 1

    DT v DT v v Dz ª 1 = 1 2 cos q (v 2 – v 2 )1 2 21

    Note that there is some approximation in this formula- tion, since the ray travelling to the downthrown side of the fault is not the critically refracted ray at A and in- volves diffraction at the base B of the fault step. However, the error will be negligible where the fault throw is small compared with the refractor depth.

    Seismic Refraction Surveying 105 (a) t (c) t (b) t

    x x x Fig. 5.8 Various types of pro?le geometry used in refraction surveying. (a) Conventional reversed pro?le with end shots. (b) Split-pro?le with central shot. (c) Single-ended pro?le with repeated shots.

    ?x x x ?x S1 S2 D1 D2

    v z1 1z 2 ? ? ? v >v 21 Fig. 5.9 Refraction interpretation using the single-ended pro?ling method. (After Cunningham 1974.)

    and from S to D the travel time is given by 22 x sin(q + g ) 2z cosq t = + 2 (5.14) 2 vv 11

    where z and z are the perpendicular depths to the re- 12 fractor under shot points S and S , respectively. Now, 12

    z – z = Dx sin g 21 (5.15) \ z = z + Dx sin g 21 Substituting equation (5.15) in (5.14) and then subtract- ing equation (5.13) from (5.14) yields Dx t-t=Dt= (2singcosq) 21 v 1

    Dx sin(q + g ) Dx sin(q – g ) =- vv 11 Substituting equations (5.11) and (5.12) in the above equation and rearranging terms Dt 1 1 =- Dx v v 2d 2u

    where v and v are the updip and downdip apparent 2u 2d velocities, respectively. In the case considered v is 2d derived from the single-ended travel-time curves, hence v can be calculated from the difference in travel time 2u of refracted rays from adjacent shots recorded at the same offset distance x. With both apparent velocities calcu- lated, interpretation proceeds by the standard methods for conventional reversed pro?les discussed in Section 5.2.4.

    5.4 Geometry of refracted ray paths: irregular (non-planar) interfaces The assumption of planar refracting interfaces would often lead to unacceptable error or imprecision in the interpretation of refraction survey data. For example, a survey may be carried out to study the form of the con- cealed bedrock surface beneath a valley ?ll of alluvium or glacial drift. Such a surface is unlikely to be modelled ad- equately by a planar refractor. In such cases the constraint that refracting interfaces be interpreted as planar must be dropped and different interpretation methods must be The travel-time plot derived from a survey provides a ?rst test of the prevailing refractor geometry. A layered sequence of planar refractors gives rise to a travel-time plot consisting of a series of straight-line segments, each segment representing a particular refracted phase and Irregular travel-time plots are an indication of irregular refractors (or of lateral velocity variation within individ- ual layers — a complication not discussed here). Methods of interpreting irregular travel-time plots, to determine the non-planar refractor geometry that gives rise to them, are based on the concept of delay time.

    5.4.1 Delay time Consider a horizontal refractor separating upper and 121 5.1). The travel time of a head wave arriving at an offset distance x is given (see equation (5.3)) by

    Seismic Refraction Surveying 107 delay time can be calculated in a similar way, referring 1 z=dv cosq=dvv (v2-v2)2 (5.17) to Fig. 5.10, t 1 t 1 2 2 1 Thus the delay time can be converted into a refractor d =t -t t AB BC depth if v and v are known. 12 = – BC The intercept time ti in equation (5.3) can be parti- AB v1 2 tioned into two delay times v

    2q) z == v cosq v x z cosq z cosq x 2z cosq 1 1 t= + + = + 12 v v v v v z(v 2 – v 2 ) 2 1 1 2 1 = 2 1 (5.16) zz = – tan q t = x v + d + d (5.18) 2 ts td v cosq v 12 z z sin q sin q where d and d are the delay times at the shot end and ts td = – detector end of the refracted ray path. Note that in this v cosq v cosq 11 case of a horizontal refractor, z(1 – sin cosq

    vv 1 2 This is the same result as derived earlier in equation (5.1), showing that the delay-time concept is implicit even in Solving equation (5.16) for the depth z to the refractor yields In the presence of refractor dip the delay time is simi- larly de?ned except that the geometry of triangle ABC (a) (b) rotates with the refractor. The delay time is again related AA to depth by equation (5.17), where z is now the refractor z v1 z Using this de?nition of delay time, the travel time of a ray v 1

    ? refracted along a dipping interface (see Fig. 5.11(a)) is ? C B C given by v >v B 21 t = x¢ v + d + d (5.19) v > v 2 ts td 21

    Fig. 5.10 The concept of delay time. where d = t – t and d = t – t . ts AB BC td DE DF

    (a) x AE

    v 1 C B x’ D F v >v 21 (b) x AE

    Fig. 5.11 Refracted ray paths associated CB F with (a) a dipping and (b) an irregular x’ D refractor.

    (a) l S2 S1 x D

    v 1 z B v >v A 21

    (b) t t S1S2 t S1D t S2D SxD xS 1 c1 c2 2

    For shallow dips, x¢ (unknown) is closely similar to the t SD 1 offset distance x (known), in which case equation (5.18) can be used in place of (5.19) and methods applicable to a horizontal refractor employed. This approximation is valid also in the case of an irregular refractor if the relief on the refractor is small in amplitude compared to the Delay times cannot be measured directly but occur in pairs in the travel-time equation for a refracted ray from a surface source to a surface detector. The plus–minus method of Hagedoorn (1959) provides a means of solving equation (5.18) to derive individual delay time values for the calculation of local depths to an irregular refractor.

    Fig. 5.12 The plus–minus method of refraction interpretation (Hagedoorn 1959). (a) Refracted ray paths from each end of a reversed seismic pro?le line to an intermediate detector position. (b)Travel-time curves in the forward and reverse directions.

    =xv+d+d 2 t S t D (5.21) 1

    for the reverse ray, from shot point S 2 t = (l – x) v + d + d (5.22) S D 2 tS tD 22

    tD V cannot be obtained directly from the irregular 2 travel-time curve of refracted arrivals, but it can be estimated by means of Hagedoorn’s minus term. This is obtained by taking the difference of equations (5.21) and (5.22)

    plot will curve away from a central straight section. Also, any lateral change of refractor velocity v along the pro- 2 ?le line will show up as a change of gradient in the minus For the valid range of detectors determined from the Adding equations (5.21) and (5.22) t + t = l v + d + d + 2d SD SD 2 tS tS tD 12 12

    Substituting equation (5.20) in the above equation yields t + t = t + 2d SD SD SS tD 1 2 12

    Hence 1 dt D = (tS D + tS D – tS S ) (5.23) 2 1 2 12

    This delay time is the plus term of the plus–minus method and may be used to compute the perpendicular depth z to the underlying refractor at D using equation (5.17). v is found from the minus-time plot and v is 21 computed from the slope of the direct ray travel-time plot (see Fig. 5.12(b)). Note that the value of all delay times depends on the reciprocal time. Errors in this time, which is recorded at maximum range along the pro?le, and often with the lowest signal-to-noise ratio, intro- duce a constant error into all delay times. Great care must A plus term and, hence, a local refractor depth can be computed at all detector positions at which head wave In practice, this normally means the portion of the pro- ?le line between the crossover distances; that is, between c1 c2 Where a refractor is overlain by more than one layer, equation (5.17) cannot be used directly to derive a re- fractor depth from a delay time (or plus term). In such a case, either the thickness of each overlying layer is com- puted separately using refracted arrivals from the shal- lower interfaces, or an average overburden velocity is used in place of v in equation (5.17) to achieve a depth 1 The plus–minus method is only applicable in the case of shallow refractor dips, generally being considered valid for dips of less than 10°. With steeper dips, x¢ be- Further, there is an inherent smoothing of the inter- preted refractor geometry in the plus–minus method.

    Seismic Refraction Surveying 109 ?x SDDS 1212 v 1 v >v 21

    Fig. 5.13 The generalized reciprocal method of refraction When computing the plus term for each detector, the refractor is assumed to be planar between the points of emergence from the refractor of the forward and reverse rays, for example between A and B in Fig. 5.12(a) for rays arriving at detector D.

    5.4.3 The generalized reciprocal method This problem of smoothing is solved in the generalized reciprocal method (GRM) of refraction interpretation (Palmer 1980) by combining the forward and reverse rays which leave the refractor at approximately the same point and arrive at different detector positions separated by a distance Dx (see Fig. 5.13). The method uses a velocity analysis function t given by v

    tv = (tS D + tS D – tS S ) 2 (5.24) 11 22 12

    the values being referred to the mid-point between each pair of detector positions D and D . For the 12 case where D = D = D (i.e. Dx = 0), equation (5.24) 12 reduces to a form similar to Hagedoorn’s minus term (see above). The optimal value of Dx for a particular survey is that which produces the closest approach to a linear plot when the velocity analysis function t is v plotted against distance along the pro?le line, and is derived by plotting curves for a range of possible Dx values. The overall interpretation method is more complex than the plus–minus method, but can deliver better velocity discrimination, greater lateral resolution and better depth estimates to boundaries. The method also demands denser data coverage than the plus–minus method. The principles of the method, its imple- mentation and example datasets are clearly laid out in Palmer’s book (Palmer 1980), but beyond the scope of this one.

    Fig. 5.14 Modelling of complex geology by ray-tracing in the case of a refraction pro?le between quarries in southWales, UK. Refracted ray paths from Cornelly Quarry (located in Carboniferous Limestone) are modelled through a layered Palaeozoic sedimentary sequence overlying an irregular Precambrian basement surface at a depth of about 5 km.This model accounts for the measured travel times of refracted arrivals observed along the pro?le. (From Bayerly & Brooks 1980.)

    5.5 Construction of wavefronts and ray-tracing Given the travel-time plots in the forward and reverse directions along a pro?le line it is possible to reconstruct the con?guration of successive wavefronts in the subsur- face and thereby derive, graphically, the form of refract- ing interfaces.This wavefront method (Thornburgh 1930) represents one of the earliest refraction interpretation With the massive expansion in the speed and power of digital computers, and their wide availability, an increas- ingly important method of refraction interpretation is a 1974). In this method structural models are postulated and the travel-times of refracted (and re?ected) rays through these models are calculated by computer for comparison with observed travel-times. The model is then adjusted iteratively until the calculated and ob- served travel-times are in acceptable agreement. This method is especially useful in the case of complex sub- surface structures that are dif?cult to treat analytically.An example of a ray-tracing interpretation is illustrated in Fig. 5.14.The ray-tracing method is particularly valuable in coping with such complexities as horizontal or verti- cal velocity gradients within layers, highly irregular or steeply dipping refractor interfaces and discontinuous layers.

    (a) t Direct arrivals Seismic Refraction Surveying 111 l ayer 3 Arrivals from layer 2 Arr va s from il

    x v 1 v >v 21 v >v 32 (b) t l ayer 3 Arr va s from il Direct arrivals x

    v 1 Fig. 5.15 The undetected layer problem in refraction seismology. (a) A hidden layer: a thin layer that does not give v2

    rise to ?rst arrivals. (b) A blind layer: a layer of low velocity v >v that does not generate head waves. 3 1

    result from the thinness of the layer, or from the closeness of its velocity to that of the overlying layer. In such a case, a method of survey involving recognition of only ?rst ar- rivals will fail to detect the layer. It is good practice to ex- amine the seismic traces for possible arrivals occurring behind the ?rst arrivals.These should then be examined to ensure they are compatible with the structural model A blind layer presents a more insidious problem, resulting from a low-velocity layer, as illustrated in Fig. 5.15(b). Rays cannot be critically refracted at the top of such a layer and the layer will therefore not give rise to head waves. Hence, a low-velocity layer cannot be detected by refraction surveying, although the top of the low-velocity layer gives rise to wide-angle re?ections that may be detected as later arrivals during a In the presence of a low-velocity layer, the interpreta- tion of travel-time curves leads to an overestimation of the depth to underlying interfaces. Low-velocity layers are a hazard in all types of refraction seismology. On a small scale, a peat layer in muds and sands above bedrock may escape detection, leading to a false estimation of foundation conditions and rockhead depths beneath a construction site; on a much larger scale, low-velocity zones of regional extent are known to exist within the continental crust and may escape detection in crustal seismic experiments.

    5.7 Refraction in layers of continuous velocity change In some geological situations, velocity varies gradually as a function of depth rather than discontinuously at dis- crete interfaces of lithological change. In thick clastic se- quences, for example, especially clay sequences, velocity increases downwards due to the progressive compaction effects associated with increasing depth of burial. A seis- mic ray propagating through a layer of gradual velocity change is continuously refracted to follow a curved ray path. For example, in the special case where velocity in- creases linearly with depth, the seismic ray paths describe arcs of circles. The deepest point reached by a ray travel- In such cases of continuous velocity change with depth, the travel-time plot for refracted rays that return to the surface along curved ray paths is itself curved, and the geometrical form of the curve may be analysed to derive information on the distribution of velocity as a Velocity increase with depth may be signi?cant in thick surface layers of clay due to progressive compaction and dewatering, but may also be signi?cant in deeply buried layers. Refracted arrivals from such buried layers are not true head waves since the associated rays do not travel along the top surface of the layer but along a curved path in the layer with a turning point at some depth below the interface. Such refracted waves are referred to as diving waves (Cerveny & Ravindra 1971). Methods of interpreting refraction data in terms of diving waves are Indeed, some ray-tracing programmes require velocity gradients to be introduced into all layers of an interpreta- tion model in order to generate diving waves rather than true head waves.

    5.8 Methodology of refraction pro?ling Many of the basic principles of refraction surveying have been covered in the preceding sections but in this section several aspects of the design of refraction pro?le lines are brought together in relation to the particular objectives of a refraction survey.

    Seismic Refraction Surveying 113 Sonobuoy Firing/recording ship Radio link Water layer Layer 1 Shot v 1

    v >v Layer 2 2 1

    Layer 3 v3 >v 2

    t S ope 1 v l /3 Arrivals from layer 3 Slope 1/v 2 Arrivals from layer 2 1 Slope 1/v Arrivals from layer 1 Fig. 5.16 Single-ship seismic refraction pro?ling. x

    10–50 Hz and travel times need to be known to about A large-scale seismic refraction line on land to investi- Seismic events need to be recorded at a series of inde- pendently operated recording stations all receiving a standard time signal to provide a common time base for the recordings. Usually this is provided by the signal from the global positioning system (GPS) satellite system.Very large energy sources, such as military depth charges (det- onated at sea or in a lake) or large quarry blasts, are re- quired in order that suf?cient energy is transmitted over the length of the pro?le line.The dominant frequency of such sources is less than 10 Hz and the required accuracy of seismic travel times is about 50 ms. Such an experi- ment requires the active involvement of a large and well- Along extended refraction lines, wide-angle re?ec- tion events are often detected together with the refracted phases. These provide an additional source of infor- mation on subsurface structure. Wide-angle re?ection events are sometimes the most obvious arrivals and may Surveys speci?cally designed for the joint study of refracted and wide-angle re?ection events are often referred to as wide-angle surveys.

    5.8.2 Recording scheme For complete mapping of refractors beneath a seismic line it is important to arrange that head wave arrivals CG

    B v 1 F v >v 21 DH AE v >v 32 Fig. 5.17 Variation in the travel time of a head wave associated with variation in the thickness of a surface layer.

    Fig. 5.18 A possible observational scheme to obtain shallow and deeper refraction coverage along a survey line.The inclined lines indicate the range of coverage from the individual shots shown.

    Fig. 5.18. Such a scheme might include off-end shots into individual reversed pro?le lines, since off-end shots extend the length of refractor traversed by recorded head waves and provide insight into the structural causes of Selection of detector spacing along the individual pro?le lines is determined by the required detail of the refractor geometry, the sampling interval of interpretation points on the refractor being approximately equal to the de- tector spacing. Thus, the horizontal resolution of the It is often the case that there are insuf?cient detectors available to cover the full length of the pro?le with the desired detector spacing. In this case the procedure is to deploy the detectors to cover one segment of the line at The detectors are then moved to another segment of the line and all shot points ?red again.The process can be re- peated until full data are compiled for the complete pro- ?le. At the price of repeating the shots, a pro?le can thus be recorded of any length with a limited supply of equip- ment.The same principle is equally applicable to shallow penetration, to detailed refraction surveys for engineer- ing, to environmental and hydrological applications, and to crustal studies.

    5.8.3 Weathering and elevation corrections The type of observational scheme illustrated in Fig. 5.18 is often implemented for the speci?c purpose of map- ping the surface zone of weathering and associated low velocity across the length of a longer pro?le designed to investigate deeper structure. The velocity and thickness of the weathered layer are highly variable laterally and travel times of rays from underlying refractors need to be This weathering correction is directly analogous to that applied in re?ection seismology (see Section 4.6). The weathering correction is particularly important in shal- low refraction surveying where the size of the correction is often a substantial percentage of the overall travel time of a refracted ray. In such cases, failure to apply an accu- rate weathering correction can lead to major error in A weathering correction is applied by effectively re- placing the weathered layer of velocity v with material w of velocity v equal to the velocity of the underlying 1 layer. For a ray critically refracted along the top of the layer immediately underlying the weathered layer, the weathering correction is simply the sum of the delay times at the shot and detector ends of the ray path. Appli- cation of this correction replaces the refracted ray path by 1 For rays from a deeper refractor a different correction is required. Referring to Fig. 5.19, this correction effec- tively replaces ray path ABCD by ray path AD. For a ray critically refracted in the nth layer the weathering cor- rection t is given by w

    t = -(z + z ) wsd ¥{(v2-v2)12vv-(v2-v2)12vv} n 1 1n n w wn

    A v w B v 1 CD Fig. 5.19 The principle of the weathering correction in refraction seismology.

    common datum plane. The elevation correction t for e rays critically refracted in the nth layer is given by

    t=-(h+h){(v2-v2)12vv} e s d n 1 1n

    where h and h are the heights above datum of the shot sd point and detector location respectively. It is worth not- ing that these corrections are more complex than those used for seismic re?ection surveys. The difference arises since the assumption of vertical ray paths through the weathered layer used in the re?ection case cannot be In shallow water marine refraction surveying the water layer is conventionally treated as a weathered layer and a correction applied to replace the water layer by material of velocity equal to the velocity of the sea bed.

    5.8.4 Display of refraction seismograms In small-scale refraction surveys the individual seismo- grams are conventionally plotted out in their true time relationships in a format similar to that employed to dis- 4.8). From such displays, arrival times of refracted waves may be picked and, after suitable correction, used to make the time–distance plots that form the basis of Interpretation of large-scale refraction surveys is often as much concerned with later arriving phases, such as wide-angle re?ections or S-wave arrivals, as with ?rst Seismic Refraction Surveying 115

    arrivals. To aid recognition of weak coherent phases, the individual seismograms are compiled into an overall record section on which the various seismic phases can be correlated from seismogram to seismogram. The optimal type of display is achieved using a reduced time scale in which any event at time t and offset distance x is plotted at the reduced time T where T=t-xv R

    R Thus, for example, a seismic arrival from deep in the Earth’s crust with an overall travel time of 30 s to an offset distance of 150 km would, with a reduction velocity of 6 Plotting in reduced time has the effect of pro- gressively reducing travel-time as a function of offset and, therefore, rotating the associated time–distance curves towards the horizontal. For example, a time– distance curve with a reciprocal slope of 6 km s-1 on a t–x graph would plot as a horizontal line on a T–x graph using a reduction velocity of 6 km s-1. By appropriate choice of reduction velocity, seismic arrivals from a par- ticular refractor of interest can be arranged to plot about a horizontal datum, so that relief on the refractor will show up directly as departures of the arrivals from a hor- izontal line.The use of reduced time also enables the dis- play of complete seismograms with an expanded time An example of a record section from a crustal seismic ex- 5.20.

    Fig. 5.20 Part of a time section from a large-scale refraction pro?le, plotted in reduced time using a reduction velocity of 6 km s-1.The section was derived from the LISPB lithospheric seismic pro?le across Britain established in 1974. Phase a : head wave arrivals from a 1 shallow crustal refractor with a velocity of about 6.3 km s-1; phases c and e: wide-angle re?ections from lower crustal interfaces: phase d: head wave arrivals from the uppermost mantle (the P phase of earthquake seismology). (From Bamford et al. 1978.) n

    (a) (b) t S /D 13 S2 D 2

    D 4 D 1 S 1 Direct arrivals Seismic Refraction Surveying 117

    Refracted arrivals x Fig. 5.22 (a) An example of the type of network of shots and detectors from which the travel times of refracted arrivals can be used in a time term analysis of the underlying refractor geometry. (b)The plot of travel time as a function of distance identi?es the set of refracted arrivals that may be used in the analysis.

    t =x v+d +d +e ij ij ti tj ij

    where t is the travel time of head waves from the ith site ij to the jth site, x is the offset distance between site i and ij site j, d and d are the delay times (time terms), v is the re- ti tj fractor velocity (assumed constant), and e is an error ij ij If there are n sites there can be up to n(n – 1) observa- tional linear equations of the above type, representing the situation of a shot and detector at each site and all sites suf?ciently far apart for the observation of head waves from the underlying refractor. In practice there will be fewer observational equations than this because, nor- mally, only a few of the sites are shot points and head wave arrivals are not recognized along every shot– detector path (Fig. 5.22(b)). There are (n + 1) un- knowns, namely the individual delay times at the n sites If the number m of observational equations equals the number of unknowns, the equations can be solved to de- rive the unknown quantities, although it is necessary ei- ther that at least one shot and detector position should coincide or that the delay time should be known at one site. In fact, with the time term approach to refraction surveying it is normally arranged for m to well exceed (n + 1), and for several shot and detector positions to be interchanged.The resulting overdetermined set of equa- tions is solved by deriving values for the individual delay times and refractor velocity that minimize the sum of squares of the errors e . Delay times can then be con- ij verted into local refractor depths using the same proce- dure as in the plus–minus method described earlier.

    Ground surface Fig. 5.23 Idealized observation scheme for a simple cross-hole seismic transmission tomography survey. Dots mark receivers, stars mark sources. For clarity, only the ray paths from one source to all receivers (solid lines), and all sources Also shown is the regular grid of elements for which velocity values are derived.

    ticularly with large velocity variations, it can produce The information derived from seismic tomography may be used to predict spatial variations in, for example, lithology, pore ?uids, or rock fracturing, and the method is therefore of potential value in a wide range of explo- ration and engineering applications. As with many geo- physical methods, it can also be applied on a variety of spatial scales, from ranges of hundreds of metres, down to engineering or archaeological investigations of single columns in ancient buildings (Cardarelli & de Nardis 2001).

    5.11 Applications of seismic refraction surveying Exploration using refraction methods covers a very wide range of applications. Refraction surveys can provide es- timates of the elastic constants of local rock types, which have important engineering applications: use of special sources and geophones allows the separate recording of Seismic Refraction Surveying 119

    shear wave arrivals, and the combination of P- and S- wave velocity information enables calculation of Pois- son’s ratio (Section 3.3.1). If an estimate of density is available, the bulk modulus and shear modulus can also be calculated from P- and S-wave velocities. Such esti- mates of the elastic constants, based on the propagation of seismic waves, are referred to as dynamic, in contrast to the static estimates derived from load-testing of rock samples in the laboratory. Dynamic estimates tend to yield slightly higher values than loading tests.

    5.11.1 Engineering and environmental surveys On the local scale, refraction surveys are widely used in foundation studies on construction sites to derive esti- mates of depth to rockhead beneath a cover of super?cial material. Use of the plus–minus method or the general- ized reciprocal method (Section 5.4) allows irregular rockhead geometries to be mapped in detail and thus re- duces the need for test drilling with its associated high costs. Figure 5.24 shows a typical pro?le across ?uvial

    Fig. 5.24 T–x graph of a seismic refraction pro?le recorded over Holocene ?uvial sediments overlying Palaeozoic rocks.The geophone separation was 2 m and the shot point separation 30 m.The multiple, overlapping, reversed data allow a continuous plus–minus interpretation of the rockhead interface.

    Velocity (m s–1) 0 500 1000 1500 2000 2500 3000 3500 4000 4500 5000 Topsoil Clay Boulders Shale Sandstone Gneiss Limestone Granite Breccia Caliche Conglomerate Slate Could be ripped using D-9 tractor Marginal zone Could not be ripped Fig. 5.25 Table showing the variation of rippability with seismic P-wave velocity for a range of lithologies. (After Bell 1993.)

    sediments. Here the observation scheme speci?ed a 2 m geophone spacing, and a 30 m shot spacing. The data were recorded with a 48-channel seismograph, with shot points re-?red as the 48 geophones were moved The P-wave seismic velocity is related to the elastic constants and the density of the material. It is possible to derive an empirical relationship between the seismic velocity and the `hardness’ of the rock. In engineering usage, an important parameter of rock lithology is its resistance to excavation. If the rock can be removed by mechanical excavation it is termed `rippable’, rather than requiring fracturing by explosives. Empirical tables have been derived relating the `rippability’ of rock units by particular earthmoving equipment to the P-wave seismic velocity. Figure 5.25 shows a typical example of such a table. The range of velocities considered as rippable varies for different lithologies based on empiri- cal averages of such relevant factors as their typical degree of cementation and frequency of jointing. Simple re- versed P-wave refraction surveys are suf?cient to provide critical information to construction and quarrying For surveys of near-surface geology, the data collec- tion and interpretation must be ef?cient and rapid, to make the survey cost-effective against the alternative of direct excavation. The interpretation of seismic refrac- tion pro?le data is most conveniently carried out using commercial software packages on personal computers.A wide range of good software is available for the plotting, In some situations the option of excavation instead of geophysical survey is very undesirable. Seismic surveys may be used to de?ne the extent and depth of unrecord- ed land?ll sites, or structures on`brown-?eld’redevelop- ments. Commonly seismic and resistivity surveys may be used together to attempt to `characterize’ the nature of the land?ll materials. There is an increasing demand for this sort of investigation in many parts of the world.

    5.11.2 Hydrological surveys The large difference in velocity between dry and wet sediments renders the water table a very effective refrac- tor. Hence, refraction surveys ?nd wide application in exploration programmes for underground water sup- plies in sedimentary sequences, often employed in con- junction with electrical resistivity methods (see Chapter 8). There can, however, be an ambiguity in interpreta- tion of P-wave refraction data since a layer at depth with a velocity in excess of 1500 m s-1 could be either the Recording both P- and S-wave data overcomes this problem, since the water table will affect the P-wave velocity, but not that of the S-waves (Fig. 5.26).

    Seismic Refraction Surveying 121 S/P-wave comparison 220 200 S-wave 180 P-wave 160 140 Fig. 5.26 T–x graph of a seismic 120 refraction pro?le with a water-table 100 refractor.The rock unit is the Sherwood 80 Sandstone, having P-wave velocities of 60 800 and 2000 m s-1 for unsaturated and 40 saturated rock respectively (lower line). 20 The equivalent S-wave plot (upper line) 0 20 30 40 50 60 70 80 90 100 110 120 130 140 150 160 170 shows no effect at the water-table interface. Offset (m) First arrival (ms) NS GGF HBF SUF NW Highlands Grampians Midland Southern Northern England Valley Uplands 0 6.0 – 6.2 5.8 – 6.0 6.40 – 6.45 6.40 – 6.45 20 ?

    6.7 7.3 6.25 – 6.30 Moho 40 8.0 8.0 km 0 200 km

    Fig. 5.27 Crustal cross-section across northern Britain based on interpretation of a large-scale seismic refraction experiment. Numbers refer to velocities in km s-1. (After Bamford et al. 1978.) Contrast the distance scale with Figs 5.24 and 5.26.

    (a) (b) Layer 1 (L 1) Layer 2 5.0 2.02.0sediment fractured basalt massive basalt with dykes

    dykes with massive basalt metagabbros and gabbros with pockets of plagiogranite and protrusions of serpentinite 0 Depth below basement (km) 2

    4 6 8 Layer 3 6.7 Mantle 8.1 3.5 (L 2A) 5.2 (L 2B) (L 2C) 6.1 (L 3A) 6.8 (L 3B) 7.3 7.8 <6.9 Mantle 8.1 gabbros and metagabbros with serpentinite protrusions and pockets of cumulate ultramafics anomalous mantle (close to ridge axis) serpentinized ultramafics harzburgite and lherzolite Fig. 5.28 Velocity (km s-1) structure of typical oceanic lithosphere in terms of layered structures proposed in 1965 (a) and (From Kearey &Vine 1990.)

    granitic or granodioritic material. Lower crustal veloc- ities are normally in the range 6.5–7.0 km s-1 and may represent any of a variety of igneous and metamorphic rock types, including gabbro, gabbroic anorthosite and basic granulite. The latter rock type is regarded as the most probable major constituent of the lower crust on the basis of experimental studies of seismic velocities (Christensen & Fountain 1975).

    5.11.4 Two-ship seismic surveying: combined refraction and re?ection surveying Marine surveys, usually single-ship experiments, have shown the ocean basins to have a crust only 6–8 km thick, composed of three main layers with differing seismic velocities. This thickness and layering is main- The results of deep-sea drilling, together with the re- cognition of ophiolite complexes exposed on land as analogues of oceanic lithosphere, have enabled the nature of the individual seismic layers to be identi?ed Specialized methods of marine surveying involving the use of two survey vessels and multichannel recording include expanding spread pro?les and constant offset pro?les (Stoffa & Buhl 1979). These methods have been devel- oped for the detailed study of the deep structure of the crust and upper mantle under continental margins and oceanic areas.

    Expanding spread pro?ling (ESP) is designed to ob- tain detailed information relating to a localized region of the crust. The shot-?ring vessel and recording vessel travel outwards at the same speed from a central position, obtaining re?ected and refracted arrivals from subsurface interfaces out to large offsets. Thus, in addition to near- normal incidence re?ections such as would be recorded in a conventional common mid-point (CMP) re?ection survey, wide-angle re?ections and refracted arrivals are also recorded from the same section of crust. The com- bined re?ection/refraction data allow derivation of a highly-detailed velocity–depth structure for the local- Expanding spread pro?les have also been carried out on land to investigate the crustal structure of continental In constant offset pro?ling (COP), the shot-?ring and recording vessels travel along a pro?le line at a ?xed, wide separation. Thus, wide-angle re?ections and re- fractions are continuously recorded along the line. This survey technique facilitates the mapping of lateral changes in crustal structure over wide areas and allows continuous mapping of the types of refracting interface that do not give rise to good near-normal incidence re?ections and which therefore cannot be mapped adequately using conventional re?ection pro?ling. Such interfaces include zones of steep velocity gradient, in contrast to the ?rst-order velocity discontinuities that constitute the best re?ectors.

    Seismic Refraction Surveying 123 Problems 1. A single-ended refraction pro?le designed to determine the depth to an underlying horizontal refractor reveals a top layer velocity of 3.0 km s-1 and a refractor velocity of 5.0 km s-1. The crossover distance is found to be 500 m. What is 2. What is the delay time for head wave arrivals from layer 3 in the following case?

    Layer Depth (m) Vel. (km s-1) 1 100 1.5 2 50 2.5 3 – 4.0

    3. In order that both the horizontal-layer models given below should produce the same time– distance curves for head wave arrivals, what must be the thickness of the middle layer in Model 2?

    Vel. (km s-1) Depth (km) Model 1 Layer 1 3.0 1.0 Layer 2 5.0 –

    Model 2 Layer 1 3.0 0.5 Layer 3 5.0 –

    4. A single-ended refraction survey (Section 5.3) established to locate an underlying planar dipping refractor yields a top layer velocity of 2.2 km s-1 and a downdip apparent refractor velocity of 4.0 km s-1. When the shot point and geophones are moved forward by 150 m, in the direction of refractor dip, head wave arrival times to any offset distance are increased by 5 ms. Cal- culate the dip and true velocity of the refractor. If the intercept time of the refracted ray travel-time curve at the original shot point is 20 ms, what is 5. A split-spread refraction pro?le (Section 5.3) with a central shot point is established to locate an underlying planar dipping refractor.The resul- tant time–distance curves yield a top layer veloc- ity of 2.0 km s-1 and updip and downdip appar- ent velocities of 4.5 km s-1 and 3.5 km s-1, re- Calculate the true velocity and dip of the refrac- 6. The following dataset was obtained from a re- versed seismic refraction line 275 m long. The survey was carried out in a level area of alluvial cover to determine depths to the underlying bedrock surface.

    Offset (m) Travel time (ms) Forward direction: 12.5 6.0 25 12.5 37.5 19.0 50 25.0 75 37.0 100 42.5 125 48.5 150 53.0 175 57.0 200 61.5 225 66.0 250 71.0 275 76.5 Reverse direction: 12.5 6.0 25 12.5 37.5 17.0 50 19.5 75 25.0 100 30.5 125 37.5 150 45.5 175 52.0 200 59.0 225 65.5 250 71.0 275 76.5

    Carry out a plus–minus interpretation of the data and comment brie?y on the resultant bedrock 7. What subsurface structure is responsible for the travel-time curves shown in Fig. 5.29?

    60 Travel time (ms) 40 20 0 Fig. 5.29 Time–distance curves obtained in the 0 50 100 150 200 forward and reverse directions along a refraction pro?le Distance (m) across an unknown subsurface structure.

    Further reading Cardarelli, E. & de Nardis, R. (2001) Seismic refraction, isotropic and anisotropic seismic tomography on an ancient monument (Antonino and Faustina temple AD141). Geophysical Prospecting, Dobrin, M.B. & Savit, C.H. (1988) Introduction to Geophysical Giese, P., Prodehl, C. & Stein, A. (eds) (1976) Explosion Seismology Ivansson, S. (1986) Seismic borehole tomography — theory and computational methods: Proc. IEEE, 74, 328–38.

    Palmer, D. (1980) The Generalised Reciprocal Method of Seismic Refraction Interpretation. Society of Exploration Geophysicists, Palmer, D. (1986) Handbook of Geophysical Exploration: Section 1, Seismic Exploration. Vol. 13: Refraction Seismics. Enpro Science Sjagren, B. (1984) Shallow Refraction Seismics. Chapman & Hall, Stoffa, P.L. & Buhl, P. (1979) Two-ship multichannel seismic ex- periments for deep crustal studies: expanded spread and con- Willmore, P.L. & Bancroft, A.M. (1960) The time-term approach to refraction seismology. Geophys. J. R. Astr. Soc., 3, 419–32.

    6.1 Introduction In gravity surveying, subsurface geology is investigated on the basis of variations in the Earth’s gravitational ?eld arising from differences of density between subsurface rocks. An underlying concept is the idea of a causative body, which is a rock unit of different density from its sur- roundings.A causative body represents a subsurface zone of anomalous mass and causes a localized perturbation in the gravitational ?eld known as a gravity anomaly.A very wide range of geological situations give rise to zones of anomalous mass that produce signi?cant gravity anoma- lies. On a small scale, buried relief on a bedrock surface, such as a buried valley, can give rise to measurable anom- alies. On a larger scale, small negative anomalies are asso- ciated with salt domes, as discussed in Chapter 1. On a larger scale still, major gravity anomalies are generated by granite plutons or sedimentary basins. Interpreta- tion of gravity anomalies allows an assessment to be made of the probable depth and shape of the causative The ability to carry out gravity surveys in marine areas or, to a lesser extent, from the air extends the scope of the method so that the technique may be employed in most areas of the world.

    6.2 Basic theory The basis of the gravity survey method is Newton’s Law of Gravitation, which states that the force of attraction F between two masses m and m , whose dimensions are 12 small with respect to the distance r between them, is given by Gm m F = 1 2 (6.1) r2 where G is the Gravitational Constant (6.67 ¥ 10-11 Consider the gravitational attraction of a spherical, non-rotating, homogeneous Earth of mass M and radius R on a small mass m on its surface. It is relatively simple to show that the mass of a sphere acts as though it were con- centrated at the centre of the sphere and by substitution in equation (6.1) GM F = m = mg (6.2) R2

    Force is related to mass by an acceleration and the term g = GM/R2 is known as the gravitational accelera- tion or, simply, gravity. The weight of the mass is given On such an Earth, gravity would be constant. How- ever, the Earth’s ellipsoidal shape, rotation, irregular sur- face relief and internal mass distribution cause gravity to The gravitational ?eld is most usefully de?ned in terms of the gravitational potential U: GM U = (6.3) r

    Whereas the gravitational acceleration g is a vector quan- tity, having both magnitude and direction (vertically downwards), the gravitational potential U is a scalar, hav- ing magnitude only. The ?rst derivative of U in any di- Consequently, a potential ?eld approach provides com- putational ?exibility. Equipotential surfaces can be de?ned on which U is constant.The sea-level surface, or geoid, is the most easily recognized equipotential surface, which is everywhere horizontal, that is, at right angles to the direction of gravity.

