ALBERT

Notes: We present a new method for the extraction and removal of the source wavelet from the reflection seismogram. In contrast to all other methods currently in use, this one does not demand that there be any mathematically convenient relationship between the phase spectrum of the source wavelet and the phase spectrum of the earth impulse response. Instead, it requires a fundamental change in the field technique such that two different seismograms are now generated from each source-receiver pair: the source and receiver locations stay the same, but the source used to generate one seismogram is a scaled version of the source used to generate the other. A scaling law provides the relationship between the two source signatures and permits the earth impulse response to be extracted from the seismograms without any of the usual assumptions about phase.We derive the scaling law for point sources in an homogeneous isotropic medium. Next, we describe a method for the solution of the set of three simultaneous equations and test it rigorously using a variety of synthetic data and two types of synthetic source waveform: damped sine waves and non-minimum-phase air gun waveforms. Finally we demonstrate that this method is stable in the presence of noise.

Notes: In this paper a theorem is demonstrated which allows—after the introduction of a suitable dipole kernel function or dipole resistivity transform function—to write the apparent resistivity function as an Hankel transformable integral expression.As a practical application of the theorem a procedure of quantitative interpretation of dipole soundings is suggested in which the dipole resistivity transform function obtained after inversion of the original dipole apparent resistivity data is used to control the goodness of the set of layering parameters which have been derived with our previous method of transformation of dipole sounding curves into equivalent Schlumberger diagrams.

Notes: The Hankel transform theorem can be applied to the inversion of gravity data for the buried sphere, the horizontal cylinder, and the vertical rod. This new approach leads to exact solutions of the transforms for the assumed bodies. A comparison with the classical procedure by Fourier transform reveals that for the sphere and the vertical rod, the Hankel transform is preferable.

Notes: Air guns have been used in various applications for a number of years. They were first used in coal-mining operations and were operated at up to 16000 psi charge pressures. Later, single air guns, operated at 2000 psi, found application as an oceanographic survey tool. Air gun arrays were first used in offshore seismic exploration in the mid-1960's. These early arrays were several hundred cubic inches in total volume and were operated at 2000 psi; they were either tuned arrays or several large guns of the same size with wave-shape kits. Today's arrays have total volumes greater than 5000 cu in. and are typically operated at 2000 psi. Recently, higher-pressure, lower-volume arrays operated at 4000–5000 psi have been introduced; guns used in these arrays are descendants of the coal-mining gun.On first thought one would equate increased gun pressure linearly with the amplitude of the initial pulse. This is approximately true for the signature radiated by a “free-bubble” (no confining vessel) and recorded broadband. The exact relation depends on the depth at which the gun is operated; from solution of the free-bubble oscillation equation, the relation is 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR700:GPR_700_mu1"/〉 If Pc,1= 6014.7 psia, Pc,2= 2014.7 psia and PO, 1=PO, 2= 25.8 psia (corresponding to absolute pressure at 25 ft water depth), then 〈displayedItem type="mathematics" xml:id="mu2" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR700:GPR_700_mu2"/〉 Experiments were conducted offshore California in deep water to determine the performance of several models of air guns at pressures ranging from 2000 to 6000 psi and gun volumes ranging from 5 to 300 cu in. At a given gun pressure, the initial acoustic pulse Pa correlated with gun volume Vc according to the classical relation 〈displayedItem type="mathematics" xml:id="mu3" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR700:GPR_700_mu3"/〉 For 1 ms sampled data the ratio 〈displayedItem type="mathematics" xml:id="mu4" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR700:GPR_700_mu4"/〉 varied between 4.5 and 5.5 dB depending on gun model. Pulse width of the 2000 psi signatures indicated they are compatible with 2 ms sample-rate recording while pulse width of the 6000 psi signatures was greater, indicating they are less compatible with 2 ms sample-rate recording.Conclusions reached were that 2000 psi air guns are more efficient than higher pressure guns and are more compatible with 2 ms sample-rate requirements.