    6.3 Units of gravity The mean value of gravity at the Earth’s surface is about 9.8 m s-2. Variations in gravity caused by density varia- tions in the subsurface are of the order of 100 mm s-2.This unit of the micrometre per second per second is referred to as the gravity unit (gu). In gravity surveys on land an accuracy of ±0.1 gu is readily attainable, corresponding to about one hundred millionth of the normal gravita- tional ?eld.At sea the accuracy obtainable is considerably less, about ±10 gu.The c.g.s. unit of gravity is the milligal (1 mgal = 10-3 gal = 10-3 cm s-2), equivalent to 10 gu.

    6.4 Measurement of gravity Since gravity is an acceleration, its measurement should However, such apparently simple measurements are not easily achievable at the precision and accuracy required The measurement of an absolute value of gravity is dif?cult and requires complex apparatus and a lengthy period of observation. Such measurement is classically made using large pendulums or falling body techniques (see e.g. Nettleton 1976, Whitcomb 1987), which can be made with a precision of 0.01 gu. Instruments for measuring absolute gravity in the ?eld were originally bulky, expensive and slow to read (see e.g. Sakuma 1986).A new generation of absolute reading instruments (Brown et al. 1999) is now under development which does not suffer from these drawbacks and may well be in The measurement of relative values of gravity, that is, the differences of gravity between locations, is simpler and is the standard procedure in gravity surveying. Ab- solute gravity values at survey stations may be obtained by reference to the International Gravity Standardiza- tion Network (IGSN) of 1971 (Morelli et al. 1971), a network of stations at which the absolute values of grav- ity have been determined by reference to sites of absolute gravity measurements (see Section 6.7). By using a rela- tive reading instrument to determine the difference in gravity between an IGSN station and a ?eld location the absolute value of gravity at that location can be Previous generations of relative reading instruments were based on small pendulums or the oscillation of torsion ?bres and, although portable, took considerable time to read. Modern instruments capable of rapid s s + ?s

    m m mg m (g + ?g) gravity measurements are known as gravity meters or Gravimeters are basically spring balances carrying a constant mass.Variations in the weight of the mass caused by variations in gravity cause the length of the spring to 6.1 a spring of initial length s has been stretched by an amount ds as a result of an increase in gravity dg increas- ing the weight of the suspended mass m. The extension of the spring is proportional to the extending force (Hooke’s Law), thus mdg = kds

    and m ds = dg (6.4) k

    Adjusting screw Beam ? mg ?’ Hinge m (g + ?g) problem is overcome in modern meters (unstable or astatic) which employ an additional force that acts in the same sense as the extension (or contraction) of the spring An example of an unstable instrument is the LaCoste and Romberg gravimeter.The meter consists of a hinged beam, carrying a mass, supported by a spring attached immediately above the hinge (Fig. 6.2). The magnitude of the moment exerted by the spring on the beam is de- pendent upon the extension of the spring and the sine of the angle q. If gravity increases, the beam is depressed and the spring further extended. Although the restoring force of the spring is increased, the angle q is decreased to q ¢. By suitable design of the spring and beam geometry the magnitude of the increase of restoring moment with increasing gravity can be made as small as desired. With ordinary springs the working range of such an instru- ment would be very small. However, by making use of a `zero-length’ spring which is pretensioned during manufacture so that the restoring force is proportional to the physical length of the spring rather than its exten- sion, instruments can be fashioned with a very sensitive response over a wide range. The instrument is read by restoring the beam to the horizontal by altering the ver- tical location of the spring attachment with a micro- meter screw. Thermal effects are removed by a Gravity Surveying 127

    tidal currents, the survey ship needs to be anchored to keep it on station while the gravimeter is on the Gravity measurements can be made continuously at sea using a gravimeter modi?ed for use on ships. Such instruments are known as shipborne, or shipboard, meters.The accuracy of measurements with a shipborne meter is considerably reduced compared to measure- ments on land because of the severe vertical and hori- zontal accelerations imposed on the shipborne meter by sea waves and the ship’s motion.These external accelera- tions can cause variations in measured gravity of up to 106 gu and represent high-amplitude noise from which a signal of much smaller gravity variations must be ex- tracted.The effects of horizontal accelerations produced by waves, yawing of the ship and changes in its speed and heading can be largely eliminated by mounting the meter on a gyrostabilized, horizontal platform, so that the meter only responds to vertical accelerations. Devia- tions of the platform from the horizontal produce off- levelling errors which are normally less than 10 gu. Exter- nal vertical accelerations resulting from wave motions cannot be distinguished from gravity but their effect can be diminished by heavily damping the suspension system and by averaging the reading over an interval consider- ably longer than the maximum period of the wave mo- tions (about 8 s). As the ship oscillates vertically above and below the plane of the mean sea surface, the wave accelerations are equally negative and positive and are The operation is essentially low-pass ?ltering in which accelerations with periods of less than 1–5 min are With shipborne meters employing a beam-supported sensor, such as the LaCoste and Romberg instrument, a further complication arises due to the in?uence of hori- zontal accelerations. The beam of the meter oscillates under the in?uence of the varying vertical accelerations caused by the ship’s motions.When the beam is tilted out of the horizontal it will be further displaced by the turn- For certain phase relationships between the vertical and horizontal components of motion of the ship, the hori- zontal accelerations may cause beam displacements that do not average out with time. Consider an example where the position of a meter in space describes a circu- lar motion under the in?uence of sea waves (Fig. 6.3). At time t , as shown in Fig. 6.3, the ship is moving down, 1 displacing the beam upwards, and the horizontal com- ponent of motion is to the right, inducing an anticlock- t 2

    DC current Servo loop Permanent magnet Coil Induced magnetic field Permanent magnetic field

    Permanent magnet Fig. 6.4 Principle of the accelerometer unit of the Bell marine gravimeter. (After Bell &Watts 1986.)

    proportional to the square root of gravity. Changes in Gravimeters based on this mechanism have never found much favour because of relatively low reported accura- The most successful axially symmetric instrument to date is the Bell gravimeter (Bell &Watts 1986).The sensing 6.4 which is mounted on a stable platform. The ac- celerometer, which is about 34 mm high and 23 mm in diameter, consists of a mass, wrapped in a coil, which is constrained to move only vertically between two per- manent magnets. A DC current passed through the coil causes the mass to act as a magnet. In the null position, the weight of the mass is balanced by the forces exerted by the permanent magnets. When the mass moves ver- tically in response to a change in gravity or wave acceler- ations, the motion is detected by a servo loop which regulates the current in the coil, changing its magnetic moment so that it is driven back to the null position.The varying current is then a measure of changes in the verti- cal accelerations experienced by the sensor. As with beam-type meters, a weighted average ?lter is applied to the output in order to separate gravity changes from Drift rates of the Bell gravimeter are low and uniform, and it has been demonstrated that the instrument is accurate to just a few gravity units, and is capable of This accuracy and resolution is considerably greater than that of earlier instruments, and it is anticipated that much smaller gravity anomalies will be detected than was Gravity Surveying 129

    previously possible. The factor preventing more wide- The measurement of gravity from aircraft is complex because of the large possible errors in applying correc- tions. Eötvös corrections (Section 6.8.5) may be as great as 16 000 gu at a speed of 200 knots, a 1% error in veloc- ity or heading producing maximum errors of 180 gu and 250 gu, respectively. Vertical accelerations associated with the aircraft’s motion with periods longer than the instrumental averaging time cannot readily be cor- rected. In spite of these dif?culties, tests undertaken in small aircraft (Halpenny & Darbha 1995) equipped with radar altimeters and GPS navigation have achieved re- sults which differ from those obtained with underwater meters by an average of -2 gu and standard deviation 27 gu. Bell et al. (1999) describe a more modern set-up for airborne gravity surveying, which is now in use commercially. A system is also available for use with a helicopter (Seigel & McConnell 1998) in which the gravimeter is lowered to the ground by a cable, levelled and read remotely, so that measurements can be made The calibration constants of gravimeters may vary with time and should be checked periodically.The most common procedure is to take readings at two or more locations where absolute or relative values of gravity are known. In calibrating Worden-type meters, these read- ings would be taken for several settings of the coarse ad- justing screw so that the calibration constant is checked over as much of the full range of the instrument as possible. Such a procedure cannot be adopted for the LaCoste and Romberg gravimeter, where each different dial range has its own calibration constant. In this case checking can be accomplished by taking readings at different inclinations of the gravimeter on a tilt table, a task usually entrusted to the instrument’s manufacturer.

    ?gx ?gx ?g

    + ? g + ?g g

    ?g z g + ?g z Fig. 6.5 Relationship between the gravitational ?eld and the components of the gravity anomaly of a small mass.

    (( 2 2 ) g + dg = g + dg ) + dg zx ( 2 2 2) = g + 2 gdg + dg + dg zzx

    Terms in d 2 are insigni?cantly small and can thus be ignored. Binomial expansion of the equation then gives g + dg ª g + dg z

    6 0 1 km so that dg ª dg z Consequently, measured perturbations in gravity effec- tively correspond to the vertical component of the attraction of the causative body. The local de?ection of the vertical q is given by

    q = tan -1Ê dg ^ x (6.5) Ëg¯

    and since dg < g, q is usually insigni?cant. Very large z mass anomalies such as mountain ranges can, however, produce measurable local vertical de?ections.

    6.6 Gravity anomalies of simple-shaped bodies Consider the gravitational attraction of a point mass m at a distance r from the mass (Fig. 6.6). The gravitational attraction Dg in the direction of the mass is given by r

    Gm r r2 Since only the vertical component of the attraction Dg is z measured, the gravity anomaly Dg caused by the mass is Gm Dg = cos q r2 Gravity anomaly (gu) 0 x 0 ? km zr ?g r ?g 1z m Fig. 6.6 The gravity anomaly of a point =1000kg mass or sphere.

    Plan x 8 x zr Section m or Gmz Dg = (6.6) r3

    Since a sphere acts as though its mass were concentrated at its centre, equation (6.6) also corresponds to the grav- Equation (6.6) can be used to build up the gravity anomaly of many simple geometric shapes by construct- ing them from a suite of small elements which corre- spond to point masses, and then summing (integrating) the attractions of these elements to derive the anomaly of Integration of equation (6.6) in a horizontal direction provides the equation for a line mass (Fig. 6.7) extending to in?nity in this direction 2Gmz Dg = (6.7) r2

    Equation (6.7) also represents the anomaly of a horizon- tal cylinder, whose mass acts as though it is concentrated Integration in the second horizontal direction pro- vides the gravity anomaly of an in?nite horizontal sheet, and a further integration in the vertical direction be- tween ?xed limits provides the anomaly of an in?nite horizontal slab Gravity Surveying 131

    y (x, y, z) ? x r ? ?g = ?g z ?y’ ?x’ ?z’ ( x’, y’, z’) z

    Fig. 6.8 The gravity anomaly of an element of a mass of Dg = 2pGrt (6.8) where r is the density of the slab and t its thickness. Note that this attraction is independent of both the location A similar series of integrations, this time between ?xed limits, can be used to determine the anomaly of a In general, the gravity anomaly of a body of any shape can be determined by summing the attractions of all the mass elements which make up the body. Consider a small prismatic element of such a body of density r, located at x¢, y¢, z¢, with sides of length dx¢, dy¢, dz¢ (Fig. 6.8). The mass dm of this element is given by dm = r dx¢ d y¢ dz¢

    The anomaly of the whole body Dg is then found by summing all such elements which make up the body (z¢ – z) Dg = SSSGr dx¢dy¢dz¢ (6.9) r3

    If dx¢, dy¢ and dz¢ are allowed to approach zero, then (z¢ – z) Dg = Ú Ú ÚGr dx¢ dy¢ dz¢ (6.10) r3

    where 222 r=(x¢-x)+(y¢-y)+(z¢-z) As shown before, the attraction of bodies of regular geometry can be determined by integrating equation (6.10) analytically. The anomalies of irregularly shaped bodies are calculated by numerical integration using equations of the form of equation (6.9).

    6.7 Gravity surveying ?g 3 Gravimeter reading ?g 1 ?g 2 X X ?g4 X

    Time Fig. 6.9 The principle of looping. Crosses and circles represent alternate gravimeter readings taken at two base stations.The verti- cal separations between the drift curves for the two stations (Dg ) 1–4 provide an estimate of the gravity difference between them.

    set at a known elevation and a mobile ?eld set, can pro- 6.8 Gravity reduction Before the results of a gravity survey can be interpreted it is necessary to correct for all variations in the Earth’s gravitational ?eld which do not result from the differ- ences of density in the underlying rocks. This process is known as gravity reduction (LaFehr 1991) or reduction to the geoid, as sea-level is usually the most convenient datum level.

    6.8.1 Drift correction Correction for instrumental drift is based on repeated readings at a base station at recorded times through- out the day. The meter reading is plotted against time Gravimeter reading d

    t Time Fig. 6.10 A gravimeter drift curve constructed from repeated readings at a ?xed location.The drift correction to be subtracted for a reading taken at time t is d.

    (a) Fig. 6.11 (a)The variation in angular velocity with latitude around the Earth represented by vectors whose lengths are proportional to angular velocity. (b) An exaggerated representation of the shape of the Earth.The true shape of this oblate ellipsoid of revolution results in a difference in equatorial and polar radii of some 21 km.

    Gravity Surveying 133 (Fig. 6.10) and drift is assumed to be linear between consecutive base readings. The drift correction at time After drift correction the difference in gravity be- tween an observation point and the base is found by multiplication of the difference in meter reading by the calibration factor of the gravimeter. Knowing this differ- ence in gravity, the absolute gravity at the observation point g can be computed from the known value of obs gravity at the base. Alternatively, readings can be related to an arbitrary datum, but this practice is not desirable as the results from different surveys cannot then be tied together.

    6.8.2 Latitude correction Gravity varies with latitude because of the non-spherical shape of the Earth and because the angular velocity of a point on the Earth’s surface decreases from a maximum at the equator to zero at the poles (Fig. 6.11(a)).The cen- tripetal acceleration generated by this rotation has a negative radial component that consequently causes gravity to decrease from pole to equator.The true shape of the Earth is an oblate spheroid or polar ?attened ellip- soid (Fig. 6.11(b)) whose difference in equatorial and polar radii is some 21 km. Consequently, points near the equator are farther from the centre of mass of the Earth than those near the poles, causing gravity to increase from the equator to the poles. The amplitude of this ef- fect is reduced by the differing subsurface mass distribu- tions resulting from the equatorial bulge, the mass underlying equatorial regions being greater than that The net effect of these various factors is that gravity at

    the poles exceeds gravity at the equator by some 51 860 gu, with the north–south gravity gradient at Clairaut’s formula relates gravity to latitude on the ref- erence spheroid according to an equation of the form g=g(1+ksin2f-ksin22f) (6.11) f012

    where g is the predicted value of gravity at latitude f, g f0 is the value of gravity at the equator and k , k are con- 12 stants dependent on the shape and speed of rotation of the Earth. Equation (6.11) is, in fact, an approximation of an in?nite series.The values of g , k and k in current 01 2 use de?ne the International Gravity Formula 1967 012 IAG 1971). Prior to 1967 less accurate constants were Results deduced using the earlier formula must be mod- i?ed before incorporation into survey data reduced using the Gravity Formula 1967 by using the relation- ff An alternative, more accurate, representation of the Gravity Formula 1967 (Mittermayer 1969), in which the constants are adjusted so as to minimize errors resulting from the truncation of the series, is g = 9 780 318.5 (1 + 0.005278895 sin2 f f +0.000023462sin4f)gu This form, however, is less suitable if the survey results are to incorporate pre-1967 data made compatible with The value g gives the predicted value of gravity at f sea-level at any point on the Earth’s surface and is sub- tracted from the observed gravity to correct for latitude variation.

    6.8.3 Elevation corrections Correction for the differing elevations of gravity stations is made in three parts.The free-air correction (FAC) cor-

    (a) (b) rects for the decrease in gravity with height in free air resulting from increased distance from the centre of the Earth, according to Newton’s Law. To reduce to datum an observation taken at height h (Fig. 6.12(a)), FAC = 3.086h gu (h in metres) The FAC is positive for an observation point above datum to correct for the decrease in gravity with The free-air correction accounts solely for variation in the distance of the observation point from the centre of the Earth; no account is taken of the gravitational effect of the rock present between the observation point and datum. The Bouguer correction (BC) removes this effect by approximating the rock layer beneath the observation point to an in?nite horizontal slab with a thickness equal to the elevation of the observation above datum (Fig. 6.12(b)). If r is the density of the rock, from equation (6.8) BC = 2pGrh = 0.4191rh gu (h in metres, r in Mg m-3)

    On land the Bouguer correction must be subtracted, as the gravitational attraction of the rock between obser- vation point and datum must be removed from the observed gravity value. The Bouguer correction of sea surface observations is positive to account for the lack of rock between surface and sea bed. The correction is equivalent to the replacement of the water layer by material of a speci?ed rock density r . In this case r

    BC = 2pG (r – r )z rw w The free-air and Bouguer corrections are often ap- The Bouguer correction makes the assumption that the topography around the gravity station is ?at. This is

    (c) B hhAA Datum Fig. 6.12 (a)The free-air correction for an observation at a height h above datum. (b)The Bouguer correction.The shaded region corresponds to a slab of rock of thickness h extending to in?nity in both horizontal directions. (c)The terrain correction.

    rarely the case and a further correction, the terrain correc- tion (TC), must be made to account for topographic re- lief in the vicinity of the gravity station. This correction is always positive as may be appreciated from considera- tion of Fig. 6.12(c). The regions designated A form part of the Bouguer correction slab although they do not consist of rock. Consequently, the Bouguer correction has overcorrected for these areas and their effect must be

    J I H G F Fig. 6.13 A typical graticule used in the calculation of terrain corrections. A series of such graticules with zones varying in radius from 2 m to 21.9 km is used with topographic maps of varying scale.

    Gravity Surveying 135 restored by a positive terrain correction. Region B consists of rock material that has been excluded from the Bouguer correction. It exerts an upward attraction at the observation point causing gravity to decrease. Its attraction must thus be corrected by a positive terrain Classically, terrain corrections are applied using a cir- cular graticule known, after its inventor, as a Hammer chart (Fig. 6.13), divided by radial and concentric lines into a large number of compartments. The outermost zone extends to almost 22 km, beyond which topo- graphic effects are usually negligible.The graticule is laid on a topographic map with its centre on the gravity sta- tion and the average topographic elevation of each com- partment is determined. The elevation of the gravity station is subtracted from these values, and the gravita- tional effect of each compartment is determined by ref- erence to tables constructed using the formula for the gravitational effect of a sector of a vertical cylinder at its axis. The terrain correction is then computed by sum- ming the gravitational contribution of all compart- Such operations are time consuming as the topography of over 130 compartments has to be averaged for each station, but terrain correction is the one operation Labour can be reduced by averaging topography within a rectangular grid. Only a single digitization is required as the topographic effects may be calculated at any point within the grid by summing the effects of the right rec- tangular prisms de?ned by the grid squares and their ele- vation difference with the gravity station.This operation can effectively correct for the topography of areas distant

    Zone r r n Zone r r n 12 12 B 2.0 16.6 4 H 1 529.4 2 614.4 12 C 16.6 53.3 6 I 2 614.4 4 468.8 12 D 53.3 170.1 6 J 4 468.8 6 652.2 16 E 170.1 390.1 8 K 6 652.2 9 902.5 16 F 390.1 894.8 8 L 9 902.5 14 740.9 16 G 894.8 1529.4 12 M 14 740.9 21 943.3 16

    r T=0.4191(r-r+r2+z2-r2+z2) 211 2 n where T = terrain correction of compartment (gu); r = Bouguer correction density (Mg m-3); n = number of compartments in zone; r = inner radius of zone (m); r = outer 12 radius of zone (m); and z = modulus of elevation difference between observation point and mean elevation of compartment (m).

    from the gravity station and can be readily comput- erized. Such an approach is likely to be increasingly adopted as digital elevation models for large regions be- come available (Cogbill 1990). Correction for inner zones, however, must still be performed manually as any reasonable digitization scheme for a complete survey area and its environs must employ a sampling interval that is too large to provide an accurate representation of Terrain effects are low in areas of subdued topography, rarely exceeding 10 gu in ?at-lying areas. In areas of rugged topography terrain effects are considerably greater, being at a maximum in steep-sided valleys, at the Where terrain effects are considerably less than the desired accuracy of a survey, the terrain correction may be ignored. Sprenke (1989) provides a means of assessing However, the usual necessity for this correction accounts for the bulk of time spent on gravity reduction and is thus a major contributor to the cost of a gravity survey.

    6.8.4 Tidal correction Gravity measured at a ?xed location varies with time be- cause of periodic variation in the gravitational effects of the Sun and Moon associated with their orbital motions, and correction must be made for this variation in a high- precision survey. In spite of its much smaller mass, the gravitational attraction of the Moon is larger than that of the Sun because of its proximity. Also, these gravita- tional effects cause the shape of the solid Earth to vary in much the same way that the celestial attractions cause tides in the sea. These solid Earth tides are considerably smaller than oceanic tides and lag farther behind the lunar motion.They cause the elevation of an observation point to be altered by a few centimetres and thus vary its distance from the centre of mass of the Earth. The peri- odic gravity variations caused by the combined effects of Sun and Moon are known as tidal variations. They have a maximum amplitude of some 3 gu and a minimum If a gravimeter with a relatively high drift rate is used, base ties are made at an interval much smaller than the minimum Earth tide period and the tidal variations are automatically removed during the drift correction. If a meter with a low drift rate is employed, base ties are nor- mally made only at the start and end of the day so that the tidal variation has undergone a full cycle. In such a case, a separate tidal correction may need to be made.The tidal effects are predictable and can be computed by a small computer program.

    6.8.5 Eötvös correction The Eötvös correction (EC) is applied to gravity mea- surements taken on a moving vehicle such as a ship or an aircraft. Depending on the direction of travel, vehicular motion will generate a centripetal acceleration which either reinforces or opposes gravity. The correction required is EC = 75.03V sin a cos f + 0.04154V 2 gu

    where V is the speed of the vehicle in knots, a the head- ing and f the latitude of the observation. In mid- latitudes the Eötvös correction is about +75 gu for each knot of E to W motion so that speed and heading must be accurately known.

    6.8.6 Free-air and Bouguer anomalies The free-air anomaly (FAA) and Bouguer anomaly (BA) may now be de?ned FAA = g – g + FAC (± EC) (6.12) obs f

    BA = g – g + FAC ± BC + TC (± EC) (6.13) obs f

    pro?les or as contoured (isogal) maps. Interpretation of the latter may be facilitated by utilizing digital image processing techniques similar to those used in the display of remotely sensed data. In particular, colour and shaded relief images may reveal structural features that may not This type of processing is equally appropriate to mag- 1990).

    6.9 Rock densities Gravity anomalies result from the difference in density, or density contrast, between a body of rock and its surroundings. For a body of density r embedded in 1 material of density r , the density contrast Dr is given by 2 Dr = r – r 12 The sign of the density contrast determines the sign of Rock densities are among the least variable of all geo- physical parameters. Most common rock types have The density of a rock is dependent on both its mineral Variation in porosity is the main cause of density variation in sedimentary rocks. Thus, in sedimentary rock sequences, density tends to increase with depth, due to compaction, and with age, due to progressive Most igneous and metamorphic rocks have negligible porosity, and composition is the main cause of density variation. Density generally increases as acidity decreas- es; thus there is a progression of density increase from acid through basic to ultrabasic igneous rock types. Den- sity ranges for common rock types and ores are present- A knowledge of rock density is necessary both for ap- plication of the Bouguer and terrain corrections and for Density is commonly determined by direct measure- ments on rock samples. A sample is weighed in air and in water. The difference in weights provides the volume of the sample and so the dry density can be obtained. If the rock is porous the saturated density may be calculated by following the above procedure after saturating the rock with water. The density value employed in interpreta- tion then depends upon the location of the rock above or below the water table.

    Gravity Surveying 137 Table 6.2 Approximate density ranges (Mg m-3) of some common rock types and ores.

    Alluvium (wet) 1.96–2.00 Clay 1.63–2.60 Shale 2.06–2.66 Sandstone Cretaceous 2.05–2.35 Triassic 2.25–2.30 Carboniferous 2.35–2.55 Limestone 2.60–2.80 Chalk 1.94–2.23 Dolomite 2.28–2.90 Halite 2.10–2.40 Granite 2.52–2.75 Granodiorite 2.67–2.79 Anorthosite 2.61–2.75 Basalt 2.70–3.20 Gabbro 2.85–3.12 Gneiss 2.61–2.99 Quartzite 2.60–2.70 Amphibolite 2.79–3.14 Chromite 4.30–4.60 Pyrrhotite 4.50–4.80 Magnetite 4.90–5.20 Pyrite 4.90–5.20 Cassiterite 6.80–7.10 Galena 7.40–7.60 NB. The lower end of the density range quoted in many texts is often unreasonably extended by measurements made on samples affected by physical or chemical weathering.

    obtained at the two levels, then, applying free-air and Bouguer corrections, one obtains g – g = 3.086h – 4pGrh (6.14) 12

    The Bouguer correction is double that employed on the surface as the slab of rock between the observation levels exerts both a downward attraction at the surface

    g 1 h ? g 2 Fig. 6.14 Density determination by subsurface gravity measurements.The measured gravity difference g – g over a 12 height difference h can be used to determine the mean density r of the rock separating the measurements.

    50 location and an upward attraction at the underground location. The density r of the medium separating the two observations can then be found from the difference in gravity. Density may also be measured in boreholes using a density (gamma–gamma) logger as discussed in Nettleton’s method of density determination involves taking gravity observations over a small isolated topo- graphic prominence. Field data are reduced using a series of different densities for the Bouguer and terrain correc- tions (Fig. 6.15).The density value that yields a Bouguer anomaly with the least correlation (positive or negative) with the topography is taken to represent the density of the prominence. The method is useful in that no bore- hole or mineshaft is required, and a mean density of the material forming the prominence is provided. A dis- advantage of the method is that isolated relief features may be formed of anomalous materials which are not Density information is also provided from the P-wave Figure 6.16 shows graphs of the logarithm of P-wave velocity against density for various rock types (Gardner et al. 1974), and the best-?tting linear relationship. Other

    Bulk density, ? (Mg m–3) 1.8 2.0 2.2 2.4 2.6 2.8 3.0 9.0 0.9 7.5 0.8 6.0 0.7 –1 ) 4.5 0.6 Log V 0.5 3.5 3.0 0.42.5 P-wave velocity, V (km s 0.3 1.8 0.2 1.5 0.1 Limestone

    Dolomite Rock salt Anhydrite Time average (sandstone) Sandstone Shale

    ? = 1.74V 0.25 0.2 0.3 0.4 0.5 Log ?

    Fig. 6.16 Graphs of the logarithm of P-wave velocity against density for various rock types. Also shown is the best-?tting linear 1974).

    workers (e.g. Birch 1960, 1961, Christensen & Fountain 1975) have derived similar relationships. The empirical velocity–density curve of Nafe and Drake (1963) indi- cates that densities estimated from seismic velocities are This, however, is the only method available for the esti- mation of densities of deeply buried rock units that cannot be sampled directly.

    6.10 Interpretation of gravity anomalies 6.10.1 The inverse problem The interpretation of potential ?eld anomalies (gravity, magnetic and electrical) is inherently ambiguous. The ambiguity arises because any given anomaly could be caused by an in?nite number of possible sources. For ex- ample, concentric spheres of constant mass but differing density and radius would all produce the same anomaly, since their mass acts as though located at the centre of the + Bouguer anomaly 0

    – Gravity Surveying 139 Estimated regional field Observed gravity

    Distance Residual gravity anomaly Fig. 6.17 The separation of regional and residual gravity anom- alies from the observed Bouguer anomaly.

    sphere. This ambiguity represents the inverse problem of potential ?eld interpretation, which states that, although the anomaly of a given body may be calculated uniquely, there are an in?nite number of bodies that could give rise to any speci?ed anomaly. An important task in inter- pretation is to decrease this ambiguity by using all available external constraints on the nature and form of the anomalous body. Such constraints include geological information derived from surface outcrops, boreholes and mines, and from other, complementary, geophysical techniques (see e.g. Lines et al. 1988).

    subtracted from the observed data due to the mathemat- It is necessary before carrying out interpretation to differentiate between two-dimensional and three- dimensional anomalies. Two-dimensional anomalies are elongated in one horizontal direction so that the anom- aly length in this direction is at least twice the anomaly width. Such anomalies may be interpreted in terms of structures which theoretically extend to in?nity in the elongate direction by using pro?les at right angles to the strike. Three-dimensional anomalies may have any shape and are considerably more dif?cult to interpret Gravity interpretation proceeds via the methods of direct and indirect interpretation.

    6.10.3 Direct interpretation Direct interpretation provides, directly from the gravity anomalies, information on the anomalous body which is largely independent of the true shape of the body.Vari- ous methods are discussed below.

    Limiting depth Limiting depth refers to the maximum depth at which the top of a body could lie and still produce an observed gravity anomaly. Gravity anomalies decay with the inverse square of the distance from their source so that anomalies caused by deep structures are of lower ampli-

    A A max A max 2 x 1/2 A’ max tude and greater extent than those caused by shallow sources. This wavenumber–amplitude relationship to depth may be quanti?ed to compute the maximum depth (or limiting depth) at which the top of the anoma- lous body could be situated.

    (a) Half-width method. The half-width of an anomaly (x ) is the horizontal distance from the anomaly maxi- 1/2 mum to the point at which the anomaly has reduced to If the anomaly is three-dimensional, the initial Manipulation of the point mass formula (equation (6.6)) allows its depth to be determined in terms of the half-width

    x 12 z= 3 4 -1 Here, z represents the actual depth of the point mass or the centre of a sphere with the same mass. It is an over- estimate of the depth to the top of the sphere, that is, the limiting depth. Consequently, the limiting depth for any three-dimensional body is given by

    x 12 z < (6.15) 3 4 -1

    A similar approach is adopted for a two-dimensional anomaly, with the initial assumption that the anomaly

    Fig. 6.18 Limiting depth calculations using (a) the half-width method and x (a) (b) (b) the gradient–amplitude ratio.

    results from a horizontal line mass (equation (6.7)). The depth to a line mass or to the centre of a horizontal cylin- der with the same mass distribution is given by z=x 12

    For any two-dimensional body, the limiting depth is then given by z < x (6.16) 12

    (b) Gradient–amplitude ratio method. This method re- quires the computation of the maximum anomaly am- plitude (A ) and the maximum horizontal gravity max gradient (A¢ ) (Fig. 6.18(b)). Again the initial assump- max tion is made that a three-dimensional anomaly is caused by a point mass and a two-dimensional anomaly by a line mass. By differentiation of the relevant formulae, for any three-dimensional body

    z < 0.86 A max(6.17) A¢ max and for any two-dimensional body

    z < 0.65 A max(6.18) A¢ max (c) Second derivative methods. There are a number of limiting depth methods based on the computation of the maximum second horizontal derivative, or maxi- mum rate of change of gradient, of a gravity anomaly (Smith 1959). Such methods provide rather more accu- rate limiting depth estimates than either the half-width or gradient–amplitude ratio methods if the observed anomaly is free from noise.

    Excess mass The excess mass of a body can be uniquely determined from its gravity anomaly without making any assump- tions about its shape, depth or density. Excess mass refers to the difference in mass between the body and the mass of country rock that would otherwise ?ll the space oc- cupied by the body. The basis of this calculation is a for- mula derived from Gauss’ theorem, and it involves a surface integration of the residual anomaly over the area in which it occurs.The survey area is divided into n grid squares of area Da and the mean residual anomaly Dg found for each square. The excess mass M is then given e Gravity Surveying 141

    by n 1 M = Â Dg Da (6.19) e ii 2pG i =1

    Before using this procedure it is important that the re- The method only works well for isolated anomalies whose extremities are well de?ned. Gravity anomalies decay slowly with distance from source and so these tails can cover a wide area and be important contributors to To compute the actual mass M of the body, the densi- ties of both anomalous body (r ) and country rock (r ) 12 must be known:

    rM M= 1 e (6.20) (r – r ) 12 The method is of use in estimating the tonnage of ore bodies. It has also been used, for example, in the estima- tion of the mass de?ciency associated with the Chicxu- lub crater,Yucatan (CamposEnriquez et al. 1998), whose formation due to meteorite or asteroid impact has been associated with the extinction of the dinosaurs.

    In?ection point positions where the horizontal gravity gradient changes most rapidly, can provide useful information on the na- ture of the edge of an anomalous body. Over structures with outward dipping contacts, such as granite bodies (Fig. 6.19(a)), the in?ection points (arrowed) lie near the base of the anomaly. Over structures with inward dip- ping contacts such as sedimentary basins (Fig. 6.19(b)), the in?ection points lie near the uppermost edge of the anomaly.

    Approximate thickness If the density contrast Dr of an anomalous body is known, its thickness t may be crudely estimated from its maximum gravity anomaly Dg by making use of the Bouguer slab formula (equation (6.8)):

    Distance Bouguer anomaly dg dx Depth Distance Bouguer anomaly dg dx Depth Fig. 6.19 Bouguer anomaly pro?les across (a) a granite body, and (b) a sedimentary basin.The in?ection points are marked with an arrow.The broken lines represent the horizontal derivative (rate of change of gradient) of the gravity anomaly, which is at a maximum at the in?ection points.

    This thickness will always be an underestimate for a body of restricted horizontal extent.The method is common- ly used in estimating the throw of a fault from the dif- ference in the gravity ?elds of the upthrown and The technique of source depth determination by Euler deconvolution, described in Section 7.10.2, is also applicable to gravity anomalies (Keating 1998).

    Gravity Surveying 143 (a) 125 124 123 122 (b) 70 1200 0 800 Darnley 0 Bay Bouguer anomaly (gu) Observed + + I + II + anomaly + + Computed + + anomaly ++ 400++

    0 AB ++ ++ + 0 km 40 + +++++ + ++++ AB 0 1000 69 500 20 km Model I (?? = 0.30 Mg m–3)40 0 km 25 0 0 250 km 20 Model II (?? = 0.50 Mg m–3)

    Fig. 6.20 (a)The circular gravity anomaly at Darnley Bay, NWT, Canada. Contour interval 250 gu. (b)Two possible interpretations of the anomaly in terms of a model constructed from a suite of coaxial vertical cylinders. (After Stacey 1971.)

    x (0, 0) ? 1 z r 1 (x , z ) ? 11 2 r 2 ?? 8 ?

    (x , z ) 22 Fig. 6.21 Parameters used in de?ning the gravity anomaly of a semi-in?nite slab with a sloping edge.

    Dg = 2GDr[-{x sinq + z cosq} 11 ¥{sinqlog(rr)+cosq(f-f)} e21 2 1 + z f – z f ] (6.22) 22 11

    where Dr is the density contrast of the slab, angles are ex- pressed in radians and other parameters are de?ned as in Fig. 6.21 (Talwani et al. 1959). To calculate the anomaly of a two-dimensional body of irregular cross-section, the The anomaly of the polygon is then found by pro- ceeding around it summing the anomalies of the slabs bounded by edges where the depth increases and subtracting those where the depth decreases.

    + – + – + Fig. 6.22 The computation of gravity anomalies of two- dimensional bodies of irregular cross-section.The body (dashed line) is approximated by a polygon and the effects of semi-in?nite slabs with sloping edges de?ned by the sides of the polygon are progressively added and subtracted until the anomaly of the polygon is obtained.

    0 –100 Observed Calculated –200 –300 Residual anomaly (gu) –400

    –500 10 km A South North A’ –0.10 12 km –0.16 Mg m–3 –0.13

    Fig. 6.23 A two-dimensional interpretation of the gravity anomaly of the Bodmin Moor granite, southwest England. See Fig. 6.27 for location. (After Bott & Scott 1964.)

    northerly increase in the density of the granite; a possible alternative, however, would be a northerly thinning of a Two-dimensional methods can sometimes be extend- ed to three-dimensional bodies by applying end-correc- tion factors to account for the restricted extent of the causative body in the strike direction (Cady 1980). The end-correction factors are, however, only approxima- The gravity anomaly of a three-dimensional body may be calculated by dividing the body into a series of horizontal slices and approximating each slice by a poly- gon (Talwani & Ewing 1960). Alternatively the body may be constructed out of a suite of right rectangular However a model calculation is performed, indirect interpretation involves four steps: 4. Alteration of model to improve correspondence of The process is thus iterative and the goodness of ?t be- tween observed and calculated anomalies is gradually improved. Step 4 can be performed manually for bodies of relatively simple geometry so that an interpretation is readily accomplished using interactive routines on a personal computer (Götze & Lahmeyer 1988). Bodies of complex geometry in two- or three-dimensions are not so simply dealt with and in such cases it is advantageous to employ techniques which perform the iteration The most ?exible of such methods is non-linear opti- mization (Al-Chalabi 1972). All variables (body points, density contrasts, regional ?eld) may be allowed to vary within de?ned limits. The method then attempts to minimize some function F which de?nes the goodness of ?t, for example

    n F = Â (Dg – Dg )2 obs calc ii i =1 where Dg and Dg are series of n observed and calcu- obs calc The minimization proceeds by altering the values of the variables within their stated limits to produce a successively smaller value for F for each iteration. The technique is elegant and successful but expensive in Other such automatic techniques involve the simu- lation of the observed pro?le by a thin layer of variable density. This equivalent layer is then progressively ex- panded so that the whole body is of a uniform, speci?ed density contrast. The body then has the form of a series of vertical prisms in either two or three dimensions which extend either above, below or symmetrically around the original equivalent layer. Such methods are less ?exible than the non-linear optimization technique in that usually only a single density contrast may be speci?ed and the model produced must either have a speci?ed base or top or be symmetrical about a central horizontal plane.

    where A refers to a gravitational or magnetic ?eld and is In the case of a two-dimensional ?eld there is no varia- tion along one of the horizontal directions so that A is a function of x and z only and equation (6.23) simpli?es to

    ?2A ?2A + = 0 (6.24) ? x2 ? z2 Solution of this partial differential equation is easily per- formed by separation of variables

    Ak(x,z)=(acoskx+bsinkx)ekz (6.25) where a and b are constants, the positive variable k is the spatial frequency or wavenumber, A is the potential k ?eld amplitude corresponding to that wavenumber and z is the level of observation. Equation (6.25) shows that a potential ?eld can be represented in terms of sine and co- sine waves whose amplitude is controlled exponentially Consider the simplest possible case where the two- dimensional anomaly measured at the surface A(x, 0) is a sine wave A(x, 0) = A sin kx (6.26) 0

    where A is a constant and k the wavenumber of the sine 0 wave. Equation (6.25) enables the general form of the equation to be stated for any value of z

    A(x,z)=(A0sinkx)ekz (6.27)

    The ?eld at a height h above the surface can then be determined by substitution in equation (6.27) A(x, -h) = (A sin kx)e-kh (6.28) 0

    and the ?eld at depth d below the surface A(x,d) = (A sin kx)ekd (6.29) 0

    The sign of h and d is important as the z-axis is normally Equation (6.27) is an over-simpli?cation in that a Invariably such a ?eld is composed of a range of wavenumbers. However, the technique is still valid as long as the ?eld can be expressed in terms of all its com- ponent wavenumbers, a task easily performed by use of Gravity Surveying 145

    (a) (a) –750 –800 – 600 –750 –750 –700 –650 –600 –550 –500 –450 –400 –350 –700 –750 –450 –550 –500 –550 –350 –300 –350 0 50 km

    (b) (b) –700 –650 –600 –550 –500 –450 –400 Fig. 6.24 (a) Observed Bouguer anomalies (gu) over the Saguenay area, Quebec, Canada. (b)The gravity ?eld continued upward to an elevation of 16 km. (After Duncan & Garland 1977.)

    application of wavenumber ?lters. Gravitational and mag- netic ?elds may be processed and analysed in a similar fashion to seismic data, replacing frequency by wavenumber. Such processing is more complex than the equivalent seismic ?ltering as potential ?eld data are generally arranged in two horizontal dimensions, that is, contour maps, rather than a single dimension. However, it is possible to devise two-dimensional ?lters for the se- lective removal of high- or low-wavenumber compo- nents from the observed anomalies.The consequence of the application of such techniques is similar to upward or downward continuation in that shallow structures are mainly responsible for the high-wavenumber compo- nents of anomalies and deep structures for the low wavenumbers. However, it is not possible fully to isolate local or regional anomalies by wavenumber ?ltering be- cause the wavenumber spectra of deep and shallow Other manipulations of potential ?elds may be ac- complished by the use of more complex ?lter operators (e.g. Gunn 1975, Cooper 1997). Vertical or horizontal derivatives of any order may be computed from the observed ?eld. Such computations are not widely employed, but second horizontal derivative maps are occasionally used for interpretation as they accentuate anomalies associated with shallow bodies.

    Gravity Surveying 147 gu 1000 Free-air anomaly 0 –1000 Ridge crest

    0 Crust Low density zone 40Mantle 80 km 0 1000 km

    Fig. 6.25 Free-air anomaly pro?le across the mid-Atlantic ridge. (AfterTalwani et al. 1965.)

    6.12 Applications of gravity surveying Gravity studies are used extensively in the investiga- tion of large- and medium-scale geological structures (Paterson & Reeves 1985). Early marine surveys, per- formed from submarines, indicated the existence of large positive and negative gravity anomalies associated with island arcs and oceanic trenches, respectively; sub- sequent shipborne work has demonstrated their lateral continuity and has shown that most of the major features of the Earth’s surface can be delineated by gravity sur- veying. Gravity anomalies have also shown that most of these major relief features are in isostatic equilibrium, suggesting that the lithosphere is not capable of sustain- ing signi?cant loads and yields isostatically to any change in surface loading. Figure 6.25 shows the near-zero free- air anomalies over an ocean ridge which suggest that it is in isostatic equilibrium. The gravity interpretation, which is constrained by seismic refraction results, indi- cates that this compensation takes the form of a zone of mass de?ciency in the underlying mantle. Its low seismic velocity and the high heat ?ow at the surface suggest that Gravity surveying can also be used in the study of ancient suture zones, which are interpreted as the sites of former These zones are often characterized by major linear gravity anomalies resulting from the different crustal sections juxtaposed across the sutures (Fig. 6.26).

    0 –200 –600 Site of Observed 100 km Hudsonian trench

    Computed –1000 gu 0 km 50 Granite Dorset Thrust Labrador Trough Belt Fold Belt Zone

    Superior Churchill 0.12 0.14 0.10 0.12 0.08 0.12 Nain 0.08 –0.28 –0.26 –0.30 –0.40 –0.28 –0.32 –0.28 –0.32

    Fig. 6.26 Bouguer anomaly pro?le across a structural province boundary in the Canadian Shield. Density contrasts in Mg m-3. (After Thomas & Kearey 1980.)

    200 N A’ 200 100 Bodmin Moor 0 –100 –200 0 –100 –100 –100 – 200 0 Carnmenellis 0 100 100 0A 100 200 200 St. Austell Dartmoor Land’s End

    Granite 0 30 km Fig. 6.27 Bouguer anomaly map of southwest England, showing a linear belt of large negative anomalies associated Contour interval 50 gu. (After Bott & Scott 1964.)

    Gravity Surveying 149 70°00′ 25°20′ N 25°25′ 70°W 69°W Antofagasta 24° 0 50 km Chile

    25° Survey area Taltal Argentina 69°50′ 0 2 km 100 80 60 B’ A’ 40

    A Igneous and metamorphic rocks Alluvium Borehole Gravity station Contour interval 20 gu 40 60 B 80 140 100 120 Fig. 6.28 Geological map of an area nearTaltal, Chile, showing location of gravity stations and contoured Bouguer anomalies. (After Van Overmeeren 1975.)

    (a) 80 Bouguer anomaly (gu) 60 40 Observed anomaly 20 Calculated anomaly (?? = –0.50 Mg m–3)

    N 17 20 w r e o t o f m t e e r 20 17 17 14 i r n l a e p 20 23 i 23 r

    O i g 20 17 26 26 20 0 m 30 23 29 26 Fig. 6.30 Bouguer anomalies, uncorrected for topographic (After Arzi 1975.)

    method (see Section 5.4). The seismic control allowed a mean density of the highly variable valley-?ll deposits to be determined. On the basis of the geophysical results, two boreholes (Fig. 6.28) were sunk in the deepest parts of the valley ?ll and located groundwater ponded in the In engineering and geotechnical applications, gravity surveying is sometimes used in the location of subsurface voids.Void detection has been made possible by the de- velopment of microgravimetric techniques which can detect gravity changes as small as a microgal. Arzi (1975) described a microgravity survey of the proposed site of a cooling tower serving a nuclear power plant, where it was suspected that solution cavities might be present in the dolomitic bedrock. Measurements were made on a 15 m grid at points whose elevations had been deter- The soil thickness had been determined so that its effects could be computed and `stripped’ from the observations to remove gravity variations caused by undulating bedrock topography. The resulting Bouguer anomaly map is shown in Fig. 6.30. In the NE part of the site there are two minima near the proposed perimeter of the cool- ing tower, and subsequent drilling con?rmed that they originated from buried cavities. Remedial work entailed the injection of grouting material into the cavities. A check on the effectiveness of the grouting was provided by a repeat gravity survey which, by an excess mass calculation (Section 6.10.3), showed that the change in the gravity ?eld before and after grouting was caused by the replacement of voids by grouting material. Casten and Gram (1989) have described microgravity surveys performed underground to locate cavities which might Microgravity surveys also ?nd application in archaeo- logical investigations, where they may be used in the de- The technique has also been used to study the temporal An important recent development in gravity survey- ing is the design of portable instruments capable of mea- suring absolute gravity with high precision. Although the cost of such instruments is high it is possible that they will be used in the future to investigate large-scale mass movements in the Earth’s interior and small cyclic gra- vity variations associated with neotectonic phenomena Gravitational studies, both of the type described in this chapter and satellite observations, are important in geodesy, the study of the shape of the Earth. Gravity sur- veying also has military signi?cance, since the trajectory of a missile is affected by gravity variation along its ?ight path.

    Gravity Surveying 151 of the Worden gravimeter used on the survey is 3.792 gu per dial unit. Before, during and after the survey, readings (marked BS) were taken at a base station where the value of gravity is 9 811 442.2 gu. This was done in order to moni- tor instrumental drift and to allow the absolute value of gravity to be determined at each obser- vation point.

    Station Time Dist. (m) Elev. (m) Reading BS 0805 2934.2 1 0835 0 84.26 2946.3 2 0844 20 86.85 2941.0 3 0855 40 89.43 2935.7 4 0903 60 93.08 2930.4 1 0918 2946.5 BS 0940 2934.7 1 1009 2946.3 5 1024 80 100.37 2926.6 6 1033 100 100.91 2927.9 7 1044 120 103.22 2920.0 X 1053 140 107.35 2915.1 1 1111 2946.5 BS 1145 2935.2 1 1214 2946.2 9 1232 160 110.10 2911.5 10 1242 180 114.89 2907.2 11 1300 200 118.96 2904.0 1 1315 2946.3 BS 1350 2935.5

    (a) Perform a gravity reduction of the survey data Use a density of 2.70 Mg m-3 for the Bouguer (b) Draw a series of sections illustrating the variation in topography, observed gravity, free- air anomaly and Bouguer anomaly along the (c) What further information would be required before a full interpretation could be made of the 4. Two survey vessels with shipborne gravity meters are steaming at 6 knots in opposite direc- tions along an east–west course. If the difference in gravity read by the two meters is 635 gu as the 5. The gravity anomaly Dg of an in?nite horizon- tal slab of thickness t and density contrast Dr is given by Dg = 2pGDrt where the gravitational constant G is 6.67 ¥ (a) Scale this equation to provide Dg in gu when (b) This equation is used to provide a prelimi- nary estimate of the gravity anomaly of a body of speci?ed thickness. Using this equation, calcu- late the gravity anomaly of (i) a granite 12 km thick of density 2.67 Mg m-3; and (ii) a sandstone body 4 km thick of density 2.30 Mg m-3, where the density of the surrounding metamorphic rocks is 2.80 Mg m-3. Are the anomalies so calcu- 6. Show that the half-width of the gravity anom- aly caused by a horizontal cylinder is equal to the 7. Figure 6.31 is a Bouguer anomaly map, con- toured at an interval of 50 gu, of a drift-covered (a) On the map, sketch in what you consider to be the regional ?eld and then remove it from the observed ?eld to isolate residual anomalies,

    A 50 0 –50 –100 –150 –350 –300 –200 –250 –400 –450 –500 –550 –600 –700 –650 –650 –700 –750

    318 318 315 307 302 312 316 316 290 302 280 302 285 274 285 311 312 295 266 264 279 317 318 307 259 315 280 271 305 290 266 302 268 316 285 274 311 285 311 279 295 315 299 307 316 318 295 312 318 0 km 1 311 307

    Gravity Surveying 153 Fig. 6.33 Map of geophysical observations pertaining to Question 9. Bouguer anomaly values in gu.

    0 10 km Sea 268 49 423 46 640 330 60 48 45 402490 650 698 642 481 141 78

    635 Seismic Line 51 497 N

    295 Sea 45 Mesozoic sedimentSchistGabbro Bouguer anomaly (gu)

    the gabbro. Assuming the gabbro to have the form of a vertical cylinder, determine the depth The gravity anomaly Dg of a vertical cylinder of density contrast Dr, radius r, length L, depth to top z and depth to base z is given by UL

    Dg=2pGDr(L-z2+r2+z2+r2) LU State any assumptions and possible causes of error in your interpretation.

    Typical densities and seismic velocities r (Mg m-3) Veloc. (km s-1) Jur./Cret. 2.15 1.20–1.80 Trias 2.35 2.40–3.00 Schist 2.75 3.60–4.90 Gabbro 2.95 Jur. = Jurassic; Cret. = Cretaceous.

    Seismic data Dist. (m) Time (s) 530 0.349 600 0.391 670 0.441 1130 0.739 1200 0.787 1270 0.831 1800 1.160 1870 1.177 1940 1.192 2730 1.377 2800 1.393 2870 1.409 3530 1.563 3600 1.582 3670 1.599 10. Over a typical ocean spreading centre, the free-air gravity anomaly is approximately zero Why?

    Gravity and Magnetics: Case Histories. SEG Reference Series 8 & LaCoste, L.J.B., Ford, J., Bowles, R. & Archer, K. (1982) Gravity measurements in an airplane using state-of-the-art navigation Milsom, J. (1989) Field Geophysics. Open University Press, Milton Keynes.

    Nettleton, L.L. (1971) Elementary Gravity and Magnetics for Geologists and Seismologists. Monograph Series No. 1. Society of Ramsey, A.S. (1964) An Introduction to the Theory of Newtonian Tsuboi, C. (1983) Gravity. Allen & Unwin, London.

    7.1 Introduction The aim of a magnetic survey is to investigate subsurface geology on the basis of anomalies in the Earth’s mag- netic ?eld resulting from the magnetic properties of the underlying rocks. Although most rock-forming miner- als are effectively non-magnetic, certain rock types contain suf?cient magnetic minerals to produce signi?- cant magnetic anomalies. Similarly, man-made ferrous objects also generate magnetic anomalies. Magnetic sur- veying thus has a broad range of applications, from small- scale engineering or archaeological surveys to detect buried metallic objects, to large-scale surveys carried out Magnetic surveys can be performed on land, at sea and in the air. Consequently, the technique is widely employed, and the speed of operation of airborne surveys makes the method very attractive in the search for types of ore deposit that contain magnetic minerals.

    7.2 Basic concepts Within the vicinity of a bar magnet a magnetic ?ux is developed which ?ows from one end of the magnet to the other (Fig. 7.1).This ?ux can be mapped from the directions assumed by a small compass needle suspended within it. The points within the magnet where the A freely-suspended bar magnet similarly aligns in the ?ux of the Earth’s magnetic ?eld. The pole of the magnet which tends to point in the direction of the Earth’s north pole is called the north-seeking or positive pole, and this is balanced by a south-seeking or negative pole of identical strength at the opposite end The force F between two magnetic poles of strengths m and m separated by a distance r is given by 12 mmm F = 0 1 2 (7.1) 4p m r 2 R

    where m and m are constants corresponding to the mag- 0R netic permeability of vacuum and the relative magnetic permeability of the medium separating the poles (see later). The force is attractive if the poles are of different The magnetic ?eld B due to a pole of strength m at a dis- tance r from the pole is de?ned as the force exerted on a unit positive pole at that point mm B = 0 (7.2) 4p m r 2 R

    Magnetic ?elds can be de?ned in terms of magnetic poten- tials in a similar manner to gravitational ?elds. For a single pole of strength m, the magnetic potential V at a distance r from the pole is given by mm V = 0 (7.3) 4p m r R

    S N oped within it, so that B is expressed in Vs m-2 (Weber (Wb) m-2). The unit of the Wb m-2 is designated the tesla (T). Permeability is consequently expressed in Wb A-1 m-1 or Henry (H) m-1. The c.g.s. unit of magnetic ?eld strength is the gauss (G), numerically The tesla is too large a unit in which to express the small magnetic anomalies caused by rocks, and a subunit, the nanotesla (nT), is employed (1 nT = 10-9 T). The c.g.s. system employs the numerically equivalent gamma Common magnets exhibit a pair of poles and are therefore referred to as dipoles. The magnetic moment M of a dipole with poles of strength m a distance l apart is given by M = ml (7.4) The magnetic moment of a current-carrying coil is pro- portional to the number of turns in the coil, its cross- sectional area and the magnitude of the current, so that When a material is placed in a magnetic ?eld it may acquire a magnetization in the direction of the ?eld which is lost when the material is removed from the ?eld.This phenomenon is referred to as induced magneti- +

    + – – B A + + L – – Fig. 7.2 Schematic representation of an element of material in which elementary dipoles align in the direction of an external ?eld B to produce an overall induced magnetization.

    zation or magnetic polarization, and results from the align- ment of elementary dipoles (see below) within the material in the direction of the ?eld. As a result of this alignment the material has magnetic poles distributed over its surface which correspond to the ends of the dipoles (Fig. 7.2). The intensity of induced magnetiza- tion J of a material is de?ned as the dipole moment per i unit volume of material:

    M J = (7.5) i LA where M is the magnetic moment of a sample of length L and cross-sectional area A. J is consequently expressed i in A m-1. In the c.g.s. system intensity of magnetization is expressed in emu cm-3 (emu = electromagnetic unit), The induced intensity of magnetization is propor- tional to the strength of the magnetizing force H of the inducing ?eld: J = kH (7.6) i

    Magnetic Surveying 157 rationalizing the SI system is that SI susceptibility values In a vacuum the magnetic ?eld strength B and magne- tizing force H are related by B = m H where m is the 00 permeability of vacuum (4p ¥ 10-7 H m-1). Air and water have very similar permeabilities to m and so this 0 relationship can be taken to represent the Earth’s mag- When a magnetic material is placed in this ?eld, the resulting magnetization gives rise to an additional mag- netic ?eld in the region occupied by the material, whose strength is given by m J . Within the body the total 0i magnetic ?eld, or magnetic induction, B is given by B=mH+mJ 0 0i

    Substituting equation (7.6) B = m H + m kH = (1 + k)m H = m m H 0 0 0 R0

    where m is a dimensionless constant known as the rela- R tive magnetic permeability.The magnetic permeability m is thus equal to the product of the relative permeability and the permeability of vacuum, and has the same dimen- 0R All substances are magnetic at an atomic scale. Each atom acts as a dipole due to both the spin of its electrons Quantum theory allows two electrons to exist in the same state (or electron shell) provided that their spins are in opposite directions. Two such electrons are called paired electrons and their spin magnetic moments can- cel. In diamagnetic materials all electron shells are full and no unpaired electrons exist. When placed in a magnetic ?eld the orbital paths of the electrons rotate so as to pro- Consequently, the susceptibility of diamagnetic sub- stances is weak and negative. In paramagnetic substances the electron shells are incomplete so that a magnetic ?eld results from the spin of their unpaired electrons. When placed in an external magnetic ?eld the dipoles cor- responding to the unpaired electron spins rotate to produce a ?eld in the same sense as the applied ?eld so that the susceptibility is positive. This is still, however, In small grains of certain paramagnetic substances whose atoms contain several unpaired electrons, the dipoles associated with the spins of the unpaired elec- Such a grain is then said to constitute a single magnetic do- Ferrimagnetism Ferromagnetism Antiferromagnetism

    Fig. 7.3 Schematic representation of the strength and orientation of elementary dipoles within ferrimagnetic, ferromagnetic and antiferromagnetic domains.

    main. Depending on the degree of overlap of the electron 7.3), giving rise to a very strong spontaneous magnetiza- tion which can exist even in the absence of an external magnetic ?eld, and a very high susceptibility. Ferromag- netic substances include iron, cobalt and nickel, and rarely occur naturally in the Earth’s crust. In antiferromag- netic materials such as haematite, the dipole coupling is antiparallel with equal numbers of dipoles in each direction. The magnetic ?elds of the dipoles are self- However, defects in the crystal lattice structure of an antiferromagnetic material may give rise to a small net magnetization, called parasitic antiferromagnetism. In ferri- magnetic materials such as magnetite, the dipole coupling is similarly antiparallel, but the strength of dipoles in each direction are unequal. Consequently ferrimagnetic materials can exhibit a strong spontaneous magnetiza- tion and a high susceptibility. Virtually all the minerals responsible for the magnetic properties of common The strength of the magnetization of ferromagnetic and ferrimagnetic substances decreases with tempera- ture and disappears at the Curie temperature. Above this temperature interatomic distances are increased to separations which preclude electron coupling, and the material behaves as an ordinary paramagnetic substance.

    In larger grains, the total magnetic energy is decreased if the magnetization of each grain subdivides into indi- vidual volume elements (magnetic domains) with diam- eters of the order of a micrometre, within which there is parallel coupling of dipoles. In the absence of any exter- nal magnetic ?eld the domains become oriented in such a way as to reduce the magnetic forces between adjacent domains.The boundary between two domains, the Bloch wall, is a narrow zone in which the dipoles cant over from When a multidomain grain is placed in a weak exter- nal magnetic ?eld, the Bloch wall unrolls and causes a growth of those domains magnetized in the direction of the ?eld at the expense of domains magnetized in other directions. This induced magnetization is lost when the applied ?eld is removed as the domain walls rotate back to their original con?guration. When stronger ?elds are applied, domain walls unroll irreversibly across small imperfections in the grain so that those domains magnetized in the direction of the ?eld are permanently enlarged. The inherited magnetization remaining after removal of the applied ?eld is known as remanent, or per- manent, magnetization J .The application of even stronger r magnetic ?elds causes all possible domain wall move- ments to occur and the material is then said to be Primary remanent magnetization may be acquired either as an igneous rock solidi?es and cools through the Curie temperature of its magnetic minerals (thermoremanent magnetization, TRM) or as the magnetic particles of a sediment align within the Earth’s ?eld during sedimentation (detrital remanent magneti- zation, DRM). Secondary remanent magnetizations may be impressed later in the history of a rock as mag- netic minerals recrystallize or grow during diagenesis or metamorphism (chemical remanent magnetization, CRM). Remanent magnetization may develop slowly in a rock standing in an ambient magnetic ?eld as the do- main magnetizations relax into the direction of the ?eld Any rock containing magnetic minerals may possess both induced and remanent magnetizations J and J .The ir relative intensities of induced and remanent magnetiza- tions are commonly expressed in terms of the Königs- bergerratio,J:J.Thesemaybeindifferentdirectionsand ri may differ signi?cantly in magnitude. The magnetic ef- fects of such a rock arise from the resultant J of the two magnetization vectors (Fig. 7.4). The magnitude of J controls the amplitude of the magnetic anomaly and the orientation of J in?uences its shape.

    J i J r J H Fig. 7.4 Vector diagram illustrating the relationship between induced ( J ), remanent ( J ) and total ( J ) magnetization ir components.

    7.3 Rock magnetism Most common rock-forming minerals exhibit a very low magnetic susceptibility and rocks owe their mag- netic character to the generally small proportion of magnetic minerals that they contain.There are only two geochemical groups which provide such minerals. The iron–titanium–oxygen group possesses a solid solution series of magnetic minerals from magnetite (Fe O ) to 34 ulvöspinel (Fe TiO ). The other common iron oxide, 24 haematite (Fe O ), is antiferromagnetic and thus does 23 not give rise to magnetic anomalies (see Section 7.12) unless a parasitic antiferromagnetism is developed. The iron–sulphur group provides the magnetic mineral pyrrhotite (FeS , 0 < x < 0.15) whose magnetic sus- 1+x By far the most common magnetic mineral is mag- netite, which has a Curie temperature of 578°C. Al- though the size, shape and dispersion of the magnetite grains within a rock affect its magnetic character, it is rea- sonable to classify the magnetic behaviour of rocks ac- cording to their overall magnetite content. A histogram illustrating the susceptibilities of common rock types is Basic igneous rocks are usually highly magnetic due to their relatively high magnetite content. The proportion of magnetite in igneous rocks tends to decrease with increasing acidity so that acid igneous rocks, although variable in their magnetic behaviour, are usually less magnetic than basic rocks. Metamorphic rocks are also variable in their magnetic character. If the partial pres- sure of oxygen is relatively low, magnetite becomes re- sorbed and the iron and oxygen are incorporated into other mineral phases as the grade of metamorphism increases. Relatively high oxygen partial pressure can, however, result in the formation of magnetite as an accessory mineral in metamorphic reactions.

    (S.I.) 6 Mean susceptibility × 10 100 Metamorphic Acid igneous

    Sandstone 0 Limestone Shale 0–22 0–133 0–118 0–463 0–519 4–773 Basic igneous

    Range Fig. 7.5 Histogram showing mean values and ranges in In general the magnetite content and, hence, the sus- ceptibility of rocks is extremely variable and there can be considerable overlap between different lithologies. It is not usually possible to identify with certainty the causative lithology of any anomaly from magnetic information alone. However, sedimentary rocks are effectively non-magnetic unless they contain a signi?- Where magnetic anomalies are observed over sediment- covered areas the anomalies are generally caused by an underlying igneous or metamorphic basement, or by Common causes of magnetic anomalies include dykes, faulted, folded or truncated sills and lava ?ows, massive basic intrusions, metamorphic basement rocks and magnetite ore bodies. Magnetic anomalies range in amplitude from a few tens of nT over deep metamorphic basement to several hundred nT over basic intrusions and may reach an amplitude of several thousand nT over magnetite ores.

    7.4 The geomagnetic ?eld Magnetic anomalies caused by rocks are localized effects superimposed on the normal magnetic ?eld of the Earth (geomagnetic ?eld). Consequently, knowledge of the behaviour of the geomagnetic ?eld is necessary both in the reduction of magnetic data to a suitable datum and in Magnetic Surveying 159

    True North Magnetic North

    Magnetic North pole Fig. 7.7 The variation of the inclination of the total magnetic ?eld with latitude based on a simple dipole approximation of the geomagnetic ?eld. (After Sharma 1976.)

    residual ?eld can then be approximated by the effects of a second, smaller, dipole.The process can be continued by ?tting dipoles of ever decreasing moment until the observed geomagnetic ?eld is simulated to any required degree of accuracy. The effects of each ?ctitious dipole contribute to a function known as a harmonic and the technique of successive approximations of the observed ?eld is known as spherical harmonic analysis – the equivalent of Fourier analysis in spherical polar coordi- nates. The method has been used to compute the for- mula of the International Geomagnetic Reference Field (IGRF) which de?nes the theoretical undisturbed mag- netic ?eld at any point on the Earth’s surface. In mag- netic surveying, the IGRF is used to remove from the magnetic data those magnetic variations attributable to this theoretical ?eld. The formula is considerably more complex than the equivalent Gravity Formula used for latitude correction (see Section 6.8.2) as a large number of harmonics is employed (Barraclough & Malin 1971, The geomagnetic ?eld cannot in fact result from per- manent magnetism in the Earth’s deep interior. The re- quired dipolar magnetic moments are far greater than is considered realistic and the prevailing high temperatures are far in excess of the Curie temperature of any known magnetic material.The cause of the geomagnetic ?eld is attributed to a dynamo action produced by the circula- tion of charged particles in coupled convective cells within the outer, ?uid, part of the Earth’s core. The ex- change of dominance between such cells is believed to produce the periodic changes in polarity of the geomag- netic ?eld revealed by palaeomagnetic studies. The circulation patterns within the core are not ?xed and change slowly with time. This is re?ected in a slow, progressive, temporal change in all the geomagnetic elements known as secular variation. Such variation is predictable and a well-known example is the gradual rotation of the north magnetic pole around the geo- Magnetic effects of external origin cause the geo- magnetic ?eld to vary on a daily basis to produce diurnal variations. Under normal conditions (Q or quiet days) the diurnal variation is smooth and regular and has an amplitude of about 20–80 nT, being at a maxi- mum in polar regions. Such variation results from the magnetic ?eld induced by the ?ow of charged parti- cles within the ionosphere towards the magnetic poles, as both the circulation patterns and diurnal variations vary in sympathy with the tidal effects of the Sun and Some days (D or disturbed days) are distinguished by far less regular diurnal variations and involve large, short- term disturbances in the geomagnetic ?eld, with ampli- tudes of up to 1000 nT, known as magnetic storms. Such days are usually associated with intense solar activity and result from the arrival in the ionosphere of charged solar particles. Magnetic surveying should be discontinued during such storms because of the impossibility of correcting the data collected for the rapid and high- amplitude changes in the magnetic ?eld.

    7.5 Magnetic anomalies All magnetic anomalies caused by rocks are superim- posed on the geomagnetic ?eld in the same way that gravity anomalies are superimposed on the Earth’s gravitational ?eld. The magnetic case is more complex, however, as the geomagnetic ?eld varies not only in am- plitude, but also in direction, whereas the gravitational Describing the normal geomagnetic ?eld by a vector diagram (Fig. 7.8(a)), the geomagnetic elements are related

    Section Magnetic North H I (a) Z Fig. 7.8 Vector representation of the geomagnetic ?eld with and without a superimposed magnetic anomaly.

    B A magnetic anomaly is now superimposed on the Earth’s ?eld causing a change DB in the strength of the total ?eld vector B. Let the anomaly produce a vertical component DZ and a horizontal component DH at an angle a to H (Fig. 7.8(b)). Only that part of DH in the direction of H, namely DH ¢, will contribute to the anomaly DH¢ = DHcosa (7.8) Using a similar vector diagram to include the magnetic anomaly (Fig. 7.8(c))

    222 (B+DB)=(H+DH¢)+(Z+DZ) If this equation is expanded, the equality of equation (7.7) substituted and the insigni?cant terms in D2 ignored, the equation reduces to ZH DB = DZ + DH ¢ BB Substituting equation (7.8) and angular descriptions of geomagnetic element ratios gives DB=DZsinI+DHcosIcosa (7.9) This approach can be used to calculate the magnetic anomaly caused by a small isolated magnetic pole of strength m, de?ned as the effect of this pole on a unit positive pole at the observation point. The pole is situ- ated at depth z, a horizontal distance x and radial distance r from the observation point (Fig. 7.9). The force of re- pulsion DB on the unit positive pole in the direction r is r given by substitution in equation (7.1), with m = 1, R

    Cm DB = r r2 + Magnetic anomaly – Depth (b) Plan (c) Magnetic North

    H Z + ?Z ?H’?H ? Magnetic Surveying 161 Section Magnetic North H + ?H’ I

    B + ?B ?H ?B ?Z ?Z ?B r Magnetic North ? ?H Bzr x +m Fig. 7.9 The horizontal (DH ), vertical (DZ ) and total ?eld (DB) anomalies due to an isolated positive pole.

    ?eld anomaly is a positive/negative couplet and the The total ?eld anomaly DB is then obtained by substi- tuting the expressions of equations (7.10) and (7.11) in equation (7.9), where a = 0. If the pro?le were not in the direction of magnetic north, the angle a would represent the angle between magnetic north and the pro?le direction.

    7.6 Magnetic surveying instruments 7.6.1 Introduction Since the early 1900s a variety of surveying instruments have been designed that is capable of measuring the geo- magnetic elements Z, H and B. Most modern survey in- struments, however, are designed to measure B only.The precision normally required is ±0.1 nT which is approxi- mately one part in 5 ¥ 106 of the background ?eld, a considerably lower requirement of precision than is nec- In early magnetic surveys the geomagnetic elements were measured using magnetic variometers. There were several types, including the torsion head magnetometer and the Schmidt vertical balance, but all consisted essen- tially of bar magnets suspended in the Earth’s ?eld. Such devices required accurate levelling and a stable platform for measurement so that readings were time consuming and limited to sites on land.

    7.6.2 Fluxgate magnetometer Since the 1940s, a new generation of instruments has been developed which provides virtually instantaneous readings and requires only coarse orientation so that magnetic measurements can be taken on land, at sea and The ?rst such device to be developed was the ?uxgate magnetometer, which found early application during the second world war in the detection of submarines from the air.The instrument employs two identical ferromag- netic cores of such high permeability that the geomag- netic ?eld can induce a magnetization that is a substantial Identical primary and secondary coils are wound in op- posite directions around the cores (Fig. 7.10). An alter- nating current of 50–1000 Hz is passed through the primary coils (Fig. 7.10(a)), generating an alternating magnetic ?eld. In the absence of any external magnetic (a) Volts (b) Magnetization (c) Volts (d) Volts (e) Volts Ferrite core

    Primary winding Secondary winding Combined output of secondaries

    Time Time Time Time Time Fig. 7.10 Principle of the ?uxgate magnetometer. Solid and broken lines in (b)–(d) refer to the responses of the two cores.

    voltage in the coils is equal and of opposite sign so that their combined output is zero. In the presence of an ex- ternal magnetic ?eld, such as the Earth’s ?eld, which has a component parallel to the axis of the cores, saturation occurs earlier for the core whose primary ?eld is rein- forced by the external ?eld and later for the core opposed by the external ?eld. The induced voltages are now out of phase as the cores reach saturation at different times (Fig. 7.10(d)). Consequently, the combined output of the secondary coils is no longer zero but consists of a series of voltage pulses (Fig. 7.10(e)), the magnitude of which can be shown to be proportional to the amplitude The instrument can be used to measure Z or H by aligning the cores in these directions, but the required accuracy of orientation is some eleven seconds of arc to achieve a reading accuracy of ± 1 nT. Such accuracy is dif?cult to obtain on the ground and impossible when the instrument is mobile. The total geomagnetic ?eld can, however, be measured to ± 1 nT with far less precise orientation as the ?eld changes much more slowly as a Airborne versions of the instrument employ orienting mechanisms of various types to maintain the axis of the instrument in the direction of the geomagnetic ?eld. This is accomplished by making use of the feed- back signal generated by additional sensors whenever the instrument moves out of orientation to drive servomotors which realign the cores into the desired The ?uxgate magnetometer is a continuous reading instrument and is relatively insensitive to magnetic ?eld gradients along the length of the cores. The instrument may be temperature sensitive, requiring correction.