Notes: Numerous electrodes, already used in geophysics or just perfected by us, have been compared by measuring the three main characteristics which interest the user: noise spectrum, temperature coefficient and polarization with its stability versus time.Among the most used unpolarizable electrodes, silver-silver chloride (Ag-AgCl) are the best ones. But a systematic research of all different possible metal-salt couples, have led us to use lead-lead chloride (Pb-PbCl2) for the following reasons: noise as low as the one of Ag-AgCl at 1 Hz and even lower for the low frequencies (0.4 μV at 1 Hz and 1.2 μV at 0.01 Hz for peak to peak value and ΔF=F), temperature coefficient about ten times weaker (−40 μV/°C instead of −450 μV/°C) and also better long time stability of the polarization (1 mV/month instead of 2 at 10 mV/month).We have been using these electrodes since 1977 as “tube” electrodes which are very easy to use. They allow us to record correctly the fast variations thanks to their low noise, the very slow variations, their low temperature coefficient and their stability, and this with telluric lines only about 100 m long.

Notes: The compression of seismic signals which have propagated through a dispersive medium can be achieved by a frequency-domain transformation. This transformation is formally related to the dispersion characteristic of the medium and is independent of phase and group velocities. By defining a suitable cost-function to measure the degree of dispersion of a time- signal, an iterative technique can be employed to find that transformation which gives minimum dispersion.In this paper, we assume that the inverse of the dispersion characteristic can be adequately approximated by a finite polynomial in the region of maximum signal energy density. The coefficients of this polynomial are the parameters of dispersion of the medium. These parameters can be estimated both in the presence of noise and in the case of signals made up of multiple arrivals.The techniques developed in this paper are applied to seismic signals which have been recorded underground by a set of geophones designed to detect and map discontinuities in coal-seams. Results of dispersion estimation and signal compression are discussed for data collected in the Blackshale seam, Pye Hill Colliery, near Derby, in the United Kingdom.

Notes: Sign reversals have been observed with the one-loop version of the TEM method in an area near Cloncurry, Queensland. This is the only area in which such a response has been recorded in seven years of field surveys by the Australian Bureau of Mineral Resources.The geology of the area consists mainly of pyrrhotitic graphitic shale, which has resistivities as low as 0.1 Ωm and frequency effects up to 30%. The sign reversals could be due to magnetic phenomena, reflections from layers, or complex conductivity effects.

Notes: A crucial step in the use of synthetic seismograms is the estimation of the filtering needed to convert the synthetic reflection spike sequence into a clearly recognizable approximation of a given seismic trace. In the past the filtering has been effected by a single wavelet, usually found by trial and error, and evaluated by eye. Matching can be made more precise than this by using spectral estimation procedures to determine the contribution of primaries and other reflection components to the seismic trace. The wavelet or wavelets that give the least squares best fit to the trace can be found, the errors of fit estimated, and statistics developed for testing whether a valid match can be made.If the composition of the seismogram is assumed to be known (e.g. that it consists solely of primaries and internal multiples) the frequency response of the best fit wavelet is simply the ratio of the cross spectrum between the synthetic spike sequence and the seismic trace to the power spectrum of the synthetic spike sequence, and the statistics of the match are related to the ordinary coherence function. Usually the composition cannot be assumed to be known (e.g. multiples of unknown relative amplitude may be present), and the synthetic sequence has to be split into components that contribute in different ways to the seismic trace. The matching problem is then to determine what filters should be applied to these components, regarded as inputs to a multichannel filter, in order to best fit the seismic trace, regarded as a noisy output. Partial coherence analysis is intended for just this problem. It provides fundamental statistics for the match, and it cannot be properly applied without interpreting these statistics.A useful and concise statistic is the ratio of the power in the total filtered synthetic trace to the power in the errors of fit. This measures the overall goodness-of-fit of the least squares match. It corresponds to a coherent (signal) to incoherent (noise) power ratio. Two limits can be set on it: an upper one equal to the signal-to-noise ratio estimated from the seismic data themselves, and a lower one defined from the distribution of the goodness-of-fit ratios yielded by matching with random noise of the same bandwidth and duration as the seismic trace segment. A match can be considered completely successful if its goodness-of-fit reaches the upper limit; it is rejected if the goodness-of-fit falls below the lower one.