    7.6.3 Proton magnetometer The most commonly used magnetometer for both sur- vey work and observatory monitoring is currently the nuclear precession or proton magnetometer. The sensing de- vice of the proton magnetometer is a container ?lled with a liquid rich in hydrogen atoms, such as kerosene or water, surrounded by a coil (Fig. 7.11(a)).The hydrogen nuclei (protons) act as small dipoles and normally align e 7.11(b)). A current is passed through the coil to generate a magnetic ?eld B 50–100 times larger than the geo- p magnetic ?eld, and in a different direction, causing the The current to the coil is then switched off so that the (b) (a)

    West B (c) e Magnetic Surveying B e B p East

    (d) B p 163 B e polarizing ?eld is rapidly removed.The protons return to their original alignment with B by spiralling, or precess- e ing, in phase around this direction (Fig. 7.11(d)) with a period of about 0.5 ms, taking some 1–3 s to achieve their original orientation.The frequency f of this preces- sion is given by gB pe f= 2p

    of a second. The proton magnetometer is sensitive to acute magnetic gradients which may cause protons in different parts of the sensor to precess at different rates with a consequent adverse effect on precession signal Many modern proton magnetometers make use of the Overhauser Effect. To the sensor ?uid is added a liquid The protons are then polarized indirectly using radio- frequency energy near 60 MHz. The power consump- tion of such instruments is only some 25% of classical proton magnetometers, so that the instruments are lighter and more compact. The signal generated by the ?uid is about 100 times stronger, so there is much lower sampling rates are faster.

    7.6.4 Optically pumped magnetometer Optically pumped or alkali vapour magnetometers have a signi?cantly higher precision than other types. They comprise a glass cell containing an evaporated alkali metal such as caesium, rubidium or potassium which is energized by light of a particular wavelength. In these alkali atoms there exist valence electrons partitioned into two energy levels 1 and 2.The wavelength of the en- ergizing light is selected to excite electrons from level 2 to the higher level 3, a process termed polarization. Elec- trons at level 3 are unstable and spontaneously decay back to levels 1 and 2. As this process is repeated, level 1 be- comes fully populated at the expense of level 2 becoming underpopulated.This process is known as optical pump- ing and leads to the stage in which the cell stops absorb- ing light and turns from opaque to transparent. The energy difference between levels 1 and 2 is proportional to the strength of the ambient magnetic ?eld. Depolar- ization then takes place by the application of radio- frequency power.The wavelength corresponding to the energy difference between levels 1 and 2 depolarizes the cell and is a measure of the magnetic ?eld strength. A photodetector is used to balance the cell between trans- parent and opaque states. The depolarization is extre- The sensitivity of optically pumped magnetometers can be as high as ±0.01 nT. This precision is not required for surveys involving total ?eld measurements, where the level of background `noise’ is of the order of 1 nT. The usual application is in the magnetic gradiometers de- scribed below, which rely on measuring the small differ- ence in signal from sensors only a small distance apart.

    7.6.5 Magnetic gradiometers The sensing elements of ?uxgate, proton and optically pumped magnetometers can be used in pairs to measure Magnetic gradiometers are differential magnetometers in which the spacing between the sensors is ?xed and small with respect to the distance of the causative body whose magnetic ?eld gradient is to be measured. Magnetic gra- dients can be measured, albeit less conveniently, with a magnetometer by taking two successive measurements at close vertical or horizontal spacings. Magnetic gra- diometers are employed in surveys of shallow magnetic features as the gradient anomalies tend to resolve complex anomalies into their individual components, which can be used in the determination of the location, shape and depth of the causative bodies. The method has the further advantages that regional and temporal variations in the geomagnetic ?eld are automatically removed. Marine and airborne versions of magne- tometers and gradiometers are discussed by Wold and Cooper (1989) and Hood and Teskey (1989), respectively.

    7.7 Ground magnetic surveys Ground magnetic surveys are usually performed over Consequently, station spacing is commonly of the order of 10–100 m, although smaller spacings may be employed where magnetic gradients are high. Readings should not be taken in the vicinity of metallic objects such as railway lines, cars, roads, fencing, houses, etc, which might perturb the local magnetic ?eld. For simi- lar reasons, operators of magnetometers should not carry Base station readings are not necessary for monitoring instrumental drift as ?uxgate and proton magnetometers do not drift, but are important in monitoring diurnal Since modern magnetic instruments require no precise levelling, a magnetic survey on land invariably proceeds much more rapidly than a gravity survey.

    a `bird’ to remove the instrument from the magnetic effects of the aircraft or ?xed in a`stinger’in the tail of the aircraft, in which case inboard coil installations compen- Aeromagnetic surveying is rapid and cost-effective, typically costing some 40% less per line kilometre than a ground survey.Vast areas can be surveyed rapidly without the cost of sending a ?eld party into the survey area and data can be obtained from areas inaccessible to ground The most dif?cult problem in airborne surveys used to be position ?xing. Nowadays, however, the availabil- Marine magnetic surveying techniques are similar to those of airborne surveying. The sensor is towed in a `?sh’ at least two ships’ lengths behind the vessel to re- move its magnetic effects. Marine surveying is obviously slower than aeromagnetic surveying, but is frequently carried out in conjunction with several other geo- physical methods, such as gravity surveying and con- tinuous seismic pro?ling, which cannot be employed in the air.

    7.9 Reduction of magnetic observations The reduction of magnetic data is necessary to remove all causes of magnetic variation from the observations other than those arising from the magnetic effects of the subsurface.

    7.9.1 Diurnal variation correction The effects of diurnal variation may be removed in sev- eral ways. On land a method similar to gravimeter drift monitoring may be employed in which the magnetome- ter is read at a ?xed base station periodically throughout the day. The differences observed in base readings are then distributed among the readings at stations occupied during the day according to the time of observation. It should be remembered that base readings taken during a gravity survey are made to correct for both the drift of the gravimeter and tidal effects; magnetometers do not drift and base readings are taken solely to correct for temporal variation in the measured ?eld. Such a procedure is inef?cient as the instrument has to be returned periodically to a base location and is not practi- cal in marine or airborne surveys. These problems may be overcome by use of a base magnetometer, a Magnetic Surveying 165

    continuous-reading instrument which records magnetic variations at a ?xed location within or close to the survey area.This method is preferable on land as the survey pro- Where the survey is of regional extent the records of a magnetic observatory may be used. Such observatories continuously record changes in all the geomagnetic elements. However, diurnal variations differ quite markedly from place to place and so the observatory used should not be more than about 100 km from the survey Diurnal variation during an aeromagnetic survey may alternatively be assessed by arranging numerous crossover points in the survey plan (Fig. 7.12).Analysis of the differences in readings at each crossover, representing the ?eld change over a series of different time periods, al- lows the whole survey to be corrected for diurnal varia- tion by a process of network adjustment, without the Diurnal variations, however recorded, must be exam- ined carefully. If large, high-frequency variations are apparent, resulting from a magnetic storm, the survey results should be discarded.

    7.9.2 Geomagnetic correction The magnetic equivalent of the latitude correction in gravity surveying is the geomagnetic correction which re- moves the effect of a geomagnetic reference ?eld from the survey data. The most rigorous method of geomag- netic correction is the use of the IGRF (Section 7.4), which expresses the undisturbed geomagnetic ?eld in terms of a large number of harmonics and includes temporal terms to correct for secular variation. The complexity of the IGRF requires the calculation of cor- rections by computer. It must be realized, however, that the IGRF is imperfect as the harmonics employed are based on observations at relatively few, scattered, mag- netic observatories.The IGRF is also predictive in that it extrapolates forwards the spherical harmonics derived from observatory data. Consequently, the IGRF in areas Over the area of a magnetic survey the geomagnetic reference ?eld may be approximated by a uniform gradi- ent de?ned in terms of latitudinal and longitudinal gra- dient components. For example, the geomagnetic ?eld over the British Isles is approximated by the following gradient components: 2.13 nT km-1 N; 0.26 nT km-1 W; these vary with time. For any survey area the relevant gradient values may be assessed from magnetic maps The appropriate regional gradients may also be ob- tained by employing a single dipole approximation of the Earth’s ?eld and using the well-known equations for the magnetic ?eld of a dipole to derive local ?eld gradients:

    m 2M m M Z = 0 cosq, H = 0 sinq (7.12) 4p R3 4p R3 ?Z ?H Z = -2H, = (7.13) ?q ?q 2

    where Z and H are the vertical and horizontal ?eld com- ponents, q the colatitude in radians, R the radius of the Earth, M the magnetic moment of the Earth and ?Z/?q and ?H/?q the rate of change of Z and H with An alternative method of removing the regional gra- dient over a relatively small survey area is by use of trend analysis. A trend line (for pro?le data) or trend surface (for areal data) is ?tted to the observations using the least squares criterion, and subsequently subtracted from the observed data to leave the local anomalies as positive and negative residuals (Fig. 7.13).

    + Magnetic anomaly 0 – Regional gradient Distance Fig. 7.13 The removal of a regional gradient from a magnetic ?eld by trend analysis.The regional ?eld is approximated by a linear trend.

    7.9.3 Elevation and terrain corrections The vertical gradient of the geomagnetic ?eld is only some 0.03 nT m-1 at the poles and -0.015 nT m-1 at the The in?uence of topography can be signi?cant in ground magnetic surveys but is not completely pre- dictable as it depends upon the magnetic properties of the topographic features.Therefore, in magnetic survey- Having applied diurnal and geomagnetic corrections, all remaining magnetic ?eld variations should be caused solely by spatial variations in the magnetic properties of the subsurface and are referred to as magnetic anomalies.

    Magnetic Surveying 167 400 200 0 Total field magnetic anomaly (nT) –200

    0 2000 km 20 ?g100 ?B Gravity anomaly (gu) 0

    Magnetic North Fig. 7.14 Gravity (Dg) and magnetic (DB) anomalies over the same two-dimensional body. 10 Depth (km) (a) –150 km –200

    –250 –300 0 nT 10 20 30 1.6 B ?? = 0.10 Mg m–3 J = 1 A m–1

    (b) –150 km –200 –250 –300 0 nT 10 –15.6 20 50 km 30 0.51 –16.6 50 km

    Fig. 7.15 An example of ambiguity in magnetic interpretation.The arrows correspond to the directions of magnetization vectors, whose magnitudeisgiveninAm-1.(AfterWestbrook1975.)

    Magnetic anomaly (nT) 100 0 –100 0 Depth (km) 6 0 100 km Fig. 7.16 Magnetic anomalies over the Aves Ridge, eastern Caribbean. Lower diagram illustrates bathymetry and basement/sediment interface. Horizontal bars indicate depth estimates of the Aves Ridge magnetic basement derived by spectral analysis of the magnetic data.

    geology and structure of a broad region from an assess- ment of the shapes and trends of anomalies. Sediment- covered areas with relatively deep basement are typically represented by smooth magnetic contours re?ecting Igneous and metamorphic terrains generate far more complex magnetic anomalies, and the effects of deep geological features may be obscured by short- wavelength anomalies of near-surface origin. In most types of terrain an aeromagnetic map can be a useful aid to reconnaissance geological mapping. Such qualitative interpretations may be greatly facilitated by the use of In carrying out quantitative interpretation of mag- netic anomalies, both direct and indirect methods may be employed, but the former are much more limited than for gravity interpretation and no equivalent general equations exist for total ?eld anomalies.

    (e) e n B Block u a w Central 420000 440000 ?

    (Warwickshire coalfield) East Hinckley Basin r Northern section of central block o u n d ?

    a yr F ua l t 260000 F lt Moreton Axis Central section of central block

    240000 Graben Inkberro Worcester Withycombe Southern section of central block ?LAVAS HINGE POINT Bicester B.H.

    220000 Charlton Anticline 420000 440000 ?

    Fig. 7.17 Continued respectively. The boundaries implied by the solutions have been used to construct the interpretation shown in Fig. 7.17(e).

    7.10.3 Indirect interpretation Indirect interpretation of magnetic anomalies is similar to gravity interpretation in that an attempt is made to match the observed anomaly with that calculated for a model by iterative adjustments to the model. Simple Such an approximation to the magnetization of a real geological body is often valid for highly magnetic ore bodies whose direction of magnetization tends to align with their long dimension (Fig. 7.18). In such cases the anomaly is calculated by summing the effects of both poles at the observation points, employing equations (7.10), (7.11) and (7.9). More complicated magnetic The magnetic anomaly of most regularly-shaped bodies can be calculated by building up the bodies from a series of dipoles parallel to the magnetization direction + Total field magnetic anomaly 0

    – Combined effects Negative of both poles pole

    Distance Positive pole Magnetic North Depth – B + Fig. 7.18 The total ?eld magnetic anomaly of an elongate body approximated by a dipole.

    Magnetic Surveying 171 – – – –+ – – – – – Fig. 7.19 The representation of the magnetic effects of an irregularly-shaped body in terms of a number of elements Inset shows in detail the end of one such element.

    Magnetic anomaly (nT) 0 –300 0 Fig. 7.20 The total ?eld magnetic 5 anomaly of a faulted sill.

    Depth (km) pole strength per unit area = J cos q (7.17) A consequence of the distribution of an equal number of positive and negative poles over the surface of a mag- netic body is that an in?nite horizontal layer produces no magnetic anomaly since the effects of the poles on the upper and lower surfaces are self-cancelling. Conse- quently, magnetic anomalies are not produced by continuous sills or lava ?ows.Where, however, the hori- zontal structure is truncated, the vertical edge will The magnetic anomaly of a body of regular shape is calculated by determining the pole distribution over the surface of the body using equation (7.17). Each small el- ement of the surface is then considered and its vertical and horizontal component anomalies are calculated at each observation point using equations (7.10) and (7.11).The effects of all such elements are summed (inte- grated) to produce the vertical and horizontal anomalies for the whole body and the total ?eld anomaly is calcu- lated using equation (7.9). The integration can be per- +

    + ?A J l + ?A’ +

    + –+ + ? + + 0 km 20 Magnetic North –––––––––– + J = 1A m–1 + ++++++++++ B

    formed analytically for bodies of regular shape, while irregularly-shaped bodies may be split into regular In two-dimensional modelling, an approach similar to gravity interpretation can be adopted (see Section 6.10.4) in which the cross-sectional form of the body is approximated by a polygonal outline. The anomaly of the polygon is then computed by adding or subtracting the anomalies of semi-in?nite slabs with sloping edges corresponding to the sides of the polygon (Fig. 7.21). In the magnetic case, the horizontal DH, vertical DZ and total ?eld DB anomalies (nT) of the slab shown in Fig. 7.21 are given by (Talwani et al. 1965) DZ=200sinq[J{sinqlog(rr)+fcosq} x e21 +J{cosqlog(rr)-fsinq}] (7.18a) z e21

    DH=200sinq[J{fsinq-cosqlog(rr)} x e21 +J{fcosq+sinqlog(rr)}]sina (7.18b) z e21

    x r ?1 J x r 2 i 8 J z ? Fig. 7.21 Parameters used in de?ning the magnetic J anomaly of a semi-in?nite slab with a sloping edge.

    where angles are expressed in radians, J (= J cos i) and J xz (= J sin i) are the horizontal and vertical components of the magnetization J, a is the horizontal angle between the direction of the pro?le and magnetic north, and I is the inclination of the geomagnetic ?eld. Examples of this technique have been presented in Fig. 7.15. An important difference from gravity interpretation is the increased stringency with which the two-dimensional approximation should be applied. It can be shown that two-dimensional magnetic interpretation is much more sensitive to errors associated with variation along strike than is the case with gravity interpretation; the length–width ratio of a magnetic anomaly should be at least 10 : 1 for a two-dimensional approximation to be valid, in contrast to gravity interpretation where a 2 : 1 length–width ratio is suf?cient to validate two- Three-dimensional modelling of magnetic anomalies is complex. Probably the most convenient methods are to approximate the causative body by a cluster of right rectangular prisms or by a series of horizontal slices of Because of the dipolar nature of magnetic anomalies, trial and error methods of indirect interpretation are dif- ?cult to perform manually since anomaly shape is not Consequently, the automatic methods of interpretation The continuation and ?ltering operations used in gravity interpretation and described in Section 6.11 are equally applicable to magnetic ?elds. A further process- ing operation that may be applied to magnetic anomalies is known as reduction to the pole, and involves the conver- sion of the anomalies into their equivalent form at the north magnetic pole (Baranov & Naudy 1964). This process usually simpli?es the magnetic anomalies as the ambient ?eld is then vertical and bodies with magnetiza- tions which are solely induced produce anomalies that are axisymmetric. The existence of remanent magneti- zation, however, commonly prevents reduction to the pole from producing the desired simpli?cation in the resultant pattern of magnetic anomalies.

    Magnetic Surveying 173 (c) Pseudogravity anomaly (gu) (a) Magnetic anomaly (nT) Fig. 7.22 (a) Observed magnetic anomalies over the Aves Ridge, eastern Caribbean. (b) Bouguer gravity anomalies with long-wavelength regional ?eld removed. (c) Pseudo- gravity anomalies computed for induced magnetization and a density : magnetization ratio of unity. (d) Bathymetry.

    different orientations of the magnetization vector pro- vides an estimate of the true vector orientation since this will produce a pseudogravity ?eld which most closely approximates the observed gravity ?eld. The relative amplitudes of these two ?elds then provide a measure of the ratio of intensity of magnetization to density (Ates & Kearey 1995).These potential ?eld transformations pro- vide an elegant means of comparing gravity and mag- netic anomalies over the same area and sometimes allow greater information to be derived about their causative bodies than would be possible if the techniques were treated in isolation. A computer program which per- forms pseudo?eld transformations is given in Gilbert Figures 7.22(a) and (b) show magnetic and residual gravity anomaly pro?les across the Aves Ridge, a sub- marine prominence in the eastern Caribbean which runs parallel to the island arc of the Lesser Antilles. The pseudogravity pro?le calculated from the magnetic pro- 7.22(c). It is readily apparent that the main pseudogra- 0 +200

    0 –200 6 0 100 km (a) 1000 I (b) Bouguer anomaly (gu) II III (b)

    (c) (d) 0 0 4000 (d) Depth (m) vity peak correlates with peak I on the gravity pro?le and that peaks II and III correlate with much weaker features on the pseudo?eld pro?le.The data thus suggest that the density features responsible for the gravity maxima are also magnetic, with the causative body of the central peak having a signi?cantly greater susceptibility than the Figure 7.23 shows how a variety of processing meth- ods can be used on a synthetic magnetic anomaly map and Fig. 7.24 shows their application to real data.

    7.12 Applications of magnetic surveying Magnetic surveying is a rapid and cost-effective tech- nique and represents one of the most widely-used geophysical methods in terms of line length surveyed Magnetic surveys are used extensively in the search for metalliferous mineral deposits, a task accomplished rapidly and economically by airborne methods.

    Magnetic surveys are capable of locating massive sul- phide deposits (Fig. 7.25), especially when used in con- junction with electromagnetic methods (see Section 9.12). However, the principal target of magnetic survey- ing is iron ore. The ratio of magnetite to haematite must be high for the ore to produce signi?cant anomalies, as Figure 7.26 shows total ?eld magnetic anomalies from an airborne survey of the Northern Middleback Range,

    (a) (b) 100 km 1250 0 100 km (c) (d)

    1250 0 0 800 (e) (f) 0 0 100 0 (g) (h)

    2 8 8 2 South Australia, in which it is seen that the haematitic Figure 7.27 shows the results from an aeromagnetic sur- vey of part of the Eyre Peninsula of South Australia which reveal the presence of a large anomaly elongated east–west. Subsequent ground traverses were performed over this anomaly using both magnetic and gravity methods (Fig. 7.28) and it was found that the magnetic and gravity pro?les exhibit coincident highs. Subse- quent drilling on these highs revealed the presence of a magnetite-bearing ore body at shallow depth with an Gunn (1998) has reported on the location of prospec- tive areas for hydrocarbon deposits in Australia by aeromagnetic surveying, although it is probable that this application is only possible in quite speci?c In geotechnical and archaeological investigations, magnetic surveys may be used to delineate zones of fault- ing in bedrock and to locate buried metallic, man-made features such as pipelines, old mine workings and build- ings. Figure 7.29 shows a total magnetic ?eld contour map of the site of a proposed apartment block in Bristol, England.The area had been exploited for coal in the past and stability problems would arise from the presence of old shafts and buried workings (Clark 1986). Lined shafts of up to 2 m diameter were subsequently found beneath anomalies A and D, while other isolated anomalies such as B and C were known, or suspected, to be associated with buried metallic objects.

    N 20 000 nT 12 W 10 000 nT 0 100m 0 8W 4W

    0 4E Conductor outline Magnetics 8E 12 E Fig. 7.25 Vertical ?eld ground magnetic anomaly pro?les over a massive sulphide ore body in Quebec, Canada.The shaded area represents the location of the ore body inferred from electromagnetic measurements. (AfterWhite 1966.)

    Magnetic Surveying 177 Fig. 7.26 Aeromagnetic anomalies over the Northern Middleback Range, South Australia.The iron ore bodies arc of haematite composition. Contour interval 500 nT. (AfterWebb 1966.) 137°10′

    Iron Prince 33°00′ 33°00′

    Iron Barron Iron Queen 3000 5600 3000 Iron Queen South 2000 7000 Mt. Middleback North 5000 4000 33°05′ 33°05′

    Magnetic Surveying 179 Profile 2 Gravity profile 7000 6800 6600 6400 6200 Surface 0 km 1 Profile 1 7200 Gravity profile 10 000 7000 8000 6800 Magnetic profile 6000 6600 Magnetic profile 4000 6400 Surface 2000 0 10000 8000 6000 4000 2000

    km 2 Bouguer anomaly (gu) Magnetic anomaly (nT) Magnetic anomaly (nT) Bouguer anomaly (gu) Profile 3 Bouguer anomaly (gu) 7800 7600 7400 7200 7000 6800 Gravity profile

    Magnetic profile 12 000 10 000 8000 6000 4000 0 1 km 2000 Drill holes intersecting < 20% iron oxides Drill holes intersecting > 20% iron oxides

    180° 140°W 100°W 60°N

    40°N 20°N A l e u tian Isl a n d s Pacific Ocean 0 2000 km M cino F.Z.

    o d n e rr y FZ a Mu l Mo ok North America FZ a 40°N Fig. 7.30 Pattern of linear magnetic 20°N anomalies and major fracture zones 180° 140°W in the northeast Paci?c Ocean.

    (Kearey &Vine 1996) and on views of the formation of oceanic lithosphere. Early magnetic surveying at sea showed that the oceanic crust is characterized by a pat- tern of linear magnetic anomalies (Fig. 7.30) attribut- able to strips of oceanic crust alternately magnetized in a normal and reverse direction (Mason & Raff 1961).The bilateral symmetry of these linear magnetic anomalies about oceanic ridges and rises (Vine & Matthews 1963) led directly to the theory of sea ?oor spreading and the establishment of a time scale for polarity transitions Consequently, oceanic crust can be dated on the basis of the pattern of magnetic polarity transitions preserved Transform faults disrupt the pattern of linear mag- netic anomalies (see Fig. 7.30) and their distribution can therefore be mapped magnetically. Since these faults lie along arcs of small circles to the prevailing pole of rota- tion at the time of transform fault movement, individual regimes of spreading during the evolution of an ocean basin can be identi?ed by detailed magnetic surveying.

    Such studies have been carried out in all the major oceans and show the evolution of an ocean basin to be a complex process involving several discrete phases of Magnetic surveying is a very useful aid to geological mapping. Over extensive regions with a thick sedi- mentary cover, structural features may be revealed if magnetic horizons such as ferruginous sandstones and shales, tuffs and lava ?ows are present within the sedi- mentary sequence. In the absence of magnetic sedi- ments, magnetic survey data can provide information on the nature and form of the crystalline basement. Both cases are applicable to petroleum exploration in the location of structural traps within sediments or features of basement topography which might in?uence the overlying sedimentary sequence. The magnetic method may also be used to assist a programme of reconnaissance geological mapping based on widely-spaced grid sam- ples, since aeromagnetic anomalies can be employed to delineate geological boundaries between sampling points.

    Magnetic Surveying 181 magnetic ?eld conforms to an axial dipole model, calculate the geomagnetic elements at 60°N and 75°S. Calculate also the total ?eld magnetic gradients in nT km-1 N at these 5. Using equations (7.18a,b,c), derive expres- sions for the horizontal, vertical and total ?eld magnetic anomalies of a vertical dyke of in?nite depth striking at an angle a to magnetic Given that geomagnetic inclination I is related to latitude q by tan I = 2 tan q, use these formulae to calculate the magnetic anomalies of east–west striking dykes of width 40 m, depth 20 m and intensity of magnetization 2 A m-1, at a latitude of 45°, in the following cases: (a) In the northern hemisphere with induced (b) In the northern hemisphere with reversed (c) In the southern hemisphere with normal (d) In the southern hemisphere with reversed How would the anomalies change if the width and depth were increased to 400 m and 200 m, 6. (a) Calculate the vertical, horizontal and total ?eld magnetic anomaly pro?les across a dipole which strikes in the direction of the mag- netic meridian and dips to the south at 30° with the negative pole at the northern end 5 m beneath the surface. The length of the dipole is 50 m and the strength of each pole is 300 A m.

    +40 nT50 m 0 –40 SE NW

    Fig. 7.31 Total ?eld magnetic pro?le across buried volcanic rocks south of Bristol, England. (After Kearey & Allison 1980.)

    The local geomagnetic ?eld dips to the north at (b) What is the effect on the pro?les if the dipole (c) If the anomalies calculated in (a) actually originate from a cylinder whose magnetic moment is the same as the dipole and whose diameter is 10 m, calculate the intensity of mag- (d) Fig. 7.31 shows a total ?eld magnetic anom- aly pro?le across buried volcanic rocks to the south of Bristol, England. Does the pro?le con- structed in (a) represent a reasonable simulation of this anomaly? If so, calculate the dimensions and intensity of magnetization of a possible mag- netic source. What other information would be needed to provide a more detailed interpretation of the anomaly?

    Further reading Arnaud Gerkens, J.C. d’ (1989) Foundations of Exploration Baranov,W. (1975) Potential Fields andTheirTransformation inApplied Bott, M.H.P. (1973) Inverse methods in the interpretation of mag- netic and gravity anomalies. In: Alder, B., Fernbach, S. & Bolt, Garland, G.D. (1951) Combined analysis of gravity and magnetic anomalies Geophysics, 16, 51–62.

    Gibson, R.I. & Millegan, P.S. (eds) (1998) Geologic Applications of Gravity and Magnetics: Case Histories. SEG Reference Series 8 & Gunn, P.J. (1975) Linear transformations of gravity and magnetic Kanasewich, E.R. & Agarwal, R.G. (1970) Analysis of combined Nettleton, L.L. (1971) Elementary Gravity and Magnetics for Geolo- gists and Seismologists. Monograph Series No. 1. Society of Exploration Geophysicists,Tulsa.

    Sharma, P. (1976) Geophysical Methods in Geology. Elsevier, Stacey, F.D. & Banerjee, S.K. (1974) The Physical Principles of Rock Magnetism. Elsevier, Amsterdam.

    8.1 Introduction There are many methods of electrical surveying. Some make use of ?elds within the Earth while others require the introduction of arti?cially-generated currents into the ground.The resistivity method is used in the study of horizontal and vertical discontinuities in the electrical properties of the ground, and also in the detection of three-dimensional bodies of anomalous electrical conductivity. It is routinely used in engineering and hydrogeological investigations to investigate the shallow subsurface geology. The induced polarization method makes use of the capacitive action of the subsurface to lo- cate zones where conductive minerals are dissemin-ated within their host rocks. The self-potential method makes use of natural currents ?owing in the ground that are generated by electrochemical processes to locate shallow Electrical methods utilize direct currents or low- frequency alternating currents to investigate the electri- cal properties of the subsurface, in contrast to the elec- tromagnetic methods discussed in the next chapter that use alternating electromagnetic ?elds of higher frequen- cy to this end.

    8.2 Resistivity method 8.2.1 Introduction In the resistivity method, arti?cially-generated electric currents are introduced into the ground and the resulting potential differences are measured at the surface. Devia- tions from the pattern of potential differences expected from homogeneous ground provide information on the form and electrical properties of subsurface inhomogeneities.

    8.2.2 Resistivities of rocks and minerals The resistivity of a material is de?ned as the resistance in ohms between the opposite faces of a unit cube of the material. For a conducting cylinder of resistance dR, length dL and cross-sectional area dA (Fig. 8.1) the resistivity r is given by

    dRdA r = (8.1) dL

    The SI unit of resistivity is the ohm-metre (ohm m) and the reciprocal of resistivity is termed conductivity (units: siemens (S) per metre; 1 S m-1 = 1 ohm-1 m-1; the term Resistivity is one of the most variable of physical properties. Certain minerals such as native metals and Most rock-forming minerals are, however, insulators, and electrical current is carried through a rock mainly by the passage of ions in pore waters. Thus, most rocks conduct electricity by electrolytic rather than electronic processes. It follows that porosity is the major control of

    I ?L ?A ?R

    Resistivity (? m) 1 102 104 106 108

    Granite Gabbro Schist Quartzite Sandstone Shale Clay Alluvium Fig. 8.2 The approximate range of resistivity values of common rock types.

    the resistivity of rocks, and that resistivity generally in- creases as porosity decreases. However, even crystalline rocks with negligible intergranular porosity are conduc- tive along cracks and ?ssures. Figure 8.2 shows the range of resistivities expected for common rock types. It is ap- parent that there is considerable overlap between differ- ent rock types and, consequently, identi?cation of a rock Strictly, equation (8.1) refers to electronic conduction but it may still be used to describe the effective resistivity of a rock; that is, the resistivity of the rock and its pore water. The effective resistivity can also be expressed in terms of the resistivity and volume of the pore water present according to an empirical formula given by Archie (1942)

    r = af -b f -c rw (8.2)

    where f is the porosity, f the fraction of pores containing water of resistivity r and a, b and c are empirical con- w stants. r can vary considerably according to the quanti- w ties and conductivities of dissolved materials.

    8.2.3 Current ?ow in the ground Consider the element of homogeneous material shown in Fig. 8.1. A current I is passed through the cylinder causing a potential drop -dV between the ends of the Ohm’s law relates the current, potential difference and resistance such that -dV = dRI, and from equation (8.1) dR = r dL dA . Substituting I

    ? r ?V Current flow line Equipotential surface dV rI = – = -ri (8.3) dL dA

    dV/dL represents the potential gradient through the In general the current density in any direction within a material is given by the negative partial derivative of the Now consider a single current electrode on the sur- face of a medium of uniform resistivity r (Fig. 8.3).The circuit is completed by a current sink at a large distance from the electrode. Current ?ows radially away from the electrode so that the current distribution is uniform over hemispherical shells centred on the source. At a distance r from the electrode the shell has a surface area of 2pr 2, so the current density i is given by

    I i = (8.4) 2pr 2

    From equation (8.3), the potential gradient associated with this current density is

    ?V rI = -ri = – (8.5) ?r 2pr 2

    The potential V at distance r is then obtained by r integration

    rI ?r rI V = Ú ?V = -Ú = (8.6) r 2pr 2 2pr

    Electrical Surveying 185 I r Ar B ?V +I –I ACDB RA RB

    Fig. 8.4 The generalized form of the electrode con?guration Equation (8.6) allows the calculation of the potential at any point on or below the surface of a homogeneous half -space. The hemispherical shells in Fig. 8.3 mark surfaces of constant voltage and are termed equipotential Now consider the case where the current sink is a ?nite distance from the source (Fig. 8.4). The potential V at an internal electrode C is the sum of the potential C contributions V and V from the current source at A AB and the sink at B V =V +V CAB

    From equation (8.6) rI Ê 1 1 ^ V = – (8.7) C 2p Ë r r ¯ AB

    Similarly rI Ê 1 1 ^ V = – (8.8) D 2p Ë R R ¯ AB

    Absolute potentials are dif?cult to monitor so the poten- tial difference DV between electrodes C and D is measured rI ÏÊ 1 1 ^ Ê 1 1 ^ ¸ DV =V -V = Ì – – – ? C D ÓË ¯ Ë ¯ 2p r r R R ? ABAB

    Thus 2pDV r = (8.9) ÏÊ 1 1 ^ Ê 1 1 ^ ¸ IÌ – – – ? ÓË r r ¯ Ë R R ¯ ? ABAB

    Where the ground is uniform, the resistivity calcul- ated from equation (8.9) should be constant and inde- 1.0

    0.8 0.6 Fraction of current 0.4 0.2 0 0 2 4 6 8 10 L/Z Fig. 8.5 The fraction of current penetrating below a depth Z for a current electrode separation L. (AfterTelford et al. 1990.)

    sively expanded about a ?xed central point. Conse- quently, readings are taken as the current reaches pro- gressively greater depths. The technique is extensively used in geotechnical surveys to determine overburden thickness and also in hydrogeology to de?ne horizontal Constant separation traversing (CST), also known as `electrical pro?ling’, is used to determine lateral varia- tions of resistivity. The current and potential electrodes are maintained at a ?xed separation and progressively moved along a pro?le.This method is employed in min- eral prospecting to locate faults or shear zones and to de- tect localized bodies of anomalous conductivity. It is also used in geotechnical surveys to determine variations in Results from a series of CST traverses with a ?xed elec- trode spacing can be employed in the production of resistivity contour maps.

    8.2.4 Electrode spreads Many con?gurations of electrodes have been designed (Habberjam 1979) and, although several are occasional- ly employed in specialized surveys, only two are in com- mon use. The Wenner con?guration is the simpler in that current and potential electrodes are maintained at an equal spacing a (Fig. 8.6). Substitution of this condition into equation (8.9) yields DV ra = 2pa (8.10) I

    DuringVES the spacing a is gradually increased about a ?xed central point and in CST the whole spread is moved along a pro?le with a ?xed value of a. The ef?- ciency of performing vertical electrical sounding can be greatly increased by making use of a multicore cable to which a number of electrodes are permanently attached at standard separations (Barker 1981). A sounding can then be rapidly accomplished by switching between dif- ferent sets of four electrodes. Such a system has the addi- tional advantage that, by measuring ground resistances at two electrode array positions, the effects of near- surface lateral resistivity variations can be substantially In surveying with the Wenner con?guration all four electrodes need to be moved between successive read- ings. This labour is partially overcome by the use of the Schlumberger con?guration (Fig. 8.6) in which the inner, potential electrodes have a spacing 2l which is a small ?V

    aaa Wenner 2L ?V 2l x Schlumberger Fig. 8.6 TheWenner and Schlumberger electrode con?gurations.

    In CST surveys with the Schlumberger con?guration several lateral movements of the potential electrodes may be accommodated without the necessity of moving the current electrodes. In VES surveys the potential elec- trodes remain ?xed and the current electrodes are ex- With very large values of L it may, however, be necessary to increase l also in order to maintain a measurable For the Schlumberger con?guration

    2 p (L2 – x2) DV r = (8.11) a 2l (L2 + x 2 ) I

    where x is the separation of the mid-points of the poten- tial and current electrodes. When used symmetrically, x = 0, so pL2 DV r = (8.12) a 2l I

    Measured potential difference Electrodes + – XX XX X True potential difference Telluric shift

    XXXXX Electrodes – + Time Fig. 8.7 The use of alternating current to remove the effects of telluric currents during a resistivity measurement. Summing the measured potential difference over several cycles provides the true potential difference.

    levels of resistance commonly encountered in resistivity surveying.Apparent resistivity values are computed from the resistance measurements using the formula relevant Most resistivity meters employ low-frequency alter- nating current rather than direct current, for two main reasons. Firstly, if direct current were employed there would eventually be a build-up of anions around the negative electrode and cations around the positive elec- trode; that is, electrolytic polarization would occur, and this would inhibit the arrival of further ions at the elec- trodes. Periodic reversal of the current prevents such an accumulation of ions and thus overcomes electrolytic polarization. Secondly, the use of alternating current overcomes the effects of telluric currents (see Chapter 9), which are natural electric currents in the ground that ?ow parallel to the Earth’s surface and cause regional po- tential gradients. The use of alternating current nulli?es their effects since at each current reversal the telluric cur- rents alternately increase or decrease the measured po- tential difference by equal amounts. Summing the results The frequency of the alternating current used in resistiv- ity surveying depends upon the required depth of pene- tration (see equation (9.2)). For penetration of the order of 10 m, a frequency of 100 Hz is suitable, and this is de- creased to less than 10 Hz for depths of investigation of about 100 m. For very deep ground penetration direct currents must be used, and more complex measures adopted to overcome electrolytic polarization and tel- luric current effects. Many modern instruments make use of a square wave current input to overcome the polarization.

    Electrical Surveying 187 Resistivity meters are designed to measure potential differences when no current is ?owing. Such a null method is used to overcome the effects of contact resis- tance of the electrodes with the ground. The potential between the potential electrodes is balanced by the po- tential tapped from a variable resistance. No current then ?ows in the resistivity circuit so that contact resistance will not register, and the variable resistance reading represents the true resistance of the ground (equal to Previous generations of resistivity meters required the nulling of a displayed voltage by manual manipula- tion of a resistor bank. Modern instruments have microprocessor-controlled electronic circuitry which accomplishes this operation internally and, moreover, performs checks on the circuitry before display of the Resistivity surveying for shallow penetration can be made more ef?cient by the use of spike electrodes which are mounted on small wheels and towed along a pro?le by the operator. Improvements in instrument technology have also led to the development of elec- trodes in the form of antennae which are capacitively coupled to the ground (Panissod et al. 1998), so that there is no need for spike electrodes to be placed in the ground and a CST may be accomplished by an operator towing the array at a walking pace by foot or vehicle. Measure- ments can be taken automatically and are no longer re- stricted to areas where electrodes can be in-serted, such as road metal, ice, permafrost, etc. Such a system allows the collection, by a single operator, of 500% more data in the same time as a conventional instrument with a crew of two. However, the limitations of the physical dimensions of such equipment considerably restricts penetration.

    ? a Chapter 8 ? 1 ? 2 a ? 1 ?

    solution of Laplace’s equation (Section 6.11) and inser- tion of the boundary conditions for the particular struc- ture under consideration, or by integrating it directly. In practice such solutions are invariably complex. Conse- quently, a simpli?ed approach is initially adopted here in which electric ?elds are assumed to act in a manner similar to light. It should be remembered, however, that such an optical analogue is not strictly valid in all cases.

    8.2.7 Vertical electrical sounding interpretation Consider aWenner electrode spread above a single hori- zontal interface between media with resistivities r 1 (upper) and r (lower) with r > r (Fig. 8.8). On passing 2 12 through the interface the current ?ow lines are de?ected towards the interface in a fashion similar to refracted seismic waves (Chapter 3) since the less resistive lower layer provides a more attractive path for the current.When the electrode separation is small, most of the current ?ows in the upper layer with the conse- quence that the apparent resistivity tends towards r . As 1 the electrode separation is gradually increased, more and more current ?ows within the lower layer and the appar- ent resistivity then approaches r . A similar situation ob- 2 tains when r > r , although in this case the apparent 21 resistivity approaches r more gradually as the more re- 2 Where three horizontal layers are present the apparent resistivity curves are more complex (Fig. 8.9). Although the apparent resistivity approaches r and r for small and 13 (a) ? a (b) ? a ? >? >? 231? >? >? 123

    ? >? >? 312? >? >? 321 aa ? 1 ? 2 ? 3 Fig. 8.9 The variation of apparent resistivity r , with electrode a separation a over three horizontal layers.

    C’ 2 C’ 1 C 0 r 2 r 1 r0 P

    2z?1 z 4z 4zC 1 r1 ? 2

    r 2 C 2 Fig. 8.10 Parameters used in the calculation of the potential due to a single surface electrode above a single horizontal interface using the method of images.

    Table 8.1 Distribution and intensity of electrical sources due to a single horizontal interface.

    Source Intensity Depth/height Distance CI0r 00 C kI 2z r 11 C¢ kI 2z r 11 C k2I 4z r 22 C¢ k2I 4z r 22 etc

    C is the image of C¢ in the medium 1/air interface at 21 height 2z, C is the image of C ¢ in the medium 1/2 21 interface at depth 4z, etc. Each image in the medium 1/2 interface is reduced in intensity by a factor k, the re?ec- tion coef?cient of the interface. (There is no reduction in intensity of images in the medium 1/air interface, as its re?ection coef?cient is unity.)A consequence of the pro- gressive reduction in intensity is that only a few images have to be considered in arriving at a reasonable estimate of the potential at point P. Table 8.1 summarizes this The potential V at point P is the sum of the contribu- P tions of all sources. Employing equation (8.6)

    Ir 2kIr 2k2Ir 2kir P 2pr 2pr 2pr 2pr 012i

    Thus Electrical Surveying 189 Ir Ê 1 · kn ^ V = 1 Á + 2Â ~ (8.13) P 2p Ë r r ¯ 0 n =1 n

    where 2 r = r2+(2nz) n0 The ?rst term in the brackets of equation (8.13) refers to the normal potential pertaining if the subsurface were homogeneous, and the second term to the disturbing potential caused by the interface. The series is conver- gent as the dimming factor, or re?ection coef?cient, k is less than unity (k = (r – r ) (r + r ), cf. Section 2121 Knowledge of the potential resulting at a single point from a single current electrode allows the computation of the potential difference DV between two electrodes, resulting from two current electrodes, by the addition and subtraction of their contribution to the potential at these points. For theWenner system with spacing a

    Ir DV = 1 (1 + 4F ) (8.14) 2pa

    where · F = Â kn ÊË 12 2 2 1^ – (8.15) n=1 1 + 4n z a 4 + 4n2z2 a2 ¯

    Relating this to the apparent resistivity r measured by a theWenner system (equation (8.10))

    r = r (1 + 4F ) (8.16) a1

    5.0 4.0 3.0 1 /? a ? 2.0 1.5 1.0 0.2 0.3 0.4 Field curve

    0.6 0.8 1.0 2.0 3.0 4.0 5.0 a/z 0 k= 0.8 0.6 0.4 .

    02 ?m 400 300 200 ? a 150 100 10 z 20 30 40 50 60 80 100 1

    dimensionless form for a number of values of the re?ec- tion coef?cient k by dividing the calculated apparent re- sistivity values r by the upper layer resistivity r (the a1 latter derived from the ?eld curve at electrode spacings approaching zero), and by dividing the electrode spacings a by the upper layer thickness z . The curves are plotted 1 on logarithmic paper, which has the effect of producing a more regular appearance as the ?uctuations of resistivity then tend to be of similar wavelength over the entire length of the curves. The ?eld curve to be interpreted is plotted on transparent logarithmic paper with the same modulus as the master curves. It is then shifted over the master curves, keeping the coordinate axes parallel, until a reasonable match is obtained with one of the master curves or with an interpolated curve.The point at which r /r = a/z = 1 on the master sheet gives the true values a1 of r and z on the relevant axes. r is obtained from the k- 11 2 Curve matching is simple for the two-layer case since only a single sheet of master curves is required. When three layers are present much larger sets of curves are required to represent the increased number of possible combinations of resistivities and layer thicknesses. Curve matching is simpli?ed if the master curves are arranged according to curve type (Fig. 8.9), and sets of master curves for both Wenner and Schlumberger electrode con?gurations are available (Orellana & Mooney 1966, 1972).The number of master curves required for full in- terpretation of a four-layer ?eld curve is prohibitively The interpretation of resistivity curves over multilay- ered structures may alternatively be performed by partial curve matching (Bhattacharya & Patra 1968).The method Fig. 8.11 The interpretation of a two-layer apparent resistivity graph by comparison with a set of master curves.The upper layer resistivity r is 68 W m and its thickness z is 11 150 200 m 19.5 m. (After Grif?ths & King 1981.)

    ? a Master 2 Master 1 Master 3 a 12 e ? 2 ? 1z 1 ? z e ? 3 Fig. 8.12 The technique of partial curve matching. A two-layer curve is ?tted to the early part of the graph and the resistivities r 1 and r and thickness z of the upper layer determined. r , r and 2 1 12 z are combined into a single equivalent layer of resistivity r and 1e thickness z , which then forms the upper layer in the e interpretation of the next segment of the graph with a second two-layer curve.

    involves the matching of successive portions of the ?eld curve by a set of two-layer curves. After each segment is ?tted the interpreted resistivities and layer thickness are combined by use of auxiliary curves into a single layer with an equivalent thickness z and resistivity r . This ee equivalent layer then forms the upper layer in the inter- pretation of the next segment of the ?eld curve with an- other two-layer curve (Fig. 8.12). Similar techniques are available in which successive use is made of three-layer master curves.

    I ? r z (r, ?, z ) The curve-matching methods have been almost completely superseded by more sophisticated interpre- tational techniques described below. Curve-matching methods might still be used, however, to obtain interpre- tations in the ?eld in the absence of computing facilities, or to derive an approximate model that is to be used as a Equation (8.13) represents the potential at the surface resulting from a single point of current injection over two horizontal layers as predicted by the method of im- ages. In general, however, the potential arising from any number of horizontal layers is derived by solution of Laplace’s equation (see Section 6.11). The equation in this case is normally represented in cylindrical coordi- nates as electrical ?elds have cylindrical symmetry with respect to the vertical line through the current source (Fig. 8.13). The solution and application of the relevant boundary conditions are complex (e.g. Koefoed 1979), but show that the potential V at the surface over a series of horizontal layers, the uppermost of which has a resis- tivity r , at a distance r from a current source of strength 1 I is given by rI · V = 1 Ú K (l ) J (lr ) dl (8.17) 0 2p 0

    l is the variable of integration. J (lr) is a specialized 0 function known as a Bessel function of order zero whose behaviour is known completely. K(l) is known as a ker- nel function and is controlled by the thicknesses and re- sistivities of the underlying layers. The kernel function can be built up relatively simply for any number of layers using recurrence relationships (Koefoed 1979) which pro- gressively add the effects of successive layers in the se- Electrical Surveying 191

    quence. A useful additional parameter is the resistivity transform T(l) de?ned by

    T (l ) = r K (l ) (8.18) i ii

    where T (l) is the resistivity transform of the ith layer i ii T(l) can similarly be constructed using recurrence By methods analogous to those used to construct equation (8.16), a relationship between the apparent resistivity and resistivity transform can be derived. For example, this relationship for aWenner spread with elec- trode spacing a is

    layered model derived by an approximate interpretat- ion method in order to improve the correspondence In addition to this indirect modelling there are also a number of direct methods of interpreting resistivity data which derive the layer parameters directly from the ?eld pro?les (e.g. Zohdy 1989). Such methods usually involve the following steps: 1. Determination of the resistivity transform of the ?eld 2. Determination of the parameters of the upper layer by ?tting the early part of the resistivity transform curve 3. Subtraction of the effects of the upper layer by reduc- ing all observations to the base of the previously deter- mined layer by the use of a reduction equation (the inverse Steps 2 and 3 are then repeated so that the parameters of successively deeper layers are determined. Such methods suffer from the drawback that errors increase with depth so that any error made early in the interpre- tation becomes magni?ed. The direct interpretation methods consequently employ various techniques to The indirect and direct methods described above have now largely superseded curve-matching techniques and Interpretation of VES data suffers from non- uniqueness arising from problems known as equivalence van Overmeeren 1989) is illustrated by the fact that identical bell-shaped or basin-shaped resistivity curves Identical bell-shaped curves are obtained if the product of the thickness z and resistivity r, known as the trans- For basin-shaped curves the equivalence function of the middle layer is z/r, known as the longitudinal conduc- tance. The problem of suppression applies to resistivity curves in which apparent resistivity progressively in- creases or decreases as a function of electrode spacing (Fig. 8.9(b)). In such cases the addition of an extra inter- mediate layer causes a slight horizontal shift of the curve without altering its overall shape. In the interpretation of relatively noisy ?eld data such an intermediate layer may It is the conventional practice in VES interpretation to make the assumption that layers are horizontal and isotropic. Deviations from these assumptions result in errors in the ?nal interpretation.

    C 4 C 2 ? C 0 C 1 C 3 C 5 The sources C –C are successive images of the primary source C 15 0 in the interface and the surface.The sources lie on a circle centred on the outcrop of the interface, and their number is dependent upon the magnitude of the dip of the interface, q.

    The assumption of isotropy can be incorrect for indi- vidual layers. For example, in sediments such as clay or shale the resistivity perpendicular to the layering is usu- Anisotropy cannot be detected in subsurface layers dur- ing vertical electrical sounding and normally results in too large a thickness being assigned to the layers. Other anisotropic effects are depth-dependent, for example the reduction with depth of the degree of weathering, and the increase with depth of both compaction of sediments and salinity of pore ?uids.The presence of a vertical con- tact, such as a fault, gives rise to lateral inhomogeneity which can greatly affect the interpretation of an electri- If the layers are dipping, the basic theory discussed above is invalid. Using the optical analogue, the number of images produced by a dipping interface is ?nite, the images being arranged around a circle (Fig. 8.14). Be- cause the intensity of the images progressively decreases, only the ?rst few need to be considered in deriving a reasonable estimate of the resulting potential. Conse- quently, the effect of dip can probably be ignored for in- clinations up to about 20°, which provide a suf?cient Topography can in?uence electrical surveys as Equipotential surfaces are thus distorted and anomalous readings can result.

    Electrical Surveying 193 (a) 0 N 1 2 3 4 5 6 Tunnel route survey 60 120 180 240 300 360 420 480 m

    Measured apparent resistivity in ? m Electrode spacing = 25 m Iteration 5 completed with 7.4% RMS error Borehole (b) 0 60 120 180 240 300 360 420 480 m Depth (m) 25

    50 75 Clay Microdiorite Model resistivity in ? m 16 32 64 128 ? m Fig. 8.15 (a) Contoured apparent resistivity pseudosection measured along the route of a proposed tunnel. (b) Electrical image and depths to bedrock determined in four boreholes. (After Barker 1997.)

    VES data from several soundings can be presented in the form of a pseudosection (Section 8.3.3) and it is now possible to invert the data into a full, two-dimensional geoelectric model (e.g. Loke & Barker 1995, 1996) rather than a sequence of discrete, unidimensional geo- electric sections. This technique is known as electrical imaging or electrical tomography. An example of elec- trical imaging illustrating how a pseudosection can be transformed into a geoelectric structure is given in Fig. 8.15. Cross-borehole tomography can also be If electrode spreads are arranged in parallel, many 2D pseudosections can be determined that can be combined into a 3D model.

    (a) cXXXXXXXXX pXXXXXXXXX pXXXXXXXXX cXXXXXXXXX c = current electrode p = potential electrode Plan

    XXXXXXXXX ?? 12 Section ? 1 ? a ? 2 Distance (b) ? 1 ? a ? 2

    Distance cppc ? 1? 2 Fig. 8.16 (a) A transverse traverse across a single vertical interface. (b) A longitudinal traverse across a single vertical interface (After Parasnis 1973.)

    longitudinal traversing across a series of faulted strata in Illinois, USA. Both sets of results illustrate well the strong resistivity contrasts between the relatively con- A vertical discontinuity distorts the direction of cur- rent ?ow and thus the overall distribution of potential in its vicinity. The potential distribution at the surface can be determined by an optical analogue in which the dis- continuity is compared with a semitransparent mirror which both re?ects and transmits light. Referring to Fig. 8.18, current I is introduced at point C on the sur- Longitudinal traverse Transverse traverse ? a

    0 500 m Distance Shear zone Lime.

    Fig. 8.17 Longitudinal and transverse traverses across a series of faulted strata in Illinois, USA. (After Hubbert 1934.)

    I kI

    C C’ r 3 r 1r 2 P’

    P ? 1? 2 Fig. 8.18 Parameters used in the calculation of the potential due to a single surface current electrode on either side of a single vertical interface.

    face of a medium of resistivity r in the vicinity of a ver- 1 2 In the optical analogue, a point P on the same side of the mirror as the source would receive light directly and via a single re?ection. In the latter case the light would appear to originate from the image of C in the mirror, C¢, and would be decreased in intensity with respect to the source by a factor corresponding to the re?ection co- ef?cient. Both the electric source and its image con- tribute to the potential V at P, the latter being decreased P in intensity by a factor k, the re?ection coef?cient. From equation (8.6)

    Ir Ê 1 k ^ V = 1 + (8.20) P 2p Ë r r ¯ 12

    (a) 300 (? m) a ? 100 Fig. 8.19 (a)The observedWenner 0 resistivity pro?le over a shale-?lled sink of known geometry in Kansas, USA. (b)The m (After Cook &Van Nostrand 1954.) 15 (b)

    0 Electrical Surveying 195 100 m Alluvium 50 Limestone 250 ?m Shale

    source, the optical analogue indicates that light would be received only after transmission through the mirror, re- sulting in a reduction in intensity by a factor correspond- ing to the transmission coef?cient.The only contributor to the potential V at P¢ is the current source reduced in P¢ intensity by the factor (1 – k). From equation (8.6) I (1 – k)r V = 2 (8.21) P¢ 2pr 3

    Equations (8.20) and (8.21) may be used to calculate the measured potential difference for any electrode spread between two points in the vicinity of the interface and thus to construct the form of an apparent resistivity pro?le produced by longitudinal constant separation traversing. In fact, ?ve separate equations are required, corresponding to the ?ve possible con?gurations of a The method can also be used to construct apparent resis- tivity pro?les for constant separation traversing over a number of adjacent discontinuities. Albums of master curves are available for single and double vertical con- Three-dimensional resistivity anomalies may be ob- tained by contouring apparent resistivity values from a number of CST lines. The detection of a three- dimensional body is usually only possible when its top is close to the surface, and traverses must be made directly over the body or very near to its edges if its anomaly is to Three-dimensional anomalies may be interpreted by laboratory modelling. For example, metal cylinders, blocks or sheets may be immersed in water whose resis- tivity is altered by adding various salts and the model moved beneath a set of stationary electrodes. The shape Plan

    mapping equipotential lines (lines joining the electrodes when the indicated potential difference is zero). The method provides much more information on the extent, dip, strike and continuity of the body than the normal CST techniques. An example of the delineation of a massive sulphide body by the mise-à-la-masse method is given in Bowker (1991).

    8.2.9 Limitations of the resistivity method Resistivity surveying is an ef?cient method for delineat- ing shallow layered sequences or vertical discontinuities involving changes of resistivity. It does, however, suffer from a number of limitations: 1. Interpretations are ambiguous. Consequently, independent geophysical and geological controls are necessary to discriminate between valid alternative 2. Interpretation is limited to simple structural con?gu- rations. Any deviations from these simple situations may 3. Topography and the effects of near-surface resistivity 4. The depth of penetration of the method is limited by the maximum electrical power that can be introduced into the ground and by the physical dif?culties of laying out long lengths of cable. The practical depth limit for most surveys is about 1 km.

    8.2.10 Applications of resistivity surveying Resistivity surveys are usually restricted to relatively small-scale investigations because of the labour involved in physically planting the electrodes prior to each measurement. For this reason resistivity methods are not commonly used in reconnaissance exploration. It is probable, however, that with the increasing availability of non-contacting conductivity measuring devices (see Resistivity methods are widely used in engineering geological investigations of sites prior to construction (Barker 1997).VES is a very convenient, non-destructive method of determining the depth to rockhead for foun- dation purposes and also provides information on the degree of saturation of subsurface materials. CST can be used to determine the variation in rockhead depth between soundings and can also indicate the presence of potentially unstable ground conditions. Figure 8.21 shows a CST pro?le which has revealed the presence of a buried mineshaft from the relatively high resistivity val- 400

    300 Apparent resistivity (?m) 200 100 0 10 20 m

    Fig. 8.21 CST resistivity pro?le across a buried mineshaft. (After Aspinall &Walker 1975.)

    36 26 36 Apparent resistivity (?m) 26 36 26 0 10 20 m

    Electrical Surveying 197 Fig. 8.23 Simpli?ed geology and freshwater lenses of Grand Cayman. (After Bugg & Lloyd 1976.)

    ? (? m) 30.5 a 305 (a) (b) 762 ?m WT ?m Fre 359 500 ppm Salinity profile wa 1 Metres 5

    10 15 20 25 30 48 ? m Transition Zone Saline (c) sh ter

    Fig. 8.24 (a) Vertical electrical sounding adjacent to a test borehole in the Central Lens, Grand Cayman. (b) Layered model interpretation of theVES. (c) Interpreted salinity pro?le. (After Bugg & Lloyd 1976.)

    number of exploratory boreholes required for both essential aquifer tests and control of the geophysical The resistivity method was used by Bugg and Lloyd (1976) to delineate freshwater lenses in Grand Cayman Island off the northern Caribbean (Fig. 8.23). Because of N 81°20′ 81°25′

    19°25′ Bluff Limestone Formation Ironshore Formation Fresh water lenses 1 Lower Valley Lens 2 Central Lens 3 East End Lens

    19°20′ 2 3

    1 0 4 km its relatively low density, fresh water tends to ?oat on the denser saline water which penetrates the limestone sub- strate of the island from the sea. Figure 8.24 shows a ?uid conductivity pro?le from a borehole sunk in the Central Lens compared with the results of a VES interpretation from a sounding adjacent to the borehole. It is apparent that fresh water can be distinguished from saline water by its much higher resistivity.The resistivity survey took the form of a series of VES which were interpreted using the sounding by the borehole as control. Contours on the base of the Central Lens, de?ned from these inter- pretations, are shown in Fig. 8.25. A similar investigation using resistivity to investigate the intrusion of saline Resistivity surveys can also be used to locate and mon- itor the extent of groundwater pollution. Merkel (1972) described the use of this technique in the delineation of contaminated mine drainage from old coal workings in Pennsylvania, USA. Figure 8.26 shows a geoelectric sec- tion across part of the area, constructed from a series of VES, and its geological interpretation which indicates that no pollution is present. Figure 8.27 shows a further geoelectric section from an adjacent area in which acid mine drainage has increased the conductivity of the groundwater, allowing its delineation as a band of low re- sistivity. FurtherVES enabled the extent of the pollution to be de?ned. Since contamination of this type is associ- ated with a signi?cant change in resistivity, periodic mea- surements at electrodes sited in a borehole penetrating the water table could be used to monitor the onset of pol- lution and the degree of contamination. Ebraheem et al.

    N 0 1 km Test Borehole –6 –9 –12 –3 –15 Swamp Fresh water lens Offshore reef Resistivity expansion centres –6 Depth in m below M.S.L.

    Test Borehole Fig. 8.25 Con?guration of base of Central Lens, Grand Gayman. (After Bugg & Lloyd 1976.)

    N S 180 92 230 260 300 374 290 150 300 200 776 870 400 240 276 300 210 200 150 146 450 28

    0 10 m Coal Shale, clay, claystone Fig. 8.26 Geoelectric section and geological interpretation of a pro?le near Kylertown, Pennsylvania. Numbers refer to resistivity in ohm m. (After Merkel 1972.)

    (1990) have also described how the resistivity method can be used to study acid mine drainage and, in a similar envi- ronmental context, Carpenter et al. (1991) have reported the use of repeated resistivity measurements to monitor the integrity of the cover of a land?ll site in Chicago.

    8.3 Induced polarization (IP) method 8.3.1 Principles When using a standard four-electrode resistivity spread in a DC mode, if the current is abruptly switched off, the voltage between the potential electrodes does not drop to zero immediately. After a large initial decrease the voltage suffers a gradual decay and can take many sec- onds to reach a zero value (Fig. 8.28). A similar phenom- enon is observed as the current is switched on. After an initial sudden voltage increase, the voltage increases gradually over a discrete time interval to a steady-state value.The ground thus acts as a capacitor and stores elec- If, instead of using a DC source for the measurement ofresistivity,avariablelow-frequencyACsourceisused, it is found that the measured apparent resistivity of the subsurface decreases as the frequency is increased.This is because the capacitance of the ground inhibits the pas- sage of direct currents but transmits alternating currents The capacitive property of the ground causes both the transient decay of a residual voltage and the variation of apparent resistivity as a function of frequency. The two effects are representations of the same phenomenon in the time and frequency domains, and are linked by Fourier transformation (see Chapter 2). These

    Fig. 8.28 The phenomenon of induced polarization. At time t the current is 0 switched off and the measured potential difference, after an initial large drop from the steady-state value DV , decays gradually c to zero. A similar sequence occurs when the current is switched on at time t . A 3 represents the area under the decay curve 12 Potential difference ?V c A Electrical Surveying 199

    two manifestations of the capacitance property of the ground provide two different survey methods for the The measurement of a decaying voltage over a certain time interval is known as time-domain IP surveying. Mea- surement of apparent resistivity at two or more low AC frequencies is known as frequency-domain IP surveying.

    8.3.2 Mechanisms of induced polarization Laboratory experiments indicate that electrical energy is stored in rocks mainly by electrochemical processes.This The passage of current through a rock as a result of an externally imposed voltage is accomplished mainly by electrolytic ?ow in the pore ?uid. Most of the rock- forming minerals have a net negative charge on their outer surfaces in contact with the pore ?uid and attract positive ions onto this surface (Fig. 8.29(a)). The con- centration of positive ions extends about 100 mm into the pore ?uid, and if this distance is of the same order as the diameter of the pore throats, the movement of ions in the ?uid resulting from the impressed voltage is inhib- ited. Negative and positive ions thus build up on either side of the blockage and, on removal of the impressed voltage, return to their original locations over a ?nite This effect is known as membrane polarization or elec- trolytic polarization. It is most pronounced in the presence The effect decreases with increasing salinity of the pore When metallic minerals are present in a rock, an Figure 8.29(b) shows a rock in which a metallic mineral

    Time tt t t 01 2 3

    (a) –––– ++++ ++ ++ +++– ––– Rock – – –++ ––+ + + – – Pore +– –+ –++ –– (b)

    Rock – +– +++–?+ –– Pore ++–+–– +– Mineral grain Fig. 8.29 Mechanisms of induced polarization: (a) membrane polarization and (b) electrode polarization.

    grain blocks a pore, When a voltage is applied to either side of the pore space, positive and negative charges are imposed on opposite sides of the grain. Negative and positive ions then accumulate on either side of the grain which are attempting either to release electrons to the grain or to accept electrons conducted through the grain. The rate at which the electrons are conducted is Consequently, ions accumulate on either side of the grain and cause a build-up of charge. When the im- pressed voltage is removed the ions slowly diffuse back to their original locations and cause a transitory decaying This effect is known as electrode polarization or overvolt- age.All minerals which are good conductors (e.g. metallic The magnitude of the electrode polarization effect de- pends upon both the magnitude of the impressed voltage and the mineral concentration. It is most pronounced when the mineral is disseminated throughout the host rock as the surface area available for ionic–electronic interchange is then at a maximum. The effect decreases with increasing porosity as more alternative paths be- In prospecting for metallic ores, interest is obviously Membrane polarization, however, is indistinguishable from this effect during IP measurements. Membrane polarization consequently reduces the effectiveness of IP surveys and causes geological `noise’ which may be equivalent in magnitude to the overvoltage effect of a rock with up to 2% metallic minerals.

    8.3.3 Induced polarization measurements Time-domain IP measurements involve the monitoring The most commonly measured parameter is the charge- ability M, de?ned as the area A beneath the decay curve over a certain time interval (t –t ) normalized by the 12 steady-state potential difference DV (Fig. 8.28) c 1 Resistive region

    ? a 2 Warberg region Electromagnetic 3 induction 10–1 1 101 102 103 Log current frequency

    Fig. 8.30 The relationship between apparent resistivity and log measuring current frequency.

    A1t M= = Ú2v(t)dt (8.22) DV DV t c c1

    and mineral concentration, IP measurements are usually made at frequencies at, or below, 10 Hz to remain in the Two measurements are commonly made.The percent- age frequency effect (PFE) is de?ned as

    (r – r ) PFE = 100 0.1 10 (8.23) r 10

    where r and r are apparent resistivities at measuring 0.1 10 frequencies of 0.1 and 10 Hz. The metal factor (MF) is de?ned as (r – r ) MF = 2p ¥ 105 0.1 10 (8.24) rr 0.1 10

    This factor normalizes the PFE with respect to the lower frequency resistivity and consequently removes, to a certain extent, the variation of the IP effect with the A common method of presenting IP measurements is the pseudosection, in which readings are plotted so as to re?ect the depth of penetration. Figure 8.31 illustrates how a pseudosection is constructed for the double- dipole array geometry illustrated in Fig. 8.33. Measured values are plotted at the intersections of lines sloping at 45° from the centres of the potential and current elec- trode pairs.Values are thus plotted at depths which re?ect the increasing depth of penetration as the length of the di- VES resistivity data can also be presented in this way with the plotted depth proportional to the current electrode separation. Pseudosections give only a crude representa- tion of the IP response distribution at depth: for example, the apparent dip of the anomalous body is not always the same as the true dip. An example of this method of presentation is shown in Fig. 8.32.

    n=1 ?V n=2 ?V n=3 ?V n=4 ?V n=1 n=2 n=3 n=4 Fig. 8.31 The presentation of double-dipole IP results on a pseudosection. n represents the relative spacing between the current and potential electrode pairs.

    Electrical Surveying 201 8.3.4 Field operations IP equipment is similar to resistivity apparatus but uses a current about 10 times that of a resistivity spread; it is also rather more bulky and elaborate.Theoretically, any stan- dard electrode spread may be employed but in practice the double-dipole, pole–dipole and Schlumberger con- ?gurations (Fig. 8.33) are the most effective. Electrode spacings may vary from 3 to 300 m with the larger spacings used in reconnaissance surveys. To reduce the labour of moving current electrodes and generator, several pairs of current electrodes may be used, all con- nected via a switching device to the generator.Traverses are made over the area of interest plotting the IP reading at the mid-point of the electrode array (marked by Noise in an IP survey can result from several phenom- ena. Telluric currents cause similar anomalous effects to those encountered in resistivity measurements. Noise also results from the general IP effect of barren rocks caused by membrane polarization. Noise generated by the measuring equipment results from electromagnetic coupling between adjacent wires. Such effects are com- mon when alternating current is used since currents can be induced to ?ow in adjacent conductors. Conse- quently, cables should be at least 10 m apart and if they must cross they should do so at right angles to minimize electromagnetic induction effects.

    ? a 340 140 126 106 90 800 200 485 365 332 252 954 208 84 193 165 211 306 248 384 350 320 342 333 105 108 287 320 94 285 248 550 323 353 368 144 116 535 159 106 296 312 550 350

    PFE 0.8 2 4.9 3.8 4.8 4.5 3.8 3.6 2.4 2.6 1 1.1 2.4 4.6 3.9 4 6.5 6.7 4.5 3.4 2.6 2.2 1.8 1.8 5 3.2 1.3 5.8 8.5 6.3 3.5 3.6 2.8 2.4 2.4 2.9 2.8 4.7 6.5 10.2 5.3 4.1 3.2 3.4

    MF 2.2 14 38 36 53 5.6 19 7.5 6.6 7.9 3.6 1.2 12 55 20 24 31 18 8.8 7.4 6.9 3.8 22 5.4 47 30 13 18 91 22 14 6.6 6.7 6.4 20 24 8.7 40 96 18 13 5.9 9.7

    Barren porphyry 0/B Economic sulphides >5% Pyrite minor chalco <3% 0 100 ft

    a na a ?V Plotting point Fig. 8.32 Pseudosections of apparent resistivity ( r ), percentage frequency effect a (PFE) and metal factor parameter (MF) for a double-dipole IP traverse across a zone of massive sulphides whose shape is known from subsequent test drilling. Current and potential electrode spacing a was 100 feet (30.5 m). Frequencies used for the IP measurements were 0.31 and 5.0 Hz. (After Fountain 1972.)

    economic importance, for example water-?lled shear zones and graphite-bearing sediments can both generate strong IP effects. Field operations are slow and the method is consequently far more expensive than most other ground geophysical techniques, survey costs being comparable with those of a gravity investigation.

    X cc pp Double-dipole c

    X c pp Pole – dipole

    X c pp c Schlumberger c = current electrode p = potential electrode X = reading plotted

    Fig. 8.33 Electrode con?gurations used in induced polarization measurements.

    20 Chargeability (ms) 10 0 0 100 m M ? a 2000

    1000 Apparent resistivity (?m) 0 Fault Devonian (Old Red Sandstone) Carboniferous dolomitic limestone

    1–2 0.5 –1 0.25 – 0.5 % Cu Fig. 8.34 Time-domain IP pro?le using a pole–dipole array over the Gortdrum copper–silver body, Ireland. (After Seigel 1967.)

    corresponding apparent resistivity pro?le re?ects the large resistivity contrast between the Old Red Sandstone and dolomitic limestone but gives no indication of the 8.35 which shows a traverse over a copper porphyry body in British Columbia, Canada. IP and resistivity traverses were made at three different electrode spacings of a pole–dipole array.The CST results exhibit little vari- ation over the body, but the IP (chargeability) pro?les Electrical Surveying 203

    clearly show the presence of the mineralization, allow its limits to be determined and provide estimates of the depth to its upper surface.

    8.4 Self-potential (SP) method 8.4.1 Introduction The self-potential (or spontaneous polarization) method is based on the surface measurement of natural potential differences resulting from electrochemical re- actions in the subsurface.Typical SP anomalies may have an amplitude of several hundred millivolts with respect to barren ground. They invariably exhibit a central negative anomaly and are stable over long periods of time.They are usually associated with deposits of metal- lic sulphides (Corry 1985), magnetite or graphite.

    8.4.2 Mechanism of self-potential Field studies indicate that for a self-potential anomaly to occur its causative body must lie partially in a zone of oxidation. A widely-accepted mechanism of self- potential (Sato & Mooney 1960; for a more recent analy- sis see Kilty 1984) requires the causative body to straddle the water table (Fig. 8.36). Below the water table elec- trolytes in the pore ?uids undergo oxidation and release electrons which are conducted upwards through the ore body. At the top of the body the released electrons cause reduction of the electrolytes. A circuit thus exists in which current is carried electrolytically in the pore ?uids and electronically in the body so that the top of the body acts as a negative terminal.This explains the negative SP anomalies that are invariably observed and, also, their stability as the ore body itself undergoes no chemical reactions and merely serves to transport electrons from depth. As a result of the subsurface currents, potential differences are produced at the surface.

    8.4.3 Self-potential equipment and survey procedure Field equipment consists simply of a pair of electrodes connected via a high-impedance millivoltmeter. The electrodes must be non-polarizing as simple metal spikes would generate their own SP effects. Non-polarizing electrodes consist of a metal immersed in a saturated so- The salt is contained in a porous pot which allows slow leakage of the solution into the ground.

    Array PPC 2115 10 ms 5 0 500 ? m 250 0 Chargeability aa a = 244m a = 122m Station x x a = 61m xxx x x x xx x xx x xx xx x x

    Resistivity x

    xx x xx xxxxxxx x xx xx x

    0 100m 1 1 1 Drill hole >0.50% Cu <0.50% Cu 11 2 Fault 1 2 1

    Surface – Electrons Water table Current + flow

    Negative ions Fig. 8.36 The mechanism of self-potential anomalies. (After Sato & Mooney 1960.) Station spacing is generally less than 30 m. Traverses may be performed by leapfrogging successive electrodes or, more commonly, by ?xing one electrode in barren ground and moving the other over the survey area.

    8.4.4 Interpretation of self-potential anomalies The interpretation of SP anomalies is similar to mag- Overburden Bethsaida granodiorite Skeena quartz diorite Mineralized Skeena quartz Fig. 8.35 Time domain induced polarisation and diorite – pyrite, chalcopyrite, resistivity pro?les over a copper porphyry body in bornite British Columbia, Canada. (After Seigel 1967.)

    0 –40 Self-potential anomaly (mV) –80 –120 Fig. 8.37 The SP anomaly over a sulphide ore body at Sariyer,Turkey. (AfterYüngül 1954.) Electrical Surveying

    0 25 m V Schist V V V VVVVV V V VV VV V Sulphide V VVV VV VVVV VVV V Andesite V V 205

    180 m 150 120 posits when used in conjunction with magnetic, electro- Figure 8.37 shows the SP pro?le over a sulphide ore magnetic and geochemical techniques. It has also been body inTurkey which contains copper concentrations of used in hydrogeological investigations (e.g. Fournier up to 14%.The SP anomaly is negative and has an ampli- 1989), geothermal prospecting (Apostolopoulos et al. tude of some 140 mV. The steep topography has dis- 1997) and the detection of air-?lled drainage galleries placed the anomaly minimum downhill from the true (Ogilvy et al. 1991). location of the ore body.

    Problems 1. Using the method of electrical images, derive the relationship between apparent resistivity, electrode spacing, layer thicknesses and resistiv- ities for a VES performed with a Schlumberger spread over a single horizontal interface 12 2. At locations A, B, C and D along the gravity pro?le shown in Fig. 8.38, VES were performed with a Wenner array with the spread laid perpen- dicular to the pro?le. It was found that the sound- ing curves, shown in Fig. 8.39, were similar for locations A and B and for C and D. A borehole close to A penetrated 3 m of drift, 42 m of lime- stone and bottomed in sandstone. Downhole geophysical surveys (Chapter 11) provided the values of resistivity (r ) and density (r ) shown in RD the table for the lithologies encountered.