Notes: If the conductivity of any one of the layers of a horizontally stratified earth varies exponentially with depth with or without a discontinuity at the interface, the corresponding expressions for apparent resistivity for Wenner- and Schlumberger-sounding arrays can be formulated. The general case has been broadly divided into three categories for mathematical simplicity. All previous discussions of this problem can be regarded as particular cases of the present study.

Notes: The physical properties of the serpentinized pyroxenitic and saxonitic rocks from stratiform ultramafic complexes of Roro, Singhbhum distrct, India, are examined using principal factor (R-mode) analysis technique. The variations and inter-relations of these properties reflect the compound effects of two processes—(a) degree of serpentinization, and (b) mineralogical and other changes attendant to serpentinization. Factor analysis is thus shown to be an effective tool for petrophysical inferences.

Notes: The problem of numerical evaluation of apparent resistivity curves is treated by finite difference modeling. The models proposed are set up in cylindrical coordinates and yield the potential field due to a point source located in a radially symmetric environment. The Schlumberger configuration, widely used for surface measurements, is emphasized. However, the treatment is equally applicable to other similar situations such as the computation of synthetic electric logs when the resistivity of the borehole fluid is different from that of the surrounding uniform or stratified medium. Moreover, the individual layers may not necessarily be isotropic.The medium under investigation is discretized by using a very coarse system of horizontal and vertical grid lines whose distance from the source increases logarithmically; consequently, the physical dimensions of the medium can be made “infinite” without affecting the numerical size of the model. Finer features such as a thin but anomalously resistive or conductive bed which would ordinarily be missed in coarse discretization are accurately taken into account, since the calculations are done in terms of the Dar Zarrouk parameters derived from the exact resistivity distribution of the model. This enables one to compute the potential field by inverting a small sparse matrix. When the medium comprises only a few layers, the efficiency of the finite-difference model is comparable to that of the known analytical methods; for more complicated structures, however, the finite-difference model becomes more efficient. The accuracy of finite-difference results is demonstrated by comparing them with the corresponding analytically obtained data.

Notes: A new method of estimating seismic stacking velocity from reflection seismograms is based on Fibonacci search technique and provides the highest rate of reduction of the interval of uncertainty of the stacking velocity. A review of the Fibonacci search strategy is presented, the application of the method is illustrated with synthetic and field examples.

Notes: The paper relates primarily to the borehole and the side bed correction charts for Latero-logs 3 and 7. Versions of some of these charts published by different companies—or even by the same company in different years—exhibit significant variations. Usually, such publications do not contain adequate information on how the charts were constructed and do not explain why discrepancies occur.Because of these reasons, an attempt has been made in this paper to reconstruct the borehole correction chart for Laterolog 7 and the shoulder bed correction charts for Latero-logs 3 and 7. For the latter two, the results found differ substantially from those published earlier.The paper demonstrates how departure (response) curves and correction charts for the lateral and the Laterolog 7 sondes can be computed from those for the normal sonde. An apparent resistivity formula is suggested for Laterolog 7 in which all currents that exist in the ground at the time of measurement and that produce the signal are monitored and used. Response curves and correction charts for Laterolog 7, based on such a formula, are presented as illustrations.

Notes: For horizontal layering and plane horizontal impulsive wavefronts it is theoretically possible to get rid of multiple reflections by a feedback procedure which can easily be derived using raypath philosophy. To reduce the increase of noise inherent in the method the precise theoretical formulae are altered in such a manner that a practical application becomes possible. For this purpose the autocorrelation will be used.Application of the new process to a CRP section where the shot geophone distances in the field had not been long enough to attenuate multiple reflections effectively gave favourable results.

Notes: Two in situ measurements of stress wave velocity in a granodiorite massif were made. Firstly, the velocities close to the source were investigated (for elimination of the influence of cracks), and secondly, the velocities in different horizontal directions over a large area were studied from the viewpoint of their dependence on the crack system of the medium. A correlation between the mutual orientation of the cracks and the maximum or minimum values of the stress wave velocities was obtained.

Notes: The technique of linear digital filtering as developed for the direct interpretation of Schlumberger and Wenner soundings (Ghosh 1971) has been applied here for the derivation of the resistivity transform function from the field dipole measurements as the first step in directly interpreting dipole data. Filter coefficients for this transformation have been worked out for the radial-polar, perpendicular and parallel (30°) arrays of dipole sounding. The procedure combines speed with accuracy.

Notes: Dipole soundings are more sensitive to noise caused by lateral and superficial inhomogeneities than Schlumberger soundings. However, the former are preferable for deep explorations in view of the relatively short cables required. The simple solution of carrying out the field work by means of dipole spreads, and to transform the dipole resistivity diagrams into Schlumberger ones by means of proper formulae would be valid only for smooth and regular curves; but often, owing to the presence of lateral noises, the dipole data show a considerable scatter. For such cases a “continuous dipole sounding” method is proposed for which all successive dipoles are contiguous, so that all parts of the profiles are covered and interpolation is not necessary. Obviously the moving dipoles have lengths proportional to their distances, so that they appear equal in the usual bilogarithmic scale. It follows that only polar-dipole arrays may be used. The transition from a dipole to the corresponding Schlumberger apparent resistivity diagram requires an integration constant which is not unequivocally determined. Therefore, the solution is not unique, but all possible derived Schlumberger diagrams have a common part. Similarly, they have some common interpretative results, which may be referred to the original dipole diagram obtained in the field.A special measurement technique is required since the dipole-dipole voltages to be determined are noticeably smaller than the Schlumberger ones. This is true also because dipole soundings are used for great depths and for long distances between the two dipoles.

Notes: Basic requirements for a seismic reflection system using a moderate-power controlled source are discussed. General considerations and computer modelling show promise for geophysical prospecting, especially at low penetration and very high noise level. For many applications, ranging from mineral and water prospecting, to civil and military engineering, and even archeology, a relatively cheap, small and portable device of this kind might be more convenient than conventional explosive sources or sophisticated controlled sources of the vibroseis type. The use of a simple, low frequency periodic signal facilitates rapid data processing procedures and suggests that the mechanical generator will be very simple and cheap.

Notes: A method is described to transform a dipole sounding curve, obtained with any one of the common dipole arrays over a horizontally layered earth, to the form of a Schlumberger sounding curve. Starting from the general expression which relates the dipole apparent resistivity to the Schlumberger apparent resistivity and its derivative with respect to the spacing, it is possible with some approximations to derive an easy numerical computation procedure in order to perform the transformation. The applicability of the method is discussed briefly.

Notes: Approximate deconvolution by means of Wiener filters has become standard practice in seismic data-processing. It is well-known that addition of a certain percentage of noise energy to the autocorrelation of the signal wavelet leads to a filter that does not increase, or even reduces, the noise level on the seismogram. This noise addition will, in general, cause a minimum phase signal to become mixed phase. A technique is presented for the calculation of the optimum-lag shaping filter for a contaminated signal wavelet. The advantages of this method over the more conventional approach are that it needs less arithmetic operations and that it automatically gives the filter with the optimum combination of shaping performance and noise reduction.

Notes: A set of parabolae is defined to approximate the observed gravity profile for specifying the lateral density variation in a two dimensional causative body. This variation separates the “biased” as well as “unbiased” residual anomaly structure. The method may be directly incorporated into existing numerical and graphical techniques of interpretation for subsequent delineation of structural configuration. The simple relations derived by inspection of the observed gravity profile permit universal application of the technique and in particular for the determination of the size and shape of sub-shelf structures. The suitability of the method in various problems of two dimensional interpretation has been indicated through an illustration of the Godavari Basin (India).