    10 8 6 4 Bouguer anomaly (gu) 2 0 0 200 400 600 800 1000 Distance (m) AB CD

    Fig. 8.38 Gravity anomaly pro?le pertaining to Question 2 Unit r (W m) r (Mg m-3) RD Drift 40 2.00 Limestone 2000 2.75 Sandstone 200 2.40

    1000 800 600 400 200 (? m) ? a 100 80 60 40 20 10 A, B C, D 1 2 4 6 8 10 20 40 60 80 100 200 a (m)

    Fig. 8.39 Wenner VES sounding data for the locations shown A seismic refraction line near to D revealed 15 m of drift, although the nature of the underlying basement could not be assessed from the seismic (a) Interpret the geophysical data so as to pro- (b) What further techniques might be used to (c) If a CST were to be performed along the pro?le, select, giving reasons, a suitable elec- trode spacing to map the basement. Sketch the expected form of the CST for both longitudinal 3. Calculate the variation in apparent resistivity along a CST pro?le at right angles to a vertically faulted contact between sandstone and lime- stone, with apparent resistivities of 50 ohm m and 600 ohm m, respectively, for a Wenner con?gura- tion. What would be the effect on the pro?les if 4. Figure 8.40 shows a half-Schlumberger resis- tivity array in which the second current electrode is situated at a great distance from the other elec- trodes. Derive an expression for the apparent resistivity of this array in terms of the electrode The data in the table represent measurements taken with a half-Schlumberger array along a pro?le across gneissic terrain near Kongsberg, Norway. The potential electrode half-separation was kept constant at 40 m and the current elec- trode C was ?xed at the origin of the pro?le so 1 L

    C PP 1 12

    that as L (the current electrode half-separation) increased a CST was built up. R represents the re- sistance measured by the resistivity apparatus.

    L (m) R (W m) 30.2 1244.818 53.8 255.598 80.9 103.812 95.1 73.846 106.0 58.820 120.0 45.502 143.8 31.416 168.4 22.786 179.6 19.993 205.1 15.290 229.3 12.209 244.0 10.785

    Calculate the apparent resistivity for each In this region it is known that the gneiss can be extensively brecciated. Does the CST give any 5. The following table represents the results of a frequency-domain IP survey of a Precambrian shield area. A double-dipole array was used with the separation (x) of both the current electrodes and the potential electrodes kept constant at 60 m. n refers to the number of separations be- tween the current and potential electrode pairs and c to the distance of the centre of the array from the origin of the pro?le, where the results are plotted (Fig. 8.41). Measurements were taken using direct current and an alternating current of 10 Hz. These provided the apparent resistivities dc ac (a) For each measurement point, calculate the percentage frequency effect (PFE) and metal (b) For both the PFE and MF plot four pro?les for n = 1, 2, 3 and 4.

    Electrical Surveying 207 x nx x

    I ?V c + Fig. 8.41 The double-dipole electrode con?guration. See Question 5.

    (c) Construct and contour pseudosections of the (d) The area is covered by highly-conductive glacial deposits 30–60 m thick. It is possible that massive sulphide mineralization is present within the bedrock. Bearing this information in mind, comment upon and interpret the pro?les 6. Why are the electrical methods of exploration particularly suited to hydrogeological investiga- tions? Describe other geophysical methods which could be used in this context, stating the reasons why they are applicable.

    n=1 n=2 n=3 n=4 rrrrrrrr dc ac dc ac dc ac dc ac c (m) (W m) (W m) (W m) (W m) (W m) (W m) (W m) (W m) 0 49.8 49.6 101.5 100.9 30 72.8 72.4 99.6 98.5 60 46.0 45.8 86.2 85.2 90 61.3 60.6 90.0 86.1 120 42.1 41.7 72.8 70.1 150 55.5 54.4 57.5 53.5 180 44.0 43.5 49.8 46.6 210 53.6 51.1 47.9 44.0 240 42.1 41.8 44.0 41.4 270 65.1 64.1 47.9 44.9 300 49.8 49.6 95.8 91.7 330 82.3 81.3 132.1 129.4 360 51.7 51.3 114.9 114.1 390 86.2 85.9 164.7 164.0 420 49.8 49.6 120.7 120.1 450 78.5 78.0 170.4 169.7

    Further reading Bertin, J. (1976) Experimental andTheoretical Aspects of Induced Polar- Fink, J.B., McAlister, E.O. &Wieduwilt,W.G. (eds) (1990) Induced Polarization. Applications and Case Histories. Society of Explo- Grif?ths, D.H. & King, R.F. (1981) Applied Geophysics for Geologists Habberjam, G.M. (1979) Apparent Resistivity and the Use of Square Keller, G.V. & Frischnecht, F.C. (1966) Electrical Methods in Koefoed, O. (1968) The Application of the Kernel Function in Interpret- Koefoed, O. (1979) Geosounding Principles. I – Resistivity Sounding Kunetz, G. (1966) Principles of Direct Current Resistivity Prospecting. Gebrüder Borntraeger, Berlin.

    Marshall, D.J. & Madden,T.R. (1959) Induced polarisation: a study Milsom, J. (1989) Field Geophysics. Open University Press, Milton Parasnis, D.S. (1996) Principles of Applied Geophysics, 5th edn. Parkhomenko, E.I. (1967) Electrical Properties of Rocks. Plenum, Sato, M. & Mooney, H.M. (1960)The electrochemical mechanism Sumner, J.S. (1976) Principles of Induced Polarisation for Geophysical Telford, W.M., Geldart, L.P. & Sheriff, R.E. (1990) Applied Geo- In: Samis, C.G. & Henyey, T.L. (eds), Methods of Experimental Physics,Vol. 24, Part B – Field Measurements, 265–375. Academic Press, Orlando.

    9.1 Introduction Electromagnetic (EM) surveying methods make use of the response of the ground to the propagation of electro- magnetic ?elds, which are composed of an alternating electric intensity and magnetizing force. Primary elec- tromagnetic ?elds may be generated by passing alternat- ing current through a small coil made up of many turns of wire or through a large loop of wire. The response of the ground is the generation of secondary electromag- netic ?elds and the resultant ?elds may be detected by the alternating currents that they induce to ?ow in a re- The primary electromagnetic ?eld travels from the transmitter coil to the receiver coil via paths both above and below the surface.Where the subsurface is homoge- neous there is no difference between the ?elds propa- gated above the surface and through the ground other than a slight reduction in amplitude of the latter with respect to the former. However, in the presence of a conducting body the magnetic component of the electromagnetic ?eld penetrating the ground induces alternating currents, or eddy currents, to ?ow in the conductor (Fig. 9.1). The eddy currents generate their own secondary electromagnetic ?eld which travels to the receiver. The receiver then responds to the resultant of the arriving primary and secondary ?elds so that the response differs in both phase and amplitude from the response to the primary ?eld alone. These differences between the transmitted and received electromagnetic ?elds reveal the presence of the conductor and provide The induction of current ?ow results from the mag- netic component of the electromagnetic ?eld. Conse- quently, there is no need for physical contact of either transmitter or receiver with the ground. Surface EM sur- veys can thus proceed much more rapidly than electrical surveys, where ground contact is required. More impor- tantly, both transmitter and receiver can be mounted in aircraft or towed behind them. Airborne EM methods are widely used in prospecting for conductive ore bodies All anomalous bodies with high electrical conductiv- ity (see Section 8.2.2) produce strong secondary electro- magnetic ?elds. Some ore bodies containing minerals that are themselves insulators may produce secondary ?elds if suf?cient quantities of an accessory mineral with a high conductivity are present. For example, electro- magnetic anomalies observed over certain sulphide ores are due to the presence of the conducting mineral pyrrhotite distributed throughout the ore body.

    9.2 Depth of penetration of electromagnetic ?elds The depth of penetration of an electromagnetic ?eld (Spies 1989) depends upon its frequency and the electri- cal conductivity of the medium through which it is propagating. Electromagnetic ?elds are attenuated dur- ing their passage through the ground, their amplitude decreasing exponentially with depth. The depth of penetration d can be de?ned as the depth at which the amplitude of the ?eld A is decreased by a factor e-1 com- d pared with its surface amplitude A 0

    A = A e-1 d 0 (9.1)

    In this case 503.8 d = (9.2) sf

    Transmitter Primary EM field Receiver Surface Modified Secondary Eddy primary field currents field

    Conductor frequency used in an EM survey can be tuned to a desired depth range in any particular medium. For ex- ample, in relatively dry glacial clays with a conductivity of 5 ¥ 10-4 S m-1, d is about 225 m at a frequency of Empirically, an effective depth of penetration z can be e de?ned which represents the maximum depth at which a conductor may lie and still produce a recognizable elec- tromagnetic anomaly 100 ze ª (9.3) sf

    The relationship is approximate as the penetration de- pends upon such factors as the nature and magnitude of the effects of near-surface variations in conductivity, the geometry of the subsurface conductor and instru- mental noise. The frequency dependence of the depth Normally, very low frequencies are dif?cult to generate and measure and the maximum achievable penetration is usually of the order of 500 m.

    9.3 Detection of electromagnetic ?elds Electromagnetic ?elds may be mapped in a number of ways, the simplest of which employs a small search coil consisting of several hundred turns of copper wire wound on a circular or rectangular frame typically be- tween 0.5 m and 1 m across.The ends of the coil are con- nected via an ampli?er to earphones. The amplitude of the alternating voltage induced in the coil by an electro- Electromagnetic Surveying 209

    H p Fig. 9.2 The rotation of a search coil about an axis corresponding to the direction of arriving electromagnetic radiation H p producing an in?nite number of null positions.

    magnetic ?eld is proportional to the component of the ?eld perpendicular to the plane of the coil. Conse- quently, the strength of the signal in the earphones is at a maximum when the plane of the coil is at right angles to the direction of the arriving ?eld. Since the ear is more sensitive to sound minima than maxima, the coil is usu- ally turned until a null position is reached. The plane of the coil then lies in the direction of the arriving ?eld.

    Vertical H s ? H p Horizontal Fig. 9.3 The polarization ellipse and tilt-angle q. H and H ps represent the primary and secondary electromagnetic ?elds.

    search coil is rotated about three orthogonal axes until a null signal is obtained so that the plane of the coil lies in the plane of the polarization ellipse. The tilt-angle may then be determined by rotating the coil about a horizon- tal axis at right angles to this plane until a further mini- mum is encountered.

    9.4.1 Tilt-angle methods employing local transmitters In the case of a ?xed, vertical transmitter coil, the pri- mary ?eld is horizontal. Eddy currents within a subsur- face conductor then induce a magnetic ?eld whose lines of force describe concentric circles around the eddy cur- rent source, which is assumed to lie along its upper edge (Fig. 9.4(a)). On the side of the body nearest the trans- mitter the resultant ?eld dips upwards.The tilt decreases towards the body and dips downwards on the side of the body remote from the transmitter. The body is located directly below the crossover point where the tilt-angle is zero, as here both primary and secondary ?elds are hori- zontal.When the ?xed transmitter is horizontal the pri- mary ?eld is vertical (Fig. 9.4(b)) and the body is located where the tilt is at a minimum. An example of the use of tilt-angle methods (vertical transmitter) in the location If the conductor is near the surface both the amplitude and gradients of the tilt-angle pro?le are large. These quantities decrease as the depth to the conductor in- creases and may consequently be used to derive semi- quantitative estimates of the conductor depth. A vertical conductor would provide a symmetrical tilt-angle pro- ?le with equal gradients on either side of the body.As the inclination of the conductor decreases, the gradients on either side become progressively less similar. The asym- metry of the tilt-angle pro?le can thus be used to obtain Tilt-angle methods employing ?xed transmitters have been largely superseded by survey arrangements in which both transmitter and receiver are mobile and which can provide much more quantitative information on subsurface conductors. However, two tilt-angle methods still in common use are the very low-frequency (VLF) and audio-frequency magnetic ?eld (AFMAG) methods, neither of which requires the erection of a special transmitter.

    9.4.2 TheVLF method The source utilized by the VLF method is electromag- netic radiation generated in the low-frequency band of 15–25 kHz by the powerful radio transmitters used in Several stations using this frequency range are available around the world and transmit continuously either an unmodulated carrier wave or a wave with superimposed Morse code. Such signals may be used for surveying up to distances of several thousand kilometres from the At large distances from the source the electromag- The electric component E lies in a vertical plane and the magnetic component H lies at right angles to the direc- tion of propagation in a horizontal plane. A conductor that strikes in the direction of the transmitter is cut by the magnetic vector and the induced eddy currents produce a secondary electromagnetic ?eld. Conductors striking at right angles to the direction of propagation are not cut The basic VLF receiver is a small hand-held device in- corporating two orthogonal aerials which can be tuned to the particular frequencies of the transmitters. The di- rection of a transmitter is found by rotating the horizon- Traverses are then performed over the survey area at right angles to this direction. The instrument is rotated about a horizontal axis orthogonal to the traverse and the tilt recorded at the null position. Pro?les are similar in form to Fig. 9.4(a), with the conductor lying beneath lo- cations of zero tilt. See Hjelt et al. (1985) for a discussion of the interpretation of VLF data and Beamish (1998) for a means of three-dimensional modelling of VLF data.

    Electromagnetic Surveying 211 (a) +20 S ?0 R ? S P P Surface ?P S –20

    (b) 90 ? 60 R Current concentration Ore ? = tilt P = primary S = secondary R = resultant

    S S Surface Fig. 9.4 Tilt-angle pro?les resulting from (a) vertical and (b) horizontal transmitter loops. (After Parasnis 1973.)

    Outcrop of 0 100m massive sulphide

    50 0 50 Tilt Transmitter ? S R N Fig. 9.5 Example of tilt-angle survey using a vertical loop transmitter. (After Parasnis 1973.) R P ? R P

    Current concentration Ore ? P Modern instruments have three coils with their axes at right angles. They can thus detect the signal whatever its direction, and ?nd the null orientation electronically and automatically. Some instruments will measure signals from two or more transmitters si- multaneously. In this case transmitters are chosen whose signals arrive in the survey area at very different The VLF method has the advantages that the ?eld equipment is small and light, being conveniently oper- ated by one person, and that there is no need to install a transmitter. However, for a particular survey area, there may be no suitable transmitter providing a mag- netic vector across the geological strike. A further disad- vantage is that the depth of penetration is somewhat less than that attainable by tilt-angle methods using a local transmitter. The VLF method can be used in airborne EM surveying.

    VLF field 9.4.3 The AFMAG method Antenna Magnetic vector Electric vector

    The AFMAG method (Labson et al. 1985) can similarly be used on land or in the air.The source in this case is the natural electromagnetic ?elds generated by thunder- storms and known as sferics. Sferics propagate around the This space constitutes an ef?cient electromagnetic waveguide and the low attenuation means that thunder- storms anywhere in the world make an effective contri- bution to the ?eld at any given point. The ?eld also penetrates the subsurface where, in the absence of electrically-conducting bodies, it is practically horizon- tal. The sferic sources are random so that the signal is The AFMAG receiver differs from conventional tilt- angle coils since random variations in the direction and intensity of the primary ?eld make the identi?cation of minima impossible with a single coil. The receiver con- sists of two orthogonal coils each inclined at 45° to the horizontal (Fig. 9.7). In the absence of a secondary ?eld the components of the horizontal primary ?eld perpen- dicular to the coils are equal and their subtracted output is zero (Fig. 9.7(a)). The presence of a conductor gives rise to a secondary ?eld which causes de?ection of the resultant ?eld from the horizontal (Fig. 9.7(b)).The ?eld components orthogonal to the two coils are then un- equal, so that the combined output is no longer zero and the presence of a conductor is indicated. The output On land both the azimuths and tilts of the resultant electromagnetic ?eld can be determined by rotating the coils about a vertical axis until a maximum signal is ob- In the air, azimuths cannot be determined as the coils are Dashed lines show a tabular conductor striking towards the antenna which is cut Direction of by the magnetic vector of the propagation electromagnetic ?eld.

    (a) (b)

    45 450 =/ 0

    Fig. 9.7 Principle of AFMAG receiver: (a) conductor absent, attached to the aircraft so that their orientation is con- trolled by the ?ight direction. Consequently, only per- turbations from the horizontal are monitored along the ?ight lines.The output signal is normally fed into an ampli?er tuned to two frequencies of about 140 and 500 Hz. Comparison of the amplitudes of the signals at the two frequencies provides an indication of the con- ductivity of the anomalous structure as it can be shown that the ratio of low-frequency response to high- frequency response is greater than unity for a good con- The AFMAG method has the advantage that the fre- quency range of the natural electromagnetic ?elds used extends to an order of magnitude lower than can be pro- duced arti?cially so that depths of investigation of sev- eral hundred metres are feasible.

    (a)2? ? (b) P = primary R S = secondary R = resultant S S cos ?

    ? P S sin ? (b)Vector diagram illustrating the phase and amplitude relationships between primary, secondary and resultant electromagnetic ?elds.

    cheap and the technique is rapid to employ. However, they provide little quantitative information on the con- ductor. More sophisticated EM surveying systems mea- sure the phase and amplitude relationships between The various types of system available are discussed in An alternating electromagnetic ?eld can be repre- sented by a sine wave with a wavelength of 2p (360°) (Fig. 9.8(a)). When one such wave lags behind another the waves are said to be out-of-phase. The phase differ- ence can be represented by a phase angle q correspond- ing to the angular separation of the waveforms. The phase relationships of electromagnetic waves can be rep- resented on special vector diagrams in which vector length is proportional to ?eld amplitude and the angle measured counterclockwise from the primary vector to the secondary vector represents the angular phase lag of The primary ?eld P travels directly from transmitter to receiver above the ground and suffers no modi?cation other than a small reduction in amplitude caused by geo- metric spreading. As the primary ?eld penetrates the ground it is reduced in amplitude to a greater extent but remains in phase with the surface primary. The primary ?eld induces an alternating voltage in a subsurface conductor with the same frequency as the primary but with a phase lag of p/2 (90°) according to the laws of electromagnetic induction. This may be represented on the vector diagram (Fig. 9.8(b)) by a vector p/2 counter- clockwise to P.

    Electromagnetic Surveying 213 The electrical properties of the conductor cause a further phase lag f,

    f = tan -1Ê 2pfL ^ Ë r ¯ (9.4)

    Compensator + Generator decomposer Re + Im Cable 30 – 100 m Transmitter Receiver Fig. 9.9 Mobile transmitter–receiver EM ?eld equipment.

    into real and imaginary components which are usually displayed as a percentage of the primary ?eld whose magnitude is relayed via the interconnecting cable. Tra- verses are generally made perpendicular to geological strike and readings plotted at the mid-point of the sys- tem. The maximum detection depth is about half the Fieldwork is simple and requires a crew of only two or three operators.The spacing and orientation of the coils is critical as a small percentage error in spacing can pro- duce appreciable error in phase measurement. The coils must also be kept accurately horizontal and coplanar as small relative tilts can produce substantial errors.The re- quired accuracy of spacing and orientation is dif?cult to Figure 9.10 shows a mobile transmitter–receiver EM pro?le across a sheet-like conductor in the Kankberg area of northern Sweden. A consequence of the coplanar horizontal coil system employed is that conducting bodies produce negative anomalies in both real and imaginary components with maximum ampli- tudes immediately above the conductor.The asymmetry of the anomalies is diagnostic of the inclination of the body, with the maximum gradient lying on the downdip side. In this case the large ratio of real to imaginary com- ponents over the ore body indicates the presence of a very good conductor, while a lesser ratio is observed over a sequence of graphite-bearing phyllites to the north.

    Electromagnetic Surveying 215 +20% 0 –20% Imaginary Real SN BH BH BH Moraine BH Fig. 9.10 Mobile transmitter–receiver Phyllites pro?le, employing horizontal coplanar Precambrian coils with a separation of 60 m and an volcanics operating frequency of 3.6 kHz, in the Kankberg area, north Sweden. Real and imaginary components are expressed as a 0 100 m percentage of the primary ?eld. (After Parasnis 1973.) Ore Impregnation V

    1 2 3 4 5 6 t t t t t t Time 123456

    Fig. 9.11 The quanti?cation of a decayingTDEM response by measurement of its amplitude in a number of channels (1–6) at increasing times (t ) after primary ?eld cut-off.The amplitudes 1–6 of the responses in the different channels are recorded along a pro?le.

    TDEM (Frischnecht & Raab 1984). Only short offsets of transmitter and receiver are necessary and the array therefore crosses a minimum of geological boundaries such as faults and lithological contacts. By contrast,VES or continuous-wave EM methods are much more affect- ed by near-surface conductivity inhomogeneities since long arrays are required. It is claimed that penetration of An example of a surface application of TDEM is pre- sented in Fig. 9.12, which shows the results of a survey undertaken near Mount Minza, Northern Territory, Australia (Duckworth 1968, see also Spies 1976). The target, which had been revealed by other geophysical methods (Fig. 9.13), was a band of highly-conductive graphitic black shale, which has a conductivity in excess of 0.1 S m-1 in its pristine condition. In Fig. 9.12 the TDEM response is expressed in terms of the induced voltage in the loop e(t) normalized with respect to the current in the transmitter loop I. The response is shown The response persists into the latest channels, indicating the presence of a good conductor which corresponds to the graphitic shale. The asymmetry of the response curves and their variation from channel to channel al- lows the dip of the conductor to be estimated. The ?rst channel, which logs the response to relatively shallow depths, peaks to the right. The maximum moves to the left in later channels, which give the response to progres- sively greater depths, indicating that the conductor dips An example of a survey using a borehole TDEM system is presented in Fig. 9.14, which shows results from the Single Tree Hill area, NSW, Australia (Boyd & Wiles 1984). Here semi-massive sulphides (pyrite and pyrrhotite), which occur in intensely sericitized tuffs with shale bands, have been penetrated by three drill- holes.TheTDEM responses at a suite of times after pri- mary ?eld cut-off, recorded as the receiver was lowered down the three drillholes, are shown. In hole PDS1, the response at early times indicates the presence of a con- ductor at a depth of 145 m.The negative response at later times at this depth is caused by the diffusion of eddy cur- rents into the conductor past the receiver and indicates that the hole is near the edge of the conductor. In holes DS1 and DS2 the negative responses at 185 m and 225 m, respectively, indicate that the receiver passed outside, but near the edges of, the conductor at these depths. Also shown in the section is an interpretation of the TDEM data in terms of a model consisting of a rectangular current-carrying loop.

    Transient decay curve over peak of anomaly (447E) µV A 1000 500 e(t) I Response 100 50

    10 1000 500 0 500 0 µV A e(t) 200 0 I Response 200 0 100 0 100 0

    100 0 0.5 1.0 2 3 45681015 Time t (ms) t = 1.1 ms t = 2.3 ms

    t = 4.1 ms t = 6.1 ms t = 8.2 ms t = 10.1 ms t = 15.3 ms 436E 438 440 442 444 446 448 450 452 454 456E Undifferentiated Weathered zone in shale conducting shale 0 200 m

    Hematitic quartz breccia Quartzite Black shale Brecciated banded ironstone Tremolitic siltstone Limestone Diamond-drill hole Conducting shale

    Fig. 9.12 TDEM pro?les and geological section near Mount Minza,NorthernTerritory,Australia.(AfterDuckworth1968.)

    9.7 Non-contacting conductivity measurement It is possible to obtain readings of ground conductivity by EM measurements (McNeill 1980). Measurements of this type can be made using standard resistivity methods (see Section 8.2), but, since these require the introduc- tion of current into the ground via electrodes, they are labour intensive, slow and therefore costly. Moreover, resistivity measurements are in?uenced by geological noise arising from near-surface resistivity variations which limit the resolution that can be achieved. The more recently developed non-contacting conductivity meters utilize EM ?elds and do not suffer from these drawbacks. No ground contact is required so that mea- surements can be made at walking pace and the subsur- face volume sampled is averaged in such a way that The secondary EM ?eld measured in a mobile transmitter–receiver survey (Section 9.5) is generally a complex function of the coil spacing s, the operating fre- quency f and the conductivity of the subsurface s . How- ever, it can be shown that if the product of s and the skin depth d (Section 9.2), known as the induction number, is much less than unity, the following relationship results:

    H iwm ss2 s ª 0 (9.5) H4 p

    where H and H are the amplitudes of the secondary and sp primary EM ?elds, respectively, w = 2pf, m is the mag- ——0 netic permeability of vacuum, and i = ÷(-1), its presence Thus the ratio H /H is proportional to the ground con- sp ductivity s. Since d depends on the product s f, estima- tion of the maximum probable value of s allows the selection of f such that the above condition of low induc- tion number is satis?ed. The depth of penetration de- pends upon s and is independent of the conductivity distribution of the subsurface. Measurements taken at low induction number thus provide an apparent con- ductivity s given by a

    4H s = s (9.6) a wm s2 H 0p

    Electromagnetic Surveying 217 Fig. 9.13 Comparison of various geophysical 9.12 near Mount Minza, NorthernTerritory, Australia. (After Duckworth 1968.) Hematitic quartz breccia Quartzite 130 120 110 Real component (%) 100 90 80 70

    Black shale Brecciated banded ironstone Tremolitic siltstone Limestone Diamond-drill hole Conducting shale 30 20real 10 0 430E 434 438 450 456E imaginary10 Slingram, 1760 Hz 20 Imaginary component (%) 30

    1.6ratio24° 1.2 Turam, 660 Hz Reduced ratio 1.416° 8° 1.00° 440E 444 450 456E 0.8–8° 0.6phase difference–16° Phase difference –24°

    1.2 Turam, 220 Hz Reduced ratio 1.4Ratio16° 8° 1.00° 440E 444 450 456E 0.8–8° 0.6phase difference–16° Phase difference 300 200 100Self-potential 0 430E 434 438 444 448 452 456E –100 SP (mV) 0 200 m –200 –300

    442E 446 450 454E Apparent resistivity (?m) 400 100 Induced 100 polarization 400 100 25 442E 446 450 454E Percentage frequency 5 10 effect (%) 5 15 10 Weathered zone in conducting shale 438 442 446 450 454E Undifferentiated shale

    instrument is used in which the transmitter and receiver, electrical sounding (see Section 8.2.3) can be under- which usually take the form of vertical coplanar coils, are taken by progressively increasing the transmitter–receiv- separate, so that their spacing is variable. Constant sepa- er separation. ration traversing (CST) can be performed with the A widely used instrument based on the above princi- subsurface energized to a desired depth, while vertical ples is the Geonics EM31.

    Drillhole PDS1 80 60 Microvolts 40 20 0 Time Scale 1.22 ms x500 1.53 ms x500 80 2.08 ms x500 2.71 ms x500 60 3.80 ms x200 5.05 ms x200 7.24 ms x50 40 9.74 ms x10 14.11 ms x5 20 19.11 ms x2 27.86 ms x2 37.86 ms 0 Microvolts Drillhole DS1 Time Scale 1.22 ms x200 1.53 ms x100 2.08 ms x50 2.71 ms x20 3.80 ms x10 5.05 ms x5 7.24 ms x2 9.74 ms 14.11 ms 19.11 ms 27.86 ms 37.86 ms

    Station no. 20 45 70 95 120 170 m Station no. 30 55 80 105 130 155 180 205 m 145

    Drillhole DS2 WE 80 60 Microvolts 40 20 0 Station no. 115 140 165 190 215 240 265 290 m Time Scale DS1 PDS1 EMP loop 1.22 ms x50 DS2 1.53 ms x10 2.08 ms x2 best fit 2.71 ms x2 1% zinc current loop 3.80 ms 5.05 ms 7.24 ms 0.2% 9.74 ms copper 14.11 ms 19.11 ms 27.86 ms . 37.86 ms Shale disseminated Sericitized tuffs pyrite Black shale Semi-massive sulphides 0 100 m End of EMP survey 170

    205 219.5 241 0 290 300.8 Fig.9.14 DrillholeTDEMpro?lesandgeologicalsectionoverSingleTreeHill,NSW,Australia.(RedrawnfromBoyd&Wiles1984.)

    9.8 Airborne electromagnetic surveying Airborne EM techniques are widely used because of their speed and cost-effectiveness, and a large number of There is a broad division into passive systems, where only the receiver is airborne, and active systems, where both transmitter and receiver are mobile. Passive systems include airborne versions of the VLF and AFMAG methods. Independent transmitter methods can also be used with an airborne receiver, but are not very attractive Active systems are more commonly used, as surveys can be performed in areas where ground access is dif?- cult and provide more information than the passive tilt- angle methods.They are, basically, ground mobile trans- mitter–receiver systems lifted into the air and interfaced with a continuous recording device. Certain specialized methods, described later, have been adopted to over- come the speci?c dif?culties encountered in airborne work. Active systems comprise two main types, ?xed separation and quadrature.

    and height is essential, and this is usually accomplished by mounting the transmitter and receiver either on the wings of an aircraft or on a beam carried beneath a heli- copter. Compensating methods have to be employed to correct for minute changes in the relative positions of transmitter and receiver resulting from such factors as Since only a small transmitter–receiver separation is used to generate and detect an electromagnetic ?eld over a relatively large distance, such minute changes in separa- Fixed-wing systems are generally ?own at a ground clearance of 100–200 m, while helicopters can survey at Greater depth of penetration can be achieved by the use of two planes ?ying in tandem (Fig. 9.15), the rear plane carrying the transmitter and the forward plane towing the receiver mounted in a bird. Although the air- craft have to ?y at a strictly regulated speed, altitude and separation, the use of a rotating primary ?eld compen- The rotating primary ?eld is generated by a transmitter consisting of two orthogonal coils in the plane perpen- dicular to the ?ight direction. The coils are powered by the same AC source with the current to one coil shifted p/2 (90°) out-of-phase with respect to the other. The resulting ?eld rotates about the ?ight line and is detected by a receiver with a similar coil con?guration which passes the signals through a phase-shift network so that the output over a barren area is zero. The presence of a conductor is then indicated by non-zero output and the

    Receiver Transmitter in bird 20m 300m 100m

    Receiver Flight direction Transmitter ? – 2 Output

    ? – 2 Electromagnetic Surveying 219 measured secondary ?eld decomposed into real and imaginary components. Although penetration is increased and orientation errors are minimized, the method is relatively expensive and the interpretation of data is complicated by the complex coil system. It is possible to upward-continue airborne EM data. This diminishes variations caused by height ?uctuations and Airborne TDEM methods, such as INPUT® (IN- duced PUlseTransient) (Barringer 1962), may be used to enhance the secondary ?eld measurement. The discon- tinuous primary ?eld shown in Fig. 9.16 is generated by passing pulses of current through a transmitter coil strung about an aircraft. The transient primary ?eld induces currents within a subsurface conductor. These currents persist during the period when the primary ?eld is shut off and the receiver becomes active. The ex- ponential decay curve is sampled at several points and the signals displayed on a strip chart.The signal amplitude in successive sampling channels is, to a certain extent, diag- nostic of the type of conductor present. Poor conductors produce a rapidly decaying voltage and only register on those channels sampling the voltage shortly after pri- mary cut-off. Good conductors appear on all channels.

    1.5msec 2msec 1.5msec (a) t (b) t (c) t (d)1 Channels 2 3 4 5 6 t

    (b) Receiver response to primary alone. (c) Receiver response in the presence of a secondary ?eld. (d) Enlargement of the receiver signal during primary ?eld cut-off.The amplitude of the decaying induced voltage is here sampled on six channels.

    6 5 4 3 2 1 Input channel 0 2 km WE ++++++++++++++++++ ++++++++ ++++++++ v v v v v ++++ ++++ ++++v v v v v v++++++++++++ +++++++++++

    ++ + Greywacke Granite Amphibolite vvvv Mafic volcanic rocks Mesozoic sediments Fig. 9.17 INPUT® pro?le across part of (After Palacky 1981.)

    INPUT® is more expensive than other airborne EM methods but provides greater depth penetration, possi- bly in excess of 100 m, because the secondary signal can be monitored more accurately in the absence of the primary ?eld. It also provides a direct indication of the type of conductor present from the duration of the As well as being employed in the location of conduct- ing ore bodies, airborne EM surveys can also be used as an aid to geological mapping. In humid and subtropical areas a weathered surface layer develops whose thickness Figure 9.17 shows an INPUT® pro?le across part of the Itapicuru Greenstone Belt in Brazil, with sampling times increasing from 0.3 ms at channel 1 to 2.1 ms at channel 6. The transient response over ma?c volcanic rocks and Mesozoic sediments is developed in all six channels, in- dicating that their weathered layer is highly conductive, while the response over greywacke is only apparent in channels 1–4, indicating a comparatively less conductive EM methods are being used increasingly in hydro- geological studies as they are more ef?cient than the re- sistivity methods classically used for this purpose.A series of case histories of the use of EM methods in ground- water studies is given in McNeill (1991).

    9.8.2 Quadrature systems Quadrature systems were the ?rst airborne EM methods devised.The transmitter is usually a large aerial slung be- tween the tail and wingtips of a ?xed-wing aircraft and a nominally-horizontal receiver is towed behind the In quadrature systems the orientation and height of the receiver cannot be rigorously controlled as the receiver `bird’ oscillates in the slipstream. Consequently, the measurement of real and imaginary components is not possible as the strength of the ?eld varies irregularly with movement of the receiver coil. However, the phase difference between the primary ?eld and the resultant ?eld caused by a conductor is independent of variation in the receiver orientation. A disadvantage of the method is that a given phase shift f¢ may be caused by either a good or a poor conductor (Fig. 9.18).This prob- lem is overcome by measuring the phase shift at two different primary frequencies, usually of the order of 400 and 2300 Hz. It can be shown that, if the ratio of low-frequency to high-frequency response exceeds Figure 9.19 shows a contour map of real component anomalies (in ppm of the primary ?eld) over the Skellefteå ore?eld, northern Sweden. A ?xed separation system was used, with vertical, coplanar coils mounted perpendicular to the ?ight direction on the wingtips of a small aircraft. Only contours above the noise level of some 100 ppm are presented. The pair of continuous anomaly belts in the southwest, with amplitudes exceed- ing 1000 ppm, corresponds to graphitic shales, which serve as guiding horizons in this ore?eld.The belt to the north of these is not continuous, and although in part re- lated to sulphide ores, also results from a power cable. In the northern part of the area the three distinct anomaly centres all correspond to strong sulphide mineralization.

    A A p m u t i l e d ?’ P h a s e s h i f t ? (a) (b) Conductivity ¥ frequency

    Fig. 9.18 The relationship between the phase/amplitude of a secondary electromagnetic ?eld and the product of conductivity and frequency. A given phase shift f¢ could result from a poor conductor (a) or a good conductor (b).

    9.9 Interpretation of electromagnetic data As with other types of geophysical data an indirect approach can be adopted in the interpretation of electromagnetic anomalies. The observed electromag- netic response is compared with the theoretical response, for the type of equipment used, to conductors of various shapes and conductivities. Theoretical computations of this type are quite complex and limited to simple geo- metric shapes such as spheres, cylinders, thin sheets and If the causative body is of complex geometry and variable conductivity, laboratory modelling may be used (Chakridi & Chouteau 1988). Because of the com- plexity of theoretical computations, this technique is used far more extensively in electromagnetic interpreta- For example, to model a massive sulphide body in a well- conducting host rock, an aluminium model immersed Master curves are available for simple interpretation of moving source–receiver data in cases where it may be as- Figure 9.20 shows such a set of curves for a simple sheet- like dipping conductor of thickness t and depth d where the distance between horizontal, coplanar coils is a.The point corresponding to the maximum real and imagi- nary values, expressed as a percentage of the primary ?eld, is plotted on the curves. From the curves coincid- ing with this point, the corresponding l/a and d/a values Electromagnetic Surveying 221

    are determined.The latter ratio is readily converted into conductor depth. l corresponds to 107/sft, where s is the conductivity of the sheet and f the frequency of the ?eld. Since a and f are known, the product st can be determined. By performing measurements at more than Much electromagnetic interpretation is, however, only qualitative, particularly for airborne data. Contour maps of real or imaginary components provide informa- tion on the length and conductivity of conductors while the asymmetry of the pro?les provides an estimate of the inclination of sheet-like bodies.

    9.10 Limitations of the electromagnetic method The electromagnetic method is a versatile and ef?cient As well as being caused by economic sources with a high conductivity such as ore bodies, electromagnetic anom- alies can also result from non-economic sources such as graphite, water-?lled shear zones, bodies of water and man-made features. Super?cial layers with a high con- ductivity such as wet clays and graphite-bearing rocks may screen the effects of deeper conductors. Penetration is not very great, being limited by the frequency range that can be generated and detected. Unless natural ?elds are used, maximum penetration in ground surveys is limited to about 500 m, and is only about 50 m in airborne work. Finally, the quantitative interpretation of electromagnetic anomalies is complex.

    Fig. 9.19 Contour map of real component anomalies over part of the Skellefteå ore?eld, northern Sweden, obtained using an airborne system with vertical coplanar coils. Mean ground clearance 30 m, operating frequency 3.5 kHz. Contours in ppm of the primary ?eld. (After Parasnis 1973.)

    frequency, ranging from 10-5 Hz up to the audio range, and overlap the frequency range utilized in the AFMAG method (Section 9.4.3).

    Electromagnetic Surveying 223 Transmitter Receiver

    a d t Thin conductor –25 –20 –15 Fig. 9.20 Example of a vector diagram –5 used in estimating the parameters of a thin dipping conductor from the peak real and 0 imaginary component values. (Redrawn from Nair et al. 1968.) Negative peak value in percentage, out-of-phase component –10 15 10 7.5 Dip 60 30 5.0

    50 2.5 d – = 0.10 a 0.25

    0.50 0.20 0.30 0.35 0.40 0.15 ? – = 0.25 a 0 –5 –10 –15 –20 –25 –30 –35 –40 –45 –50 –54 Negative peak value in percentage, in-phase component

    mineral surveys. The potential electrodes are connected to an ampli?er which drives a strip chart recorder or tape If the electrical conductivity of the subsurface were uniform the potential gradient at the surface would be constant (Fig. 9.21(a)). Zones of differing conduc- tivity de?ect the current ?ow from the horizontal and cause distortion of the potential gradients measured at the surface. Figure 9.21(b) shows the distortion of current ?ow lines caused by a salt dome which, since it is a poor conductor, de?ects the current lines into the overlying layers. Similar effects may be produced by anti- clinal structures. Interpretation of anomalous potential gradients measured at the surface permits the location of Telluric potential gradients are measured using orthogonal electrode pairs (Fig. 9.22(a)). In practice, the survey technique is complicated by temporal variation in direction and intensity of the telluric currents. To over- come this problem, one orthogonal electrode pair is read at a ?xed base located on nearby barren ground and another moved over the survey area. At each observation point the potential differences between the pairs of elec- trodes at the base and at the mobile station are recorded simultaneously over a period of about 10 min. From the magnitude of the two horizontal components of the electrical ?eld it is simple to ?nd the variation in direc- tion and magnitude of the resultant ?eld at the two locations over the recording interval. The assumption is made that the ground is uniform beneath the base Volts (a) Depth (b) (b) disturbed

    (a) normal Distance Undisturbed telluric currents Depth Deflected telluric currents Salt

    Fig. 9.21 The instantaneous potential gradient associated with telluric currents. (a) Normal, undisturbed gradient. (b) Disturbed gradient resulting from de?ection of current ?ow by a salt dome.

    (a) Base Mobile (b)

    Fig. 9.22 (a) Base and mobile potential electrode sets used in telluric surveys. (b)The ?gure traced by the horizontal component of the telluric ?eld over an undisturbed area (circle) and in the presence of a subsurface conductor (ellipse) after correction for temporal variations in telluric current intensity.

    when applied to the base electrode results, constrains the The same function is then applied to the mobile elec- trode data. Over an anomalous structure the conductiv- ity of the ground is not the same in all directions and the magnitude of the corrected resultant electric ?eld varies with direction.The resultant ?eld vector traces an ellipse whose major axis lies in the direction of maximum con- ductivity. The relative disturbance at this point is conve- niently measured by the ratio of the area of the ellipse to the area of the corresponding base circle.The results of a survey of this type over the Haynesville Salt Dome, Texas, USA are presented in Fig. 1.4. The solid circles represent locations where ellipse areas relative to a unit base circle have been computed. Contours of these values outline the known location of the dome with The telluric method is applicable to oil exploration as it is capable of detecting salt domes and anticlinal struc- tures, both of which constitute potential hydrocarbon traps. As such, the method has been used in Europe, North Africa and the former Soviet Union. It is not widely used in the USA where oil traps tend to be too small in area to cause a signi?cant distortion of telluric current ?ow.The telluric method can also be adapted to mineral exploration.

    9.11.3 Magnetotelluric surveying Prospecting using magnetotelluric ?elds is more complex than the telluric method as both the electric and magnetic ?elds must be measured. The technique does, however, provide more information on subsurface structure.The method is, for example, used in investiga- Telluric currents are monitored as before, although no base station is required. The magnetotelluric ?eld is measured by its inductive effect on a coil about a metre in Two orthogonal components are measured at each The depth z to which a magnetotelluric ?eld pene- trates is dependent on its frequency f and the resistivity r of the substrate, according to equations of the form of (9.2) and (9.3), that is,

    r z = k (9.7) f

    where k is a constant. Consequently, depth penetration increases as frequency decreases. It can be shown that the amplitudes of the electric and magnetic ?elds, E and B, are related

    2 0.2 Ê E ^ r = (9.8) a ˯ fB where f is in Hz, E in mV km-1 and B in nT. The appar- ent resistivity r thus varies inversely with frequency.The a calculation of r for a number of decreasing frequencies a thus provides resistivity information at progressively increasing depths and is essentially a form of vertical Interpretation of magnetotelluric data is most reliable in the case of horizontal layering. Master curves of ap- parent resistivity against period are available for two and three horizontal layers, vertical contacts and dykes, and interpretation may proceed in a similar manner to curve- matching techniques in the resistivity method (see Sec- tion 8.2.7). Routines are now available, however, which allow the computer modelling of two-dimensional structures.

    Electromagnetic Surveying 225 9.12 Ground-penetrating radar Ground-penetrating radar (GPR) (Davis & Annan 1989) is a technique of imaging the subsurface at high resolution. Although analogous in some ways to the seis- mic methods, it is included in this chapter as the propa- gation of radar waves through a medium is controlled by its electrical properties at high frequencies. A compre- hensive account of modern advances in GPR is given by GPR is a non-destructive technique and can conse- GPR has many geological applications, such as imaging shallow soil and rock structure at high resolution, locat- ing buried channels and mapping the water table. It also has several non-geological uses such as in archaeology, for the location of buried walls or cavities, and in foren- sic investigations, for the location of recently-disturbed GPR is similar in its principles to seismic re?ection pro?ling (see Chapter 4) and sonar (see Section 4.15) surveying. A short radar pulse in the frequency band 10–1000 MHz is introduced into the ground. Radar velocities are controlled by the dielectric constant (relative The velocity of a radar wave (V ) is given by:

    c V = (9.9) (m e ) rr

    where c is the velocity of light in vacuo (3 ¥ 108 m s-1), m r the relative magnetic permeability (Section 7.2), which is close to unity for non-magnetic rocks, and e the r In high resistivity rocks (>102 ohm m) the propaga- r Dielectric conduction takes place in such poor conduc- tors and insulators, which have no free carriers, by the slight displacement of electrons with respect to their nu- clei. Water has a dielectric constant of 80, whereas in most dry geological materials the dielectric constant is in the range 4–8. Consequently, the water content of mate- rials exerts a strong in?uence on the propagation of a A contrast in dielectric properties across an interface causes re?ection of part of a radar pulse with a diminu- tion of energy according to the re?ection coef?cient K, which is analogous to the seismic case (see Section 3.6.1), ( e – e ) (V -V ) K = r2 r1 = 2 1 (9.10) ( e + e ) (V +V ) r2 r1 2 1

    where e and e are the relative permittivities of r1 r2 the two media separated by the interface and V and 1 V the radar velocities within them. Velocities of geo- 2 logical materials generally lie within the range Dielectric permittivity does not usually vary by more than a factor of 10 in most natural materials, so it is the more highly variable resistivity that controls the depth of penetration of a radar pulse. Generally, depth of penetra- tion increases with increasing resistivity. Penetration is of the order of 20 m, although this may increase to 50 m under optimal conditions of low conductivity. As with seismic waves, there is a trade-off between depth of penetration and resolution, with the greater penetration A transmitting antenna generates a wavetrain which comprises a pulse of radio waves with a frequency of The arriving pulse is scanned at a ?xed rate for a time ad- justed to be of the order of the two-way travel time of the pulse.The pulse received by the receiving antenna is sim- ilarly a wavetrain, but differs from the transmitted wave- train because of the modi?cations caused to it during its passage through the subsurface. The fact that the wave- train comprises more than one wavelet complicates the subsequent interpretation. Since velocities of radar waves can be of the order of 0.3 m ns-1, accurate timing instrumentation is essential. The returned radar signals are ampli?ed, digitized and recorded; the resulting data can be displayed on a radargram, which is very similar to The depth of penetration of radio waves depends on their frequency and the nature of the material being surveyed. Figure 9.23 shows how the penetration varies in different materials over the frequency range 1– 500 MHz.The permittivity of water is high compared to dry materials, so the water content and porosity are There are three basic modes of deployment in GPR surveys, all of which have their seismic counterparts (Fig. 9.24): 1. Re?ection pro?ling (Fig. 9.24(a)), in which the transmitter and antenna are kept at a small, ?xed separa- tion; this is often achieved by using the same antenna for transmission and reception.

    1000 100 Probing distance (m) 10 1 Medium Granite Limestone Schist

    Best coal Coal–clay Shales Gouge 1 10 100 Frequency, f (MHz) Fig. 9.23 The relationship between 1000 probing distance and frequency for different materials. (After Cook 1975.)

    2. Velocity sounding (Fig. 9.24(b)), in which transmit- ter and antenna are moved apart about a ?xed central point (the common depth point (CDP) method), or one kept stationary while the other is progressively moved away (the wide-angle re?ection and refraction (WARR) method). The methods are designed to show how the radar velocity changes with depth. Without this infor- mation, velocities might be determined by correlating the radargram with a borehole section or with signals re?ected from a body at known depth. In many cases, 3. Transillumination (Fig. 9.24(c)), in which the trans- mitter and antenna are mounted on either side of the object of interest (e.g. a pillar in a mine). If it is arranged that there are many different con?gurations of transmit- ter and antenna, radar tomography can be carried out in a similar fashion to seismic (see Section 5.10) and resis- Filtering of the radar signal can be applied dur ing data acquisition, but is more conveniently performed on the instruments. The digital output provided by modern radar re?ections can subsequently be enhanced by digital data-processing techniques very similar to those used in re?ection seismology (see Section 4.8), of which Interpretation of a radargram is commonly per- formed by interface mapping, similar to that used in the interpretation of seismograms. If amplitude ?delity has been retained in the radargram, zones of high attenua- tion can be recognized which represent high-conduc- However, the identi?cation of each band on a radargram as a distinct geological horizon would be incorrect because of the effects of multiples, interference with a previous re?ection wavetrain, sideswipe (see Section 4.8), noise, etc. Processing of the radargram is simpli?ed by deconvolution (see Section 4.8.2), which restores the shape of the downgoing wavetrain so that primary events can be recognized more easily. Migration is also particu- larly useful in that diffraction hyperbolae are removed A GPR pro?le and its interpretation are shown in Fig. 9.25, which illustrates the detailed information provided by the technique.

    Electromagnetic Surveying 227 Reflection Common mid-point (CMP)

    Transillumination 9.13 Applications of electromagnetic surveying The principal use of EM surveys is in the exploration for metalliferous mineral deposits, which differ signi?cantly in their electrical properties from their host rocks. In spite of the limited depth of penetration, airborne techniques are frequently used in reconnaissance sur- veys, with aeromagnetic surveys often run in conjunc- tion. EM methods are also used in the follow-up ground surveys which provide more precise information on the target area. Standard moving source–receiver methods (see Section 9.5) may be used for this purpose, although in rugged or forested terrain the VLF (see Section 9.4.2) or AFMAG (see Section 9.4.3) methods may be pre- ferred as no heavy equipment is required and there is no On a small scale, EM methods can be used in geotech- nical and archaeological surveys to locate buried objects such as mine workings, pipes or treasure trove. The instruments used can take the form of metal detectors similar to the mine detectors used by army engineers, which have a depth of penetration of only a few cen- timetres and respond only to metal, or may be of the non-contacting conductivity meter-type described in Section 9.7, which have greater penetration and also respond to non-metallic resistivity anomalies.

    (a) 20 40 60 80 100 120 140 160 180 200 220 240 00

    55 10 10

    Fig. 9.25 (a) GPR pro?le. (b) Line drawing showing the interpretation of (a).Thick lines show truncation surfaces within a sequence of tufa overlying Carboniferous limestone. Data from three boreholes are also shown: dotted ornament = lime mud; horizontal ornament = sapropels; wavy lines = phytoherm framestones. All axes are in m. (After Pedley et al. 2000.)

    Electromagnetic Surveying 229 (a) +10 Dip –10 +10 Dip –10 +10 Dip –10

    +10 Dip –10 (b) +10 Dip50 –10 N 1 2 3 4 0 50 m

    3 150 m 480 Hz 1800 Hz Fig. 9.26 (a)Tilt-angle pro?les from an EM survey near Uchi Lake, Ontario. (b) Pro?le 3 repeated with dual-frequency EM equipment. See Question 2. (AfterTelford et al. 1990.)

    Ground EM In phase

    Out of phase % primary Bouguer anomaly (gu) 10 0 –10 –20 –30 5 4 3 2 1 0 Gravity

    0 100 m Time domain IP 2 n 4 20 6 40 90 20 40 80 80

    Fig. 9.27 Ground EM pro?le, Bouguer gravity pro?le and chargeability pseudosection representing results from a double-dipole IP electrode spread, all from a survey in Bahia, Brazil. See Question 4. (After Palacky & Sena 1979.) (a) 2 ? 0 1 ? 0

    (b) Dip +20 10 0 –10 (c) 1000 nT 0 (d) Bouguer anomaly (gu) 15 10 5 0 0.2 2300 Hz 0.4 400 Hz 0 500 m

    0 100 m Fig. 9.28 (a) Dual-frequency airborne EM, (b) ground tilt-angle EM, (c) magnetic and (d) gravity pro?les from the Canadian Shield. See Question 5. (After Paterson 1967.)

    10 ? 400 7 ? 2300 4 2 1.0 0.7 0.4 0.2 0.04 0.1 0.2 0.4 0.7 1.0 2 4 7 10 20 30 0.07 ?t (S)

    Fig. 9.29 Characteristic curve for an airborne EM system over a half-plane. f /f is the ratio of peak responses at 400 2300 400 Hz and 2300 Hz respectively, s and t are the conductivity See Question 5. (After Paterson 1967.)

    4. Figure 9.27 shows various ground geophysi- cal measurements taken over volcanic terrain in Bahia, Brazil.The EM survey was conducted with a system using horizontal, coplanar coils 100 m apart and a frequency of 444 Hz. The time- domain IP survey used a double-dipole array with a basic electrode separation of 25 m. Inter- pret these data as fully as possible. What further information would be necessary before an ex- 5. Figure 9.28 shows the results of airborne and ground geophysical surveys over an area of the Canadian Shield. The airborne EM survey used a quadrature system with measurements of phase angle taken at 2300 and 400 Hz. The ground tilt- angle EM survey was undertaken with a vertical- loop system using a local transmitter. Interpret and comment upon these results. Figure 9.29 can be used to estimate the product of conductivity 6. Which geophysical methods are particularly suitable for archaeological applications?

    Further reading Boissonas, E. & Leonardon, E.G. (1948) Geophysical exploration by telluric currents with special reference to a survey of the Haynesville Salt Dome, Wood County, Texas. Geophysics, 13, Cagniard, L. (1953) Basic theory of the magnetotelluric method of Davis, J.L. & Annan, A.P. (1989) Ground-penetrating radar for Dobrin, M.B. & Savit, C.H. (1988) Introduction to Geophysical Jewell, T.R. & Ward, S.H. (1963) The in?uence of conductivity Geophysics, 28, 201–21.

    Keller, G.V. & Frischnecht, F.C. (1966) Electrical Methods in Milsom, J. (1989) Field Geophysics. Open University Press, Milton Parasnis, D.S. (1996) Principles of Applied Geophysics, 5th edn. Pedley, H.M., Hill, I. & Brasington, J. (2000) Three dimensional Derbyshire, using ground penetrating radar. Sedimentology, 47, Reynolds, J.M. (1997) An Introduction to Applied and Environmental Telford, W.M., Geldart, L.P. & Sheriff, R.E. (1990) Applied Wait, J.R. (1982) Geo-Electromagnetism. Academic Press, NewYork.

    10.1 Introduction Surveying for radioactive minerals has become impor- tant over the last few decades because of the demand for nuclear fuels. Radiometric surveying is employed in the search for deposits necessary for this application, and also for non-radioactive deposits associated with radioactive elements such as titanium and zirconium. Radiometric surveys are of use in geological mapping as different rock types can be recognized from their distinctive radioactive signature (Moxham 1963, Pires & Harthill 1989).There are in excess of 50 naturally occurring radioactive iso- topes, but the majority are rare or only very weakly radioactive. The elements of principal interest in radio- metric exploration are uranium (238U), thorium (232Th) and potassium (40K). The latter isotope is widespread in potassium-rich rocks which may not be associated with concentrations of U andTh. Potassium can thus obscure the presence of economically important deposits and constitutes a form of geological`noise’in this type of sur- veying. Figure 10.1 shows a ternary diagram illustrating the relative abundances of 238U, 232Th and 40K in differ- Radiometric surveys are less widely used than the other geophysical methods as they seek a very speci?c target. Probably the most common application of radio- metric techniques is in geophysical borehole logging (see Section 11.7).

    10.2 Radioactive decay Elements whose atomic nuclei contain the same number of protons but different numbers of neutrons are termed isotopes.They are forms of the same element with differ- ent atomic weights.A conventional notation for describ- ing an element A in terms of its atomic number n and atomic weight w is wA. Certain isotopes are unstable and n may disintegrate spontaneously to form other elements.

    The disintegration is accompanied by the emission of Alpha particles are helium nuclei 4 He which are emit- 2 ted from the nucleus during certain disintegrations: wAÆw-4B+4He n n-2 2

    Beta particles are electrons which may be emitted when a neutron splits into a proton and an electron during cer- tain disintegrations. The proton remains within the nu- cleus so that the atomic weight remains the same but the atomic number increases by one to form a new element: w A Æ w B + e- n n+1

    Gamma rays are pure electromagnetic radiation re- leased from excited nuclei during disintegrations. They are characterized by frequencies in excess of about 1016 Hz and differ from X-rays only in being of higher In addition to these emissions, a further process occurs in some radioactive elements which also releases energy in the form of gamma rays. This is known as K capture and takes place when an electron from the innermost (K) shell enters the nucleus. The atomic number decreases and a new element is formed: w A + e- Æ w B n n -1

    Radioactive decay may lead to the formation of a sta- ble element or a further radioactive product which itself undergoes decay.The rate of decay is exponential so that N = N e-lt 0

    Th Feldspar-rich pegmatites Ultrabasic to basic igneous Monazite- rich rocks Acid to intermediate 50 50 igneous and siliceous clastics Contaminated carbonates to pure carbonates K U × 10–4 50 Fig. 10.1 Relative abundances of radioactive elements in different rock types. Also shown are the relative radioactivities of the radioelements. (AfterWollenberg 1977.)

    are accurately known and unaffected by external condi- tions such as temperature, pressure and chemical com- The radioactive emissions have very different pene- trating properties. Alpha particles are effectively stopped by a sheet of paper, beta particles are stopped by a few millimetres of aluminium and gamma rays are only stopped by several centimetres of lead. In air, alpha parti- cles can travel no more than a few centimetres, beta particles only a few decimetres and gamma rays several hundreds of metres. Alpha particles thus cannot be de- tected in radiometric surveying and beta particles only in ground surveys. Only gamma rays can be detected in There are three radioactive series of uranium and tho- rium whose parents are 235U, 238U and 232Th . These all 92 92 90 decay eventually to stable isotopes of lead via intermedi- ate, daughter radioisotopes. About 89% of 40K decays by beta emission to 40Ca and 11% to 40Ar by K-capture.

    10.3 Radioactive minerals There is a large number of radioactive minerals (for a full list see Durrance 1986), but the more common are The nature of the mineral in which the radioisotope is found is irrelevant for detection purposes as the prospecting techniques locate the element itself.

    Th window U window K window Relative count rate (log scale) 40K

    238U 232Th 123 Energy (MeV) Fig. 10.2 Energy spectra of 40K, 238U and 232Th and their measurement windows.

    10.4 Instruments for measuring radioactivity Several types of detector are available for radiometric surveys, results being conventionally displayed as the number of counts of emissions over a ?xed period of time. Radioactive decay is a random process following a Poisson distribution with time so that adequate count times are important if the statistical error in counting The standard unit of gamma radiation is the Roent- gen (R). This corresponds to the quantity of radiation that would produce 2.083 ¥ 1015 pairs of ions per cubic metre at standard temperature and pressure. Radiation anomalies are usually expressed in mR per hour.

    Radiometric Surveying 233 10.4.1 Geiger counter The Geiger (or Geiger–Müller) counter responds primarily to beta particles. The detecting element is a sealed glass tube containing an inert gas, such as argon, at low pres- sure plus a trace of a quenching agent such as water vapour, alcohol or methane.Within the tube a cylindri- cal cathode surrounds a thin axial anode and a power source maintains a potential difference of several hun- dred volts between them. Incoming beta particles ionize the gas and the positive ions and electrons formed are accelerated towards the electrodes, ionizing more gas en route. These cause discharge pulses across an anode resistor which, after ampli?cation, may be registered as clicks, while an integrating circuit displays the number of counts per minute. The quenching agent suppresses the secondary emission of electrons resulting from The Geiger counter is cheap and easy to use. How- ever, since it only responds to beta particles, its use is lim- ited to ground surveys over terrain with little soil cover.

    10.4.2 Scintillation counter The scintillation counter or scintillometer is used to measure gamma radiation based on the phenomenon that certain substances such as thallium-treated sodium iodide and that is, they scintillate. Photons of light impinging upon a semi-transparent cathode of a photomultiplier cause the emission of electrons.The photomultiplier ampli?es the electron pulse before its arrival at the anode where it is further ampli?ed and integrated to provide a display in The scintillation counter is more expensive than the Geiger counter and less easy to transport, but it is almost 100% ef?cient in detecting gamma rays. Versions are available which can be mounted in ground transport or aircraft.

    28 000 20 000 12 000 Magnetic field (nT) Magnetic 4000Radiometric 0 50 m

    20 Depth (m) 40 Argillites and quartzites Mineralized zones 60Boreholes 12 000

    10 000 8000 6000 4000 2000 ? -ray activity (uranium channel) (counts/min) Fig. 10.3 Radiometric and magnetic pro?les over pitchblende–magnetite mineralization in Labrador. (After Telford et al. 1990.)

    monitored then provides a diagnostic means of discrimi- nating between different sources. Figure 10.2 shows the gamma ray spectra of 238U, 232Th and 40K and it is ap- parent that measurements at 1.76, 2.62 and 1.46 MeV, respectively, provide a discrimination of the source (1 MeV = 106 electronvolts, 1 electronvolt being the energy acquired by a particle of unit charge falling through a potential of 1 volt). These devices are some- times termed pulse-height analysers as the intensity of the scintillation pulses is approximately proportional to Gamma ray spectrometers for airborne use are often calibrated by ?ying over an area of known radioisotope concentration or by positioning the aircraft on a concrete slab fabricated with a known proportion of radio- isotopes. The actual concentrations of 238U, 232Th and 40K in the ?eld can then be estimated from survey data.

    the transport of radon generated at depth (Abdoh & Pilkington 1989). This technique is advantageous when there is no great difference in rock properties across the fault that could be detected by other geophysical methods.

    10.5 Field surveys As previously stated, Geiger counter investigations are limited to ground surveys. Count rates are noted and their signi?cance assessed with respect to background effects resulting from the potassium content of the local rocks, nuclear fallout and cosmic radiation. An apprecia- ble anomaly would usually be in excess of three times the Scintillation counters may also be used in ground sur- veys and are usually sited on rock exposures.The ground surface should be relatively ?at so that radioactive emis- sions originate from the half-space below the instru- ment. If this condition does not obtain, a lead collimator can be used to ensure that radioactive emissions do not Most radiometric surveying is carried out from the air, employing larger scintillation sensors than in ground instruments, with a consequent increase in measure- ment sensitivity. Instruments are interfaced with strip recorders and position ?xing is by means of the methods discussed in Section 7.8. Radiometric measurements are normally taken in conjunction with magnetic and elec- tromagnetic readings, so providing additional datasets at minimal extra cost. In surveying for relatively small de- posits the slow speed of helicopters is often advantageous and provides greater discrimination and amplitude of response. Flight altitude is usually less than 100 m and, because of the weak penetrative powers of radioactive Radiometric Surveying 235

    emissions, the information obtained relates only to the The interpretation of radiometric data is mainly qual- itative, although characteristic curves are available for certain elementary shapes which provide the parameter: (surface area) ¥ (source intensity).

    10.6 Example of radiometric surveying Figure 10.3 shows a ground magnetic and gamma- ray pro?le across a zone of uranium mineralization in Labrador. This was obtained from contour maps of a There are strong coincident magnetic and radiometric anomalies, the source of which was investigated by two boreholes. The anomalies arise from magnetite and pitchblende, located immediately beneath the anomaly maxima, in an argillaceous and quartzitic host. Pitch- blende is a variety of massive, botryoidal or colloform uraninite.

    Further reading Durrance, E.M. (1986) Radioactivity in Geology. Ellis Horwood, Milsom, J. (1989) Field Geophysics. Open University Press, Milton In: Fitch, A.A. (ed.), Developments in Geophysical Exploration Telford, W.M., Geldart, L.P. & Sheriff, R.E. (1990) Applied Geo- Elsevier, Amsterdam, 5–36.

    11.1 Introduction to drilling Shallow boreholes may be excavated by percussion drilling, in which rock fragments are blown out of the hole by air pressure. Most boreholes, however, are sunk by rotary drilling in which the detritus produced by ro- tating teeth on a rock bit drilling head is ?ushed to the surface by a drilling ?uid (or `mud’), which holds it in suspension. The drilling ?uid also lubricates and cools the bit and its density is carefully controlled so that the pressure it exerts is suf?cient to exceed that of any pore ?uids encountered so as to prevent blowouts. Rotary drilling using a core drill in place of a rock bit to obtain core samples is not so widely applied because of its The deposition of particles held in suspension in the drilling ?uid seals porous wall rocks to form a mudcake (Fig. 11.1). Mudcakes up to several millimetres thick can build up on the borehole wall and, since the character of the mudcake is determined by the porosity and per- meability of the wallrock in which it is developed, inves- tigation of the mudcake properties indirectly provides insight into these `poroperm’ properties. The drilling ?uid ?ltrate penetrates the wallrock and completely dis- places indigenous ?uids in a `?ushed zone’ which can be several centimetres thick (Fig. 11.1). Beyond lies an annulus of invasion where the proportion of ?ltrate gradually decreases to zero. This zone of invasion is a few centimetres thick in rock such as shale, but can be up to a few metres wide in more permeable and porous Casing may be introduced into borehole sections immediately after drilling to prevent collapse of the wallrock into the hole. Cased holes are lined with pip- ing, the voids between wallrock and pipe being ?lled with cement. Boreholes with no casing are termed open holes.

    Geophysical Borehole Logging 237 Sandstone Borehole with drilling fluid Mudcake Flushed zone Annulus of invasion

    Pristine formation Shale instrumentation, including recorders, cable drums and winches, is usually installed in a special recording truck located near the wellhead. Sondes normally contain combinations of logging tools that do not mutually interfere, so that a wide suite of geophysical logs may be Several techniques of borehole logging are used together to overcome the problems of mudcake and drilling ?uid ?ltrate invasion so as to investigate the properties of the pristine wallrock. Open holes can be Casing prevents the use of logging methods based on electrical resistivity and distorts measurement of seismic velocities. Consequently only a few of the logging methods, such as those based on radioactivity, can be Logging techniques are very widely used in the inves- tigation of boreholes drilled for hydrocarbon explo- ration, as they provide important in situ properties of possible reservoir rocks.They are also used in hydrogeo- logical exploration for similar reasons. A review of the methodology and applications of borehole logging at sea is given in Goldberg (1997). Some modern case histories and reviews of recent developments are given in Lovell et al. (1999).

    permeability, proportion of water and/or hydrocarbon Formation thickness and lithology are normally determined by comparison of borehole logs with the log of a cored hole. The most useful logs are those based on resistivity (Section 11.4), self-potential (Section 11.6), radioactivity (Section 11.7) and sonic velocity (Section 11.8), and these are often used in combination to obtain an unambiguous section. The calliper log, which measures changes in borehole diameter, also provides information on the lithologies present. In general, larger diameters re?ect the presence of less cohesive wallrocks which are easily eroded during Porosity estimates are usually based on measurements of resistivity, sonic velocity and radioactivity. In addi- tion, porosity estimates may be obtained by gamma-ray density logging (Section 11.7.2), neutron–gamma-ray logging (Section 11.7.3) and nuclear magnetic reso- nance logging (Section 11.10). The methodology is Permeability and water and hydrocarbon saturation are derived from resistivity measurements. Stratal dip and temperature are determined by their own specialized logs.

    11.3 Formation evaluation 11.4 Resistivity logging The geological properties obtainable from borehole log- In this chapter the symbol R is used for resistivity to avoid ging are: formation thickness and lithology, porosity, confusion with the symbol r used for density.

    I C 1 P 1 Multicore cable ?V P 2 C 2 Fig. 11.2 The general form of electrode con?guration in resistivity logging.The shaded area represents the effective region energized by the system.

    The general equation for computing apparent resis- tivity R for any downhole electrode con?guration is a

    4pDV R = (11.1) a ÏÊ 1 1 ^ Ê 1 1 ^ ¸ IÌ – – – ? ÓË C P C P ¯ Ë C P C P ¯ ? 11 21 12 22

    where C , C are the current electrodes, P , P the po- 12 12 tential electrodes between which there is a potential dif- ference DV, and I is the current ?owing in the circuit (Fig. 11.2). This is similar to equation (8.9) but with a factor of 4 instead of 2, as the current is ?owing in a full space rather than the halfspace associated with Different electrode con?gurations are used to give Switching devices allow the connection of different sets of electrodes so that several types of resistivity log can be The region energized by any particular current elec- trode con?guration can be estimated by considering the equipotential surfaces on which the potential elec- trodes lie. In a homogeneous medium, the potential C 2

    P 1 C 1 ?V P 2 difference between the electrodes re?ects the current density and resistivity in that region. The same potential difference would be obtained no matter what the position of the potential electrode pair. The zone energized is consequently the region between the equipotential surfaces on which the potential elec- trodes lie. Figure 11.2 shows the energized zone in a homogeneous medium.

    11.4.1 Normal log In the normal log, only one potential and current elec- trode are mounted on the sonde, the other pair being By substitution in equation (11.1) DV R = 4p C P (11.2) a 11 I

    Lithology Shale Sandstone Depth (feet) 1700 1800 1900 2000 6650

    6700 0 64” Normal 10 0 16” Normal 10 Resistivity (?m)

    Fig. 11.4 A comparison of short and long normal logs through a sequence of sandstone and shale. (After Robinson & Çoruh 1988.)

    and P increases, so that measurements of resistivity 2 The presence of drilling ?uid and resistivity contrasts across lithological boundaries cause current refractions so that the zone tested changes in shape with position in It is possible to correct for the invasion of drilling ?uid by using the results of investigations with different elec- trode separations (short normal log 16 in (406 mm), long normal log 64 in (1626 mm)) which give different pene- tration into the wallrock. Comparison of these logs with standard correction charts (known as departure curves) The normal log is characterized by smooth changes in resistivity as lithological boundaries are traversed by the sonde because the zone of testing precedes the sonde Examples of short and long normal logs are given in Fig. 11.4.

    11.4.2 Lateral log In the lateral log the in-hole current electrode C is a con- 1 Geophysical Borehole Logging 239

    ?V C 2 C 1 P 1 P 2 siderable distance above the potential electrode pair, and is usually mounted on the wire about 6 m above a short 12 11.5). For this electrode con?guration

    4pDV R = (11.3) aÊ11^ I- ËCP CP¯ 11 12

    Lithology Shale Sandstone Spontaneous potential (mV) Depth (feet) Resistivity (?m) Resistivity (?m) 20 –+ 16” Normal 0 100 Lateral 0 100 64” Normal 0 100 4700

    4800 4900 Sand line Shale line Fig. 11.6 The lateral log compared with normal and self-potential logs. (After Guyod 1974.)

    produce spurious peaks below them. The lateral log does, however, give a clear indication of the lower boundary of a formation. An example of a lateral log and comparison with normal and self-potential logs is given in Fig. 11.6. As with the normal logs, corrections for the effects of invasion can be applied by making use of standard charts.

    11.4.3 Laterolog The normal and lateral logs described above have no control on the direction of current ?ow through the wallrock. By contrast, the laterolog (or guard log) is a fo- cused log in which the current is directed horizontally so that the zone tested has the form of a circular disc. This may be achieved by the use of a short electrode 75– 300 mm long between two long (guard) electrodes about 1.5 m long (Fig. 11.7). The current supply to the elec- trodes is automatically adjusted so as to maintain them all at the same potential. Since no potential difference exists between the electrodes, the current ?ows outwards hor- izontally, effectively energizing the wallrock to a depth The use of a ?xed potential has the consequence that the current in the central electrode varies in proportion to I

    Rubber pad P 2 P 1 C 1 Spring the apparent resistivity so that the output can be cali- The focusing of the log makes it sensitive to thin beds down to the same thickness as the length of the central electrode. The zone of invasion has a pronounced effect which can be estimated from the results of nor- mal and lateral logging and corrected using standard charts.

    11.4.4 Microlog The microlog (or wall-resistivity log) makes measurements at very small electrode spacings by using small, button- shaped electrodes 25–50 mm apart mounted on an Geophysical Borehole Logging 241

    insulating pad pressed ?rmly against the wallrock by a power-driven expansion device (Fig. 11.8).The depth of penetration is typically about 100 mm. Different electrode arrangements allow the measurement of micronormal, microlateral and microlaterolog apparent resistivities that are equivalent to normal, lateral and laterolog measurements with much smaller electrode spacings. The log has to be moved very slowly and it is normally used only in short borehole sections which are As the electrode spacing is so small, the effects of the borehole diameter, drilling ?uid and adjacent beds are negligible. Very thin beds register sharply, but the main use of the microlog is to measure the resistivities of the mudcake and zone of invasion, which are needed to convert log measurements into true resistivities.

    11.4.5 Porosity estimation Porosity is de?ned as the fractional volume of pore spaces in a rock.The method of porosity estimation is based on the relationship between formation factor F and porosity f dis- covered by Archie (1942). F is a function of rock texture and de?ned as

    R F = f (11.4) R w

    where R and R are the resistivities of the saturated fw Porosity and formation factor are related by f = aF -m (11.5)

    where a is an empirical constant speci?c to the rocks of the area of interest, and m a constant known as the cementation factor which depends on the grain size Normal limits on a and m, derived experimentally, are given by

    0.62 < a < 1.0, and 2.0 < m < 3.0 11.4.6 Water and hydrocarbon saturation estimation Natural pore water is generally a good conductor of electricity because of the presence of dissolved salts.