Notes: Decomposition of IP discharge curve into a sum of exponentials yields more information than present practice does. Such a work was performed, as a beginning, by hand, plotting the ordinates on semi logarithimic paper. It gave, according to the cases, two or three exponentials, each with an amplitude Ai and the time constant τi.Three examples of ground prospection are given, the third of which shows an anomaly, unnoticed with present technique but obvious on a profile curve with A1/A2 in ordinates.A computer processing technique is described which yields directly the time constants τi by seeking a differential equation which the IP voltage satisfies; the order of the equation is set arbitrarily. On a practical prospection record with only two exponentials, the assumption that the differential equation does not depend on charge duration (everything else being equal) has been checked (the shape of the curves would depend on boundary conditions). The assumption roughly holds for charge durations from 5 seconds to 40 seconds. We hope that a larger number of exponentials will yield better results.〈section xml:id="abs1-2"〉〈title type="main"〉SommaireLa décomposition de la courbe de décharge en une somme d'exponentielles permet d'en tirer plus d'information que la pratique actuelle. Un tel travail a été fait, pour commencer, à la main en portant les ordonnées sur papier logarithmique; il a fourni, suivant les cas, deux ou trois exponentielles avec, pour chacune d'elles, le coefficient Ai et la constante de temps τi.On donne trois exemples de prospection sur le terrain, dont le dernier comporte une anomalie, inaperçue avec la technique actuelle, mais bien mise en évidence en traçant la courbe de A1/A2 le long du profil.On donne ensuite une technique de calcul sur ordinateur des τi, en recherchant l'équation différentielle à laquelle obéit la tension ΔVPP enregistrée, l'ordre de cette équation étant fixé arbitrairement. On a cherchéà vérifier sur un enregistrement de terrain, avec. deux exponentielles seulement, l'hypothèse suivant laquelle l'équation différentielle ne dépend pas de la durée de charge (toutes choses égales d'ailleurs). L'hypothèse se trouve grossièrement vérifiée pour les durées de charge allant de 5 secondes à 40 secondes, et nous espérons qu'un plus grand nombre d'exponentielles donnera de meilleurs résultats.

Notes: The conventional seismic technique is subject to a recording time following each transmission of energy, in which it is forbidden to release any new pulse. The recording time depends on the deepest reflection of interest, and is often 10 seconds or more in actual practice. To each transmission corresponds one record, i.e. a fixed amount of data which cannot be increased in a given time.Pulse coding allows us to go beyond this limit, by transmitting several times during the normal recording time. The procedure gives as many records as there are pulses, but they overlap, each event being repeated every time there is a pulse. It is possible to process the composite record back to its usual appearance with all events in their proper place if the time breaks are accurately known and make up a code such that the unavoidable noise generated by the process be kept, on the final section, below the ambient noise. The processing is quite similar to that of records made from vibrating sources, though faster in practice.The additional information can be devoted to a saving of time and money as the same profile may be recorded in a shorter time; or to an improvement of quality of the section due to a higher order of coverage, a multiplication of the ray paths and a closer sampling of the reflectors. It is also possible to record information in several planes at the same time, and to work out a 3-dimensional restitution, without loss of production.The process applies to all kinds of sources provided they can be triggered according to the code with sufficient accuracy. Depending on the source and conditions of implementation, the method benefits from other advantages such as better resolution, increased flexibility, and better coupling.Two different names have been given to the process, Sosie and Seiscode, which apply to slightly different parameters for the sequence of pulses. Sosie is more useful at sea, while the normal scope for Seiscode is onshore. Both names are trademarks for SNPA.

Notes: Two-layer type curves of apparent frequency effect for the Wenner configuration are presented. The formulation is based on the normal definition of frequency effect in terms of resistivities measured at different frequencies plus the definition of apparent resistivity over two horizontal layers as a function of first and second layer resistivities. The use of these type curves in the interpretation of multilayer apparent frequency-effect curves is described and some field examples are given.

Notes: In this paper properties of the discrete zero-phase time function are derived and compared with related properties of the discrete minimum-phase time function.The two-sided minimum-length signal is introduced and it is derived that, for any given amplitude spectrum, the two-sided minimum-length signal and the signal with zero-phase spectrum are identical signals. A comparison is made between the one-sided minimum-length signal (minimum-phase signal) and the two-sided minimum-length signal (zero-phase signal).A computational scheme is discussed which determines the zero-phase correspondent of a given signal.A method is proposed to compute zero-phase least-square inverse filters. The efficiency of minimum-phase and zero-phase least-square inverse filters is shown on signals with different phase properties.A criterion is derived which determines whether a symmetric time function has the zero-phase property. The close relationship with the minimum-phase criterion is discussed.Finally the relationship between signal length and resolving power is illustrated on numerical examples.