    Hydrocarbons, however, are poor conductors and cause an increase in the measured resistivity of a rock relative to that in which water is the pore ?uid. Hydrocarbons displace pore water and cause it to be reduced to an irreducible minimum level. Archie (1942) described a method of estimating the proportion of pore water pre- sent (the water saturation S ) based on laboratory measure- ments of the resistivities of sandstone cores containing varying proportions of hydrocarbons and pore water of ?xed salinity. If R and R are the resistivities of (matrix + fh pore water) and (matrix + pore water + hydrocarbons), respectively, then

    1n Ê Rf ^ S = (11.6) ËR ¯ h

    where n is the saturation exponent. The experimentally determined limits of n are 1.5 < n < 3.0, although n is usually assumed to be 2 where there is no evidence to the Combining equations (11.4) and (11.6) gives an alter- native expression for S

    1n Ê FRw ^ S = (11.7) ËR¯ h

    R is determined in parts of the borehole which are f 11.4.7 Permeability estimation Permeability (k) is a measure of the capacity of a forma- tion to transmit ?uid under the in?uence of a pressure gradient. It is dependent upon the degree of intercon- nection of the pores, the size of the pore throats and the active capillary forces. It is estimated from the minimum pore water remaining after displacement of the rest by hydrocarbons (the irreducible water saturation S ), which irr in turn is estimated from resistivity measurements in parts of the formation where irreducible saturation obtains:

    2 Ê cf 3 ^ k = (11.8) ËS ¯ irr formation. Large errors in determining the parameters from which k is derived render permeability the most k is commonly expressed in darcies, a unit corre- sponding to a permeability which allows a ?ow of 1 mm s-1 of a ?uid of viscosity 10-3 Pa s through an area of Reservoirs commonly exhibit values of permeability from a few millidarcies to 1 darcy.

    11.4.8 Resistivity dipmeter log The sonde of the dipmeter log contains four equally- spaced microresistivity electrodes at the same horizontal level, which allow the formation dip and strike to be es- timated. The orientation of the sonde is determined by reference to a magnetic compass and its deviation from The four electrodes are mounted at right angles to each other round the sonde. If the beds are horizontal, identical readings are obtained at each electrode. Non- identical readings can be used to determine dip and strike. In fact the four electrodes can be used to make four three-point dip calculations as a control on data quality. Dipmeter results are commonly displayed on tadpole plots (Fig. 11.9).

    Section True dip 20 40 60 80 where f is determined as in Section 11.4.5 and c is a con- stant dependent on the lithology and grain size of the Fig. 11.9 A typical tadpole plot obtained from a dipmeter log.

    (a) Transmitter 11.5 Induction logging The induction log is used in dry holes or boreholes that contain non-conductive drilling ?uid which electrically insulates the sonde.The wallrock is energized by an elec- tromagnetic ?eld, typically of about 20 kHz, which gen- erates eddy currents in the wallrock by electromagnetic induction. The secondary EM ?eld created is registered at a receiver which is compensated for direct coupling with the primary ?eld and which allows a direct estimate of apparent resistivity to be made. The set-up is thus similar to the surface moving coil-receiver EM system The two-coil system shown in Fig. 11.10(a) is unfo- cused and the induced EM ?eld ?ows in circular paths around the borehole, with a depth of investigation of about 75% of the transmitter–receiver separation. Litho- logical boundaries show up as gradual changes in appar- ent resistivity as they are traversed.When combined with information from other logs, corrections for invasion Clearer indications of lithological contacts can be ob- 11.10(b), in which two extra coils are mounted near the Such an arrangement provides a depth of penetration of Geophysical Borehole Logging 243

    (b) Receiver R R

    about twice the transmitter–receiver separation. This particular focused system has the disadvantage that spu- rious apparent resistivities are produced at boundaries, but this effect may be compensated by employing addi- See Section 9.6 for the application of time-domain electromagnetic techniques in borehole surveys.

    ?V boundary and generates a potential difference of a few In sequences of sandstone and shale, the sandstone anomaly is negative with respect to the shale. This SP effect provides a sharper indication of the boundary than resistivity logs. In such sequences it is possible to draw a `shale line’through the anomaly maxima and a`sand line’ through the minima (see Fig. 11.6). The proportion of sand to shale at intermediate anomalies can then be esti- The main applications of SP logging are the identi?- cation of boundaries between shale horizons and more porous beds, their correlation between boreholes, and They have also been used to locate coal seams. In hydro- carbon-bearing zones the SP log has less de?ection than normal and this `hydrocarbon suppression’ can be an indicator of their presence.

    11.7 Radiometric logging Radiometric logs make use of either the natural radio- activity produced by the unstable elements 238U, 232Th and 40K (Section 10.2), or radioactivity induced by the bombardment of stable nuclei with gamma rays or neu- trons. Gamma rays are detected by a scintillation counter (Section 10.4.2) or occasionally by a Geiger–Müller Radioactivity in borehole measurements is usually expressed in API (American Petroleum Institute) units, which are de?ned according to reference levels in a test pit at the University of Houston.

    11.7.1 Natural gamma radiation log Shales usually contain small quantities of radioactive elements, in particular 40K which occurs in micas, alkali feldspars and clay minerals, and trace amounts of 238U and 232Th. These produce detectable gamma radiation from which the source can be distinguished by spec- trometry; that is, measurements in selected energy bands (Section 10.4.3). The natural gamma radiation log conse- quently detects shale horizons and can provide an esti- Potassium-rich evaporites are also distinguished. An The natural gamma radiation log (or gamma log) mea- sures radioactivity originating within a few decimetres of the borehole. Because of the statistical nature of gamma-ray emissions, a recording time of several sec- onds is necessary to obtain a reasonable count, so the sen- sitivity of the log depends on the count time and the speed with which the hole is logged. Reasonable results are obtained with a count time of 2 s and a speed of 150 mm s-1. Measurements can be made in cased wells, but the intensity of the radiation is reduced by about 30%.

    Geophysical Borehole Logging 245 Lithology Shaly dolomite Cherty dolomite Clean dolomite Shale and anhydrite

    Anhydritic dolomite Shale Dolomitic shale Fig. 11.12 Natural gamma and neutron logs over the same sequence of dolomite and shale. (AfterWood et al. 1974.)

    rw r = e (11.9) f 2Â N

    where w is the molecular weight of the constituents of the formation and N is the atomic number of the elements present, which speci?es the number of The sonde has a plough-shaped leading edge which cuts through the mudcake, and is pressed against the wallrock by a spring. Most of the scattering takes place within about 75 mm of the sonde. A modern version of the sonde uses long and short spacings for the detectors which are sensitive to material far from and near to the Porosity f may be estimated from the density mea- surements. For a rock of formation density r , matrix f density r and pore ?uid density r mw

    r = fr + (1 – f )r (11.10) fwm

    Thus (r – r ) f = m f (11.11) (r – r ) mw Depth (feet)

    B 2800 D B A

    E B 2900 C G A F A B F D Gamma ray API Units 3000 Percentage porosity 25 20 15 10 5 4 3 2 1

    Neutron (API units) 0 60 120 400 900 1400

    11.7.3 Neutron–gamma-ray log In the neutron–gamma-ray (or neutron) log, non- radioactive elements are bombarded with neutrons and, as a result of neutron capture by the nuclei, they are stim- ulated to emit gamma rays which provide information on porosity. The sonde contains a neutron source, con- sisting of a small quantity of a radioactive substance such as Pu–Be, and a scintillation counter (Section 10.4.2) a The neutrons collide with atomic nuclei in the wall- rock. Most nuclei are much more massive than neutrons, which rebound `elastically’ with very little loss of kinetic energy. However, a hydrogen ion has almost the same mass as a neutron, so collision transfers considerable ki- netic energy and slows the neutron to the point at which it can be absorbed by a larger nucleus. This neutron capture, which normally occurs within 600 mm of the borehole, gives rise to gamma radiation, a proportion of which impinges on the scintillation counter. The intensity of the radiation is controlled by how far it has travelled from the point of neutron capture. This distance depends mainly on the hydrogen-ion concen- tration: the higher the concentration, the closer the neu- tron capture to the borehole and the higher the level of radiation.

    In sandstone and limestone all hydrogen ions are present in pore ?uids or hydrocarbons, so the hydro- gen ion concentration is entirely dependent upon the porosity. In shales, however, hydrogen can also derive from micas and clay minerals. Consequently, the litholo- gy must be determined by other logs (e.g. gamma log) before porosity estimates can be made in this way. Simi- lar count times and logging speeds to other radiometric methods are used.The method is suitable for use in both cased and uncased boreholes. An example is given in Fig. 11.12.

    11.8 Sonic logging The sonic log, also known as the continuous velocity or acoustic log, determines the seismic velocities of the for- mations traversed.The sonde normally contains two re- ceivers about 300 mm apart and an acoustic source some The source generates ultrasonic pulses at a frequency of Since the wallrock invariably has a greater velocity than the drilling ?uid, part of the sonic pulse is critically

    (a) S R 1 R 2 (b) S 1 R 1 R 2 R 3 R 4 S 2 Fig. 11.13 (a) A simple sonic log. (b) A borehole-compensated sonic log.

    refracted in the wallrock and part of its energy returns to the sonde as a head wave (Section 3.6.3). Each sonic pulse activates a timer so that the differential travel time between the receivers can be measured. If the sonde is tilted in the well, or if the well diameter varies, different path lengths result. This problem is overcome, in a borehole-compensated log, by using a second source on the other side of the receivers (Fig. 11.13(b)) so that the tilt effect is self-cancelling when all four travel paths are Porosity f may be estimated from the sonic measure- ments (see Section 3.4). For a rock whose matrix velo- city (the velocity of its solid components) is V and pore m ?uid velocity is V , the formation velocity V is given by wf

    (11.12) VVV fwm 1 f 1-f =+ The velocity of the matrix can be determined from cut- Sondes of the dimensions described above have trans- mission path lengths that lead to penetrations of only a few centimetres into the wallrock and allow the discrim- ination of beds only a few decimetres in thickness. How- ever, they are greatly affected by drilling damage to the wallrock and, to overcome this, longer sondes with source–geophone spacings of 2.1–3.7 m may be used. In addition to providing porosity estimates, sonic logs may be used for correlation between boreholes and are also used in the interpretation of seismic re?ection data by providing velocities for the conversion of re?ection Sonic logs can also provide useful attenuation infor- mation, usually from the ?rst P-wave arrival. Attenua- tion (Section 3.5) is a function of many variables including wavelength, wave type, rock texture, type and nature of pore ?uid and the presence of fractures and ?s- sures. However, in a cased well, the attenuation is at a minimum when the casing is held in a thick annulus of cement and at a maximum when the casing is free. This forms the basis of the cement bond log (or cement evaluation probe) which is used to investigate the effec- tiveness of the casing. Other techniques make use of both P- and S-wave travel times to estimate the in situ elastic moduli (Section 5.11). See also the description of vertical seismic pro?ling in Section 4.13.

    Shale 1st white specks 600 2nd white specks Sandstone Impure siltstone Depth below surface (m) Carbonate Anhydrite Shale Carbonate minor 1200 chert Shale Carbonate minor anhydrite

    Salt Carbonate 1800 Precambrian 3 4.5 6 Shale Interval velocities (km s–1)

    Fig. 11.14 A continuous velocity log. (After Grant &West 1965.)

    11.9 Temperature logging Temperature gradients may be measured through a borehole section using a sonde on which a number of closely-spaced thermistor probes are mounted. The vertical heat ?ux H is estimated by

    dq H = kz (11.13) dz

    where dq/dz is the vertical temperature gradient and k z Geophysical Borehole Logging 247

    is the thermal conductivity of the relevant wallrock, which Temperature gradients within about 20 m of the Earth’s surface are strongly affected by diurnal and sea- sonal changes in solar heating and do not provide reliable estimates of heat ?ux. Porous strata can also strongly in- ?uence temperature gradients by the ingress of connate water and because their contained pore ?uids act as a thermal sink. Heat ?ux measurements are commonly made to assess the potential of an area for geothermal energy utilization.

    11.10 Magnetic logging 11.10.1 Magnetic log The normal magnetic log has only limited application.The magnetic ?eld is either measured with a downhole ?ux- gate or with a proton magnetometer (Section 7.6) or a susceptibility meter is utilized. Anomalous readings indicate the presence of magnetic minerals.

    11.10.2 Nuclear magnetic resonance log The nuclear magnetic resonance (or free ?uid index) log is used to estimate the hydrogen ion concentration in formation ?uids and, hence, to obtain a measure of porosity. The method of measurement resembles that of the proton magnetometer, but with the formation ?uid taking the place of the sensor. A pulsed magnetic ?eld causes the alignment of some of the hydrogen ions in a direction different from the Earth’s ?eld. A receiver measures the amplitude and decay rate of the precession of the protons as they realign in the geomagnetic ?eld direction when the polarizing ?eld is inactive. The amplitude measure- ments provide an estimate of the amount of ?uid in the pore spaces and the rate of decay is diagnostic of the type of ?uid present.

    11.11 Gravity logging In situations where density is a function of depth only, the strata being substantially horizontal, stepwise mea- surement of the vertical gravity gradient with a gravity log can be used to estimate mean densities according to the A specialized borehole gravimeter of LaCoste and Romberg type (Section 6.4) is used for gravity logging.

    The instrument has a diameter of about 100 mm, an ac- curacy of ±5 microgal, and is capable of operation in The normal vertical spacing of observations is about 6 m and, if depths are determined to ±50 mm, densities can be estimated to ±0.01 Mg m-3, which corresponds to an accuracy of porosity estimation of about ±1%. The density applies to the part of the formation lying within about ?ve times the spacing between observations. This is more accurate than other methods of measuring den- sity in boreholes and can be used in cased holes. It is, however, time consuming as each reading can take 10–20 min and the meter is so costly that it can only be risked in boreholes in excellent condition.

    Problems 1. A sandstone, when saturated with water of re- Calculate the probable range of porosity for this 2. On a sonic log, the travel time observed in a sandstone was 568 ms over a source–receiver dis- tance of 2.5 m. Given that the seismic velocities of quartz and pore ?uid are 5.95 and 1.46 km s-1, respectively, calculate the porosity of the sand- stone. What would be the effect on the observed travel time and velocity of the sandstone if the pore ?uid were methane with a velocity of 3. During the drilling of an exploratory bore- hole, the rock chippings ?ushed to the surface indicated the presence of a sandstone–shale se- quence. The lateral log revealed a discontinuity at 10 m depth below which the resistivity decreased markedly. The SP log showed no de?ection at this depth and recorded consis- tently low values. The gamma-ray density log in- dicated an increase in density with depth across (a) Infer, giving your reasons, the nature of the (b) What porosity information is provided by the 4. Figure 11.15 shows the SP and short normal (including a partial expanded scale version), long normal and lateral resistivity logs of a bore- hole penetrating a sedimentary sequence. Inter- 5. Figure 11.16 shows the SP, induction, lat- erolog, sonic, calliper and gamma logs of a bore- Spontaneous potential (mV) Depth (m) Resistivity (?m) Resistivity (?m) 5 – + 16” Normal 0 10 Lateral 0 50 0 50 64” Normal 0 50 700

    800 900 1000 1100 (After Desbrandes 1985.) hole in a sequence of shale and sandstone. Inter- 6. Two gravity readings in a borehole, 100 m apart vertically, reveal a measured gravity differ- ence of 107.5 gu. What is the average density of the rocks between the two observation levels?

    Geophysical Borehole Logging 249 Fig. 11.16 SP, induction, resistivity, sonic, calliper and gamma-ray logs pertaining to Question 5. (After Ellis 1987.) Calliper (diam. in inches) 8 18 Spontaneous potential (mV) Depth (m) Resistivity (?m) Internal transit time (µs ft–1) Gamma ray (API units) 0 100 15 – + Deep induction 0.2 1.0 10 20 150 ?t 50

    Focused resistivity 0.2 1.0 10 20 800 820 840 Further reading Asquith, G.B. & Gibson, C.R. (1982) Basic Well Log Analysis for Chapellier, D. (1992) Well Logging in Hydrogeology. A.A. Balkema Desbrandes, R. (1985) Encyclopedia of Well Logging. Graham & Dyck, A.V. &Young, R.P. (1985) Physical characterization of rock Ellis, D.V. (1987) Well Logging for Earth Scientists. Elsevier, Hearst, J.R. & Nelson, P.H. (1985) Well Logging for Physical Proper- Hurst, A., Lovell, M.A. & Morton A.C. (eds) (1990) Geological Econ. Geologists,Tulsa.

    Pirson, S.J. (1977) Geologic Well Log Analysis (2nd edn). Gulf, Segesman, F.F. (1980) Well logging method. Geophysics, 45, Serra, O. (1984) Fundamentals of Well-log Interpretation, 1. The Serra, O. (1986) Fundamentals of Well-log Interpretation, 2. The Snyder, D.D. & Fleming, D.B. (1985) Well logging – a 25 year Tittman, J. (1987) Geophysical well logging. In: Samis, C.G. & Henyey,T.L. (eds), Methods of Experimental Physics,Vol. 24, Part B – Field Measurements. Academic Press, Orlando, 441–615.

    Appendix: SI, c.g.s. and Imperial (customary USA) units and conversion factors

    Imperial (USA) Quantity SI name SI symbol c.g.s. equivalent equivalent Mass kilogram kg 103 g 2.205 lb Time second s s s Length metre m 102 cm 39.37 in 3.281 ft Acceleration metre s-2 m s-2 102 cm s-2 = 102 gal 39.37 in s-2 Gravity gravity unit gu = mm s-2 10-1 milligal (mgal) 3.937 ¥ 10-5 in s-2 Density megagram m-3 Mg m-3 g cm-3 3.613 ¥ 10-2 lb in-3 62.421 lb ft-3 Force newton N 105 dyne 0.2248 lb (force) Pressure pascal Pa = N m2 10 dyne cm-2 = 10-5 bar 1.45 ¥ 10-4 lb in-2 Energy joule J 107 erg 0.7375 ft lb Power watt W = J s-1 107 erg s-1 0.7375 ft lb s-1 1.341 ¥ 10-3 hp Temperature T °C* °C (1.8T + 32)°F Current ampere A A A Potential volt V V V Resistance ohm W = V A-1 W W Resistivity ohm m W m 102 W cm 3.281 ohm ft Conductance siemens S = W-1 mho mho Conductivity siemens m-1 S m-1 10-2 mho cm-1 0.3048 mho ft-1 Dielectric constant dimensionless Magnetic ?ux weber Wb = V s 108 maxwell Magnetic ?ux tesla T = Wb m-2 104 gauss (G) density (B) Magnetic anomaly nanotesla nT = 10-9 T gamma (g ) = 10-5 G Magnetizing ?eld ampere m-1 A m-1 4p ¥ 10-3 oersted (H) (Oe) Inductance henry H = Wb A-1 109 emu (electromagnetic unit) Permeability of vacuum (m ) henry m-1 4p ¥10-7 H m-1 1 0 Susceptibility dimensionless k 4p emu Magnetic pole strength ampere m A m 10 emu Magnetic moment ampere m2 A m2 103 emu Magnetization ( J) ampere m-1 A m-1 10-3 emu cm-3 * Strictly, SI temperatures should be stated in kelvin (K = 273.15 + °C). In this book, however, temperatures are given in the more familiar Centigrade (Celsius) scale.

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    Index Note: Page numbers in italics refer to Figures; those in bold refer toTables

    3C seismic re?ection surveys 76–7 3D seismic re?ection surveys 72–6 4D seismic surveys 77–9

    absorption coef?cient 28 acoustic impedance 28 acoustic log 246 aeromagnetic surveys 164–5 air guns 37–8 airborne electromagnetic surveying 218–20 ?xed separation systems 218–20 quadrature 218, 220 algebraic reconstruction technique (ART) 118 aliasing 10 alkali vapour magnetometer 164 alpha particles 231 analogue data 8, 9 annulus of invasion 236 antialias ?ltering 10 antiferromagnetic materials 157 apparent resistivity 185, 188 apparent velocity 102 approximate thickness 141–2 arrays 41, 53 attribute, de?nition 86 audio frequency magnetic ?eld (AFMAG) 210, 211 autocorrelation 17, 18 side lobes in 17, 18 average velocity 43, 45 axial modulus 22, 23

    band-pass frequency ?lters 18–19 band-reject frequency ?lters 18–19 Bell gravimeter 129, 129 Bessel function of order zero 191 beta particles 231 bit 9 blind layer 110–11, 111 Block wall 158 body waves 23–4 Bolt air gun 37 boomers 39, 89, 91 Bouguer anomalies 136–7, 145, 146, 148, 148, 150, 150 Bouguer correction (BC) 134–5, 138 Bouguer slab formula 141 bow-tie event 67, 69 bright spots 84 bubble pulses 37 buffalo guns 36, 36 bulk modulus 22, 23

    calliper log 237 causative body 125 cementation factor 241 chargeability 200 chemical remanent magnetization (CRM) 158 chirp systems 39 circular gravity anomaly 142, 143 Clairaut’s formula 134 coherent noise 17–18, 34, 53 combined elevation correction 134 common depth point (CDP) 50 common depth point (CDP) method 122, 226 common mid-point (CMP) gather 48, 50–1, 51, 60 common mid-point (CMP) pro?ling 51 common mid-point (CMP) surveying 54–7 common shot point gathers 49 compressional waves (longitudinal, primary or P-waves) 23, 24 velocities 27 Compton scattering 244 conductivity 183 constant offset pro?les 122 constant separation traversing (CST) 186, 196, 217 continuous velocity log (CVL) 27, 246 convolution 13–15 convolution model 48, 49 Cooley–Tukey method 12 correlation 16–17 correlogram 35 critical angle 31 critical distance 33 critical refraction 31 cross-correlation 16, 17, 18 cross-coupling 128 cross-coupling error 128 cross-dip 67 crossed array method 73 crossover distance 33 Curie temperature 157 current ?ow in the ground 184–6 curve matching 189, 191 curve of maximum convexity 70

    diffraction migration 70, 71 digital ?ltering 17–19 digital processing techniques 168 digitization of geophysical data 8–10 dip-angle 209 dip moveout 46, 47, 47 dipmeter log 242 dipping re?ector 46–7 Dirac function 12 direct hydrocarbon indicators (DHIs) 77, 86 direct problem 6 direct ray 32 diurnal variation correction 165 diurnal variations 160 diving waves 112 Dix formula 46, 61 double-dipole con?gurations 201, 202 downhole geophysical surveying 236 downward continuation methods 145 drift 127 drift correction 133 dual source array method 73, 75 dynamic correction 57, 59–61 dynamic range 8, 9

    echo-sounding 6 elastic moduli 22, 23 electrical imaging 193 electrical method 2 electrical pro?ling 186 electrical tomography 193 electrode polarization 200 electrode spreads 186 electrolytic polarization 199 electromagnetic data, interpretation 221 limitations of method 221 electromagnetic surveying 2 applications 226–8 depth of penetration of electromagnetic ?elds 208–9 detection of electromagnetic ?elds 209 electron density index 244 elevation corrections 114–15, 134–6, 166 elevation static correction 58 elliptical polarization 209 end-to-end times 104 Eötvös corrections 129, 136 equipotential surfaces 185 equivalence 192 equivalent layer 144 Euler deconvolution 142, 168 excess mass 141 expanding spread pro?les 122

    fan ?ltering 65–7 fan-shooting 4, 115–16, 116 fast Fourier transform (FFT) 12 ferrimagnetic materials 157 ferromagnetic materials 157 ?eld static 59 ?ltering 13, 13, 15 of seismic data 61–7 ?nite difference migration 70 ?xed separation systems 218–20 f-k ?ltering 66, 68 f-k-plot 66, 66 ?at spots 84 ?uxgate magnetometer 162–3, 162 fold of the stacking 57 formation factor 241 Fourier analysis 10 Fourier pair 12 Fourier transformation 12, 145, 199 free-air anomaly 136–7, 147 free-air correction (FAC) 134, 134 free ?uid index (nuclear magnetic resonance log) 247 frequency domain 11 frequency domain IP surveying 199 frequency-domain migration 70 frequency ?lters 18–19 frequency ?ltering 62 frequency spectrum 12 Fresnel zone 53 fundamental frequency 10

    gamma 156 gamma log (natural gamma radiation log) 244, 245 gamma-ray density (gamma-gamma) log 244–5 gamma-ray spectrometer 233–4 gamma rays 231 Gauss theorem 141, 156 Geiger (Geiger–Müller) counter 233 generalized reciprocal method (GRM) 109, 119 geocentric dipole 159 geoid 125 geomagnetic correction 166 geomagnetic elements 159, 159 geomagnetic ?eld 159–60 geometrical spreading 27 geophones 39 geophysical anomaly 3 geophysical borehole logging drilling 236 formation evaluation 237 principles 236–7 geophysical surveying 1 ambiguity in interpretation 6–7 ?elds of application 2, 3 methods 1–6, 2 ghost re?ections 47 global positioning system (GPS) 58, 74, 113, 132 gradient-amplitude ratio method 141 Grand Saline Salt Dome,Texas 3, 4 graphs 8, 9 gravimeters 126–9 gravitational acceleration (gravity) 125 gravitational potential 125 gravity 125 measurement of 126–9 units of 126 gravity anomaly 3, 4, 129–30 direct interpretation 140–2 indirect interpretation 142–4 interpretation of 139–44 inverse problem 139 regional ?elds and residual anomalies 139–40 of simple shaped bodies 130–2, 130, 131 Gravity Formula 160 gravity logging 247–8 gravity meters 126–9 gravity reduction 133–7 gravity surveying 132–3 applications 147–50 basic theory 125 gravity unit 126 ground magnetic surveys 164 ground-penetrating radar (GPR) 20, 225–6 group 53 guard log (laterolog) 240–1, 240

    half-width method 140–1 Hammer chart 135 hammers 36 harmonics 10, 160 Haynesville Salt Dome,Texas 6, 6 head wave 31, 31 heat ?ux 247 hidden layer 110–11, 111 high-pass frequency ?lters 18–19 Hooke’s Law 22, 126 horizontal re?ectors sequence of 45–6 single 43–5 hydrocarbon saturation estimation 241– 2 hydrophones 39, 40–1 hydrostatic stress 22

    indirect ?lter 191 induced magnetization 156 induced polarization (IP) method 183, 199–203 applications 202–3 data interpretation 201–2 ?eld operation 201 measurements 200–1 mechanisms 199–200 induction log 243, 243 induction number 216 in?ection point 141 INPUT 214, 219–20, 219, 220 intercept time 100 International Geomagnetic Reference Field (IGRF) 160, 166 International Gravity Formula 134 International Gravity Standardization Network (IGSN) 126 interval velocity 43 inverse (deconvolution) ?lters 16, 19 inverse ?ltering (deconvolution) 62–5 inverse problem 6 irreducible water saturation 242 isochron maps 81 isogal maps 137 isopach maps 81

    k-capture 231 Klauder wavelets 35 Königsberger ratio 158 LaCoste and Romberg gravimeter 127, 127, 128, 129, 247 lag 16 Laplace’s equations 144, 188, 191 lateral log 239–40, 239 laterolog (guard log) 240–1, 240 latitude correction 133–4 Lenz’s law of induction 155 limiting depth 140–1, 140, 168 line spectra 11 LISPB experiment 121 long normal log 239, 239 long-path multiples 48 longitudinal waves (compressional, primary or P-waves) 23, 24 looping 132, 132 lost-time incidents 34 Love waves 25, 25 low-pass frequency ?lters 18–19, 19

    magnetic anomalies 4, 160–2 direct 168–70 indirect 170–2 interpretation 166–72 magnetic domain 157 magnetic equator 159 magnetic ?eld 155 magnetic ?eld B 155 magnetic ?ux 155 magnetic induction 155 magnetic log 247 magnetic method 2 magnetic moment 156 magnetic observations, reduction of 165– 6 magnetic permeability 155 magnetic permeability of vacuum 155 magnetic polarization 156 magnetic potentials 155 magnetic radiometer 164 magnetic storms 160, 165 magnetic surveying applications 173–81 basic concepts 155–8 instruments 162–4 magnetic susceptibility 156 magnetic variometers 162 magnetizing force H 155 magnetotelluric ?elds 221–4 marine surveys 164–5 marine Vibroseis 38 matched ?lters 63 matrix 26 membrane polarization 199 metal factor (MF) 201 microlog (wall-resistivity) 241, 241 mid-point 50 migration 67 migration of re?ection data 67–72 milligal 126 minimum delay 12 Mini-Sosie 35–6 minus term 108 mise-à-la masse method 195, 195 Mohorovicic discontinuity 94 move-up rate 57 moveout 45 moving-coil geophone 39–40, 39 mudcake 236 multichannel re?ection survey design 51– 7 common mid-point (CMP) surveying 54–7 design of detector arrays 53–4 display of seismic re?ection data 57 vertical and horizontal resolution 52– 3 multiple re?ections 47 multiples 47

    nanotesla 1556 natural gamma radiation log (gamma log) 244, 245 Index 259

    Nettleton’s method of density determination 138, 138 neutron-gamma-ray log 245–6, 245 Newton’s Law of Gravitation 125 noise 17 noise section 54 noise spread 54 noise test 54, 55 non-contacting conductivity measurement 216–17 non-linear optimization 144 normal log 238–9, 238 normal moveout (NMO) 45 nuclear magnetic resonance log (free ?uid index) 247 nuclear precession magnetometer 163–4, 163 Nyquist frequency 10 Nyquist interval 10

    ocean bottom seismographs (OBSs) 112 oceanographic recorder 88 off-levelling errors 128 offset VSP 79, 79 optical pumping 164 optically pumped magnetometer 164 out of phase (imaginary, quadrature) component of S 213 Overhauser Effect 164 overvoltage 200

    pores 26 porosity 26 porosity estimation 241 potential ?eld manipulation 144–6 transformations 172–3 potential theory 144–6 power 9 power spectrum 17 predictive deconvolution 16, 63 primary waves (longitudinal, compressional, or P-waves) 23, 24 primary re?ections 47 principal stresses 22 proton magnetometer 163–4, 163 pseudogravitational ?elds 172 pseudomagnetic ?elds 172 pseudosection 193, 201 pulse-height analysers 234 pulsed electromagnetic surveying 214 P-wave (primary, longitudinal or compressional) 23, 24 P-wave ray 30 re?ected and refracted 30

    quadrature (out of phase, imaginary) component of S 213 quadrature systems 218, 220

    radargram 226 radioactive decay 231–2 radioactive minerals 232, 232 radiometric ?eld surveys 235 examples 235 radiometric logging 244–6 radon emanometer 234–5 random noise 17–18 ray parameter 30 ray paths in layered media 28–32 re?ection and transmission of normally incident seismic rays 28–30 ray trace migration 71 ray-tracing 110 Rayleigh waves 24, 25 real (in-phase) component of S 213 reciprocal times 104, 109 record surface 67 recurrence relationships 191 reduced time 115 reduction equation 192 reduction to the geiod 133 reduction to the pole 182 reduction velocity 115 re?ected ray 32–3 re?ection coef?cient 29 re?ection pro?ling 51–2, 225 re?ection seismogram 48–9 re?ection surveying 32–3 re?ectivity function 48 re?ector surface 67 refracted ray 30 refraction pro?ling 112–15 display of refraction seismograms 115 ?eld survey arrangements 112–13 recording scheme 113–14 weathering and elevation corrections 114–15 re?ection seismogram 48–51 refraction statics analysis 58 refraction surveying 32–3 relative magnetic permeability 155, 157 relative permittivity (dielectric constant) 225 remanent (permanent) magnetization 158 residual static analysis 59 resistivity data, interpretation of 187–8 constant separation traversing interpretation 193–6 limitations of the resistivity method 196 vertical electrical sounding interpretation 188–93 resistivity dipmeter log 242 resistivity logging 237–42 resistivity method 183–99 resistivity 183–4 resistivity surveying applications 196–9 equipment 186–7 resolution of the survey 34 retrograde motion 24 reverberations 47 ri?es 36 rippability 24, 120, 120 rock densities 137–9 rock magnetism 158–9 Roentgen 233 root-mean-square velocity 45

    seismograph 34 seismometers 39 self-potential effect 243 self-potential log 243–4, 244 self-potential (SP) method (spontaneous polarization) 183, 203–5 equipment and survey procedure 203– 4 interpretation of anomalies 204–5 mechanism 203 semblance 60 sferics 212 shallow marine seismic sources 89–90 shear modulus 22, 23 shear waves (transverse, secondary or S- waves) 23, 24 shipborne (shipboard) meters 128 short normal log 239, 239 short-path multiples 48 shot gathers 48, 49–50 shotguns 36 sidescan sonar systems 90–2 signal 17 signal amplitude 9 signal/noise ratio (SNR) 18 simultaneous reconstruction technique (SIRT) 118 single-channel marine re?ection pro?ling 86–92 single-ended pro?le method 105 single-ended spread 52 single-fold coverage 57 sleeve exploders 38 slingram system 213 Snell’s Law of Refraction 30–1, 100, 104, 118 Sodera water gun 37 solid Earth tides 136 sonde 236 sonic logging 27, 246 sonograph 92, 112 sparkers 38–9, 90 spectral analysis 10–13 spherical harmonic analysis 160 spontaneous polarization see self-potential (SP) method spike functions 14 spiking deconvolution 64 split-pro?le method 105 split spread (straddle spread) 52 stable (static) gravimeters 126 stacking velocity 60 static corrections 57–9, 59 static (stable) gravimeters 126 straddle spread (split spread) 52 strain 22 stratigraphic modelling 85 stratigraphical analysis (seismic stratigraphy) 80, 82–5 stress 21–2 stress–strain curve 22, 22 structural analysis 80, 81–2 structural contour maps 81 sub-bottom pro?ling systems 90 subweathering velocity 58 suppression 192 surface waves 23, 24–5 S-wave rays 30 re?ected and refracted 30 S-waves (secondary, shear or transverse) 23, 24

    tadpole plot 242, 242 telluric currents 6, 6, 187, 187, 201, 221– 4 temperature logging 247 term-time (delay time) 101, 106–8, 107 terrain correction (TC) 135, 135, 135, 166 tesla 156 thermal conductivity 247 thermoremanent magnetization (TRM) 158 three-dimensional migration 74 three-dimensional surveys 52 tidal correction 136 tidal variations 136 tilt-angle 209 tilt-angle methods 209–12 audio frequency magnetic ?eld (AFMAG) 210, 211 employing local transmitters 210 very low frequency (VLF) method 210–11 time-average velocity 43 time-distance curve 33, 44, 100 time domain 11 time-domain electromagnetic surveying 214–15, 216 time domain IP surveying 199 time migration 67 time-slice 75 time-structure maps 81 time term method 115, 116–17 time variable gain (TVG) 88 time-varying seismic pulse 49 torsion head magnetometer 162 tortuosity 241 total ?eld vector 159 transducer 33 transfer function 14 transient-?eld electromagnetic surveying 214 transient waveforms 10, 11 Index 261

    transillumination 226 transmission coef?cient 29 transverse resistance 192 transverse waves (S-waves, secondary or shear waves) 23, 24 travel path 45, 46 travel time of a direct ray 33 of a re?ected ray 33 of a refracted ray 33 travel-time curves 32, 33 trend analysis 166 turam system 213 turning point 112 twin-coil system 213 two-dimensional migration 67 two-dimensional surveys (re?ection pro?ling) 51–2, 225 two-frame compensator system 213 two-pass method 75, 75 T–x graph 121

    uphole surveys 58 uphole time 59 upward continuation methods 145

    velocity analysis 59–61 velocity ?ltering (fan ?ltering/pie slice ?ltering) 65–7 velocity sounding 225–6 velocity spectrum 60, 61 vertical electrical sounding (VES) (electrical drilling , expanding probe) 185–6, 196, 197 vertical seismic pro?ling 79–80 vertical time (VT) 59 vibrating string accelerometer 128–9 Vibroseis 35, 36, 63 marine 38 viscous remanent magnetization (VRM) 158 void detection 150

    wavenumber ?lters 146 waves 25–6 weathering corrections in re?ection seismology 58 in refraction seismology 114–15, 115 weight drops 36 Wenner con?guration 186, 186, 189 white noise 64 whitening 63 whitening deconvolution 64 wide-angle re?ection and refraction (WARR) method 225–6 wide-angle re?ections 99, 113 wide-angle surveys 113 Wiener ?lters 63, 64, 64 wire-line logging 236 word 9 Worden-type gravimeter 127, 129 yield strength 22 Young’s modulus 22, 23

    (a) Plate 4.4 (a) Seiscrop section at 196 ms from a three-dimensional survey in the Gulf of Thailand area, showing a meandering stream channel.