Notes: Empirical equalities derived from time domain induced polarization scale modelling with the gradient array over simple geometries, and from the potential field functions for equivalent simple charge configurations are similar. The function for the dyke like body is analogous to the magnetic case allowing both total and vertical magnetic field interpretation techniques to be applied to gradient array chargeability anomalies.

Notes: A checking method of digital multiple elimination and of deconvolution processing using computers and based on optical autocorrelation is first presented. Comparison between autocorrelograms before and after a single or several processing steps allows to estimate, on one hand, the strength of the deconvolution obtained, known by the study of the central parts which is in fact the signal autocorrelation, on the other hand, the multiple elimination given by the study of side parts of the autocorrelogram.Further, an optical deconvolution procedure, is presented. For this, it is supposed that the signal is known and optically reproduced in the same way as the one of a trace. This is achieved by sphero-cylindrical optics allowing trace to trace processing. Deconvolution is carried out in the spectral domain by inserting a filter in the Fourier plane of the optical unit, the transmission law of which expresses the Fourier transform of the antisignal. This filter device introduces a holographic technique called Fourier holography, in such a way phases as well as amplitudes are preserved.Several results are presented from a synthetic section and also from field sections.

Notes: The separation of regional from local gravity anomalies by means of the application of two-dimensional linear filters is analyzed. It was found that optimization of the filter in the least squares sense leads to filters that produce strong localized concentrations of the error, which may erroneously be interpreted as anomalies. For this reason the maximum absolute value of the error is a more important criterion for the quality of the filter than the root mean square error. This maximum absolute error is minimized by the minimax filter. Intermediate filters are derived which give a transition zone which comes appreciably closer to that of the optimal filter at only a small price in terms of increase of the maximum absolute error.

Notes: Cable feathering is defined as the angle between a line connecting the cable end points and the line of the seismic profile. It is shown that an average reflection point map is more accurate than a shot point location map for geologic interpretation. Geologic resolution is degraded by feathering and this degradation is a function of the number of channels recorded. Feathering in areas of dipping reflectors produces non-standard normal move-out because the depth points are not common, and the perpendicular distances to the reflecting surfaces vary among traces in the c.d.p. gather. An example of a profile shot across a large river is discussed.

Notes: First, we review briefly the principle of the method, the computation of theoretical curves for a layered earth, and the recording technique in use in our surveys.The case history deals with an area covered with overthrust nappes (marls of Miocene age), which had slid on a Triassic sole, obscuring the geological picture.The magnetotelluric survey followed those of gravity and aeromagnetics and preceded the seismic one from North to South, it displayed a shallow and gently dipping basin, a major fault system, and a deep basin with a thick resistive layer, often underlying a conducting one.The seismics, and later the drilling of a well East of the profile, confirmed these features; in particular, the thick resistive layer was revealed to be Jurassic; only its thickness had been slightly overestimated. This fact lead the people in charge of the operations to ask for a reinterpretation synthesis of magnetotellurics, seismics and gravity, the results of which are also presented.

Notes: The quality of results of migration before stack is sensitive to inaccuracies in the velocity field applied. This does not hold if only traces of similar sources-receiver distances (common offset traces) enter the migration process. In this case, velocity deviations generate minor shifts in travel times of migrated interfaces but no deterioration in quality. These time shifts are proportional to both the velocity error and the square of the source-receiver distance.The above observations suggest the following migration scheme: migrate separately the traces of the various common offset planes or groups of neighbouring common offset planes; for every common midpoint plane and as a function of travel-time perform a residual NMO search to find trajectories t) =t)o+px)2 of maximum coherency along which migrated events are aligned; correct for residual NMO and stack the migration results obtained in the various common offset planes to obtain the final migration result.This process not only takes care of inaccurate migration velocities but also corrects partly for effects of refraction.It is shown by means of an example that good migration results are generated even with a considerably deviating velocity field.

Notes: It is shown that the so-called Kirchhoff-summation operator is of a very wide-band nature and even contains an evanescent part. As a consequence, discretization may cause serious aliasing errors, particularly for small extrapolation steps. It is proposed to use in all practical cases band-limited versions of the summation operator, the spatial cut-off frequency being determined by the spatial Fourier spectrum of the coherent noise.

Notes: In the Andes mountains of North Chile seismic refraction measurements revealed the existence of a buried graben structure. The special geological environment permitted the deduction, by detailed analyses of diffraction patterns and delayed arrival times, of a low velocity layer underneath a high velocity ignimbritic sheet.The gravity method was chosen as an economic secondary aid to trace the course of the buried structure. This unusual combination of detailed gravity measurements following a general seismic survey was not only successful in detecting and tracing a buried structure, but also provided complementary data about the deeper subsurface conditions.

Notes: A Kunetz equation is often used as the starting point in the development of solutions for the inversion of one-dimensional, noise free, normal incident seismograms, for which |ro|= 1. In this paper we demonstrate a need for a Kunetz-type equation in which filtered signals can be used, so that noise effects can be reduced. We then show that an infinite number of Kunetz-type equations exist for the lossless wave equation in layered media. Finally, we show that it is indeed valid to formulate and solve the inverse problem using filtered signals.

Notes: A theory for the bipole-dipole method of resistivity sounding is developed. Bipole-dipole apparent resistivities are related to Schlumberger apparent resistivities at two spacings. The theory can also be used to compute exact dipole-dipole apparent resistivity curves providing an improvement over the existing techniques which involve far field approximations. A comparison of bipole-dipole and dipole-dipole systems reveals the similarity between the two. However, the resolution of the bipole-dipole system depends on the azimuth angle. The flexibility of the theoretical expressions lead to a generalized field scheme independent of the bipolar or dipolar nature of the current source.

Notes: The combined observation of first and later arrivals in shallow seismic refraction surveys, particularly on hard rock terrains, is discussed. Details of experimental weathered-zone investigations by the correlation refraction method in a granite terrain (i.e. field procedure, seismograms obtained, plotting of the data, and identification of the waves are presented). Complete travel time data and interpreted subsurface sections of a few test refraction surveys are included. In one instance the interpreted results of normal and converted refracted wave data have been tested by drilling at three points along a 220 m long profile.

Notes: A Bremmer Series decomposition of the solution y(t) to the lossless wave equation in layered media is 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR71:GPR_71_mu1"/〉 where the yj(t) are physically meaningful constituents (i.e., y1(t) are primaries, y2(t) are secondaries, etc.). This paper reviews Mendel's state space models for generating the constituents; reviews Bremmer's integral equation models for generating the constituents; and demonstrates how Mendel's state space models can be obtained by a careful decomposition of Bremmer's integral equation models. It shows that Mendel's equations can be viewed as approximate numerical solutions of Bremmer's integral equations. In a lossless homogeneous medium, the approximations become exact.

Notes: The interpretation of vertical electrical sounding data can be facilitated by the application of the reciprocal geoelectric section. If an apparent resistivity field curve has a descending right end, the apparent resistivity curve of the reciprocal geoelectric section can be obtained by the application of linear filter theory; from this the total transverse resistance of the geoelectric section can be calculated without having to interpret the field curve. In addition, Orellana's auxiliary point method can now be extended to interpret three and four layer apparent resistivity curves of all types.This paper summarizes the properties of the resistivity transform curve, the apparent resistivity curve, and the apparent resistivity curve of the reciprocal geoelectric section, with several new applications.

Notes: Past design of marine source arrays has been based on one or more of the following principles:〈list xml:id="l1" style="custom"〉(i) simultaneous operation of multiple identical sources to increase radiated signal strength by simple addition;(ii) superposition of wavelets of different fundamental frequency to achieve a total pulse of desired, front-loaded form (e.g. mixed volume air-gun arrays);(iii) horizontal spacing of units or groups to achieve spatial filtering effects.The phenomenon of interaction between sources, affecting the loading experienced by each, has usually been ignored, or else avoided by wide spacing of units. However, interactions can significantly affect the efficiency and frequency response, in a way that can be favourable.Calculations are presented for sources emitting continuous or long duration signals, showing the energy efficiency as a function of frequency for arrays in a variety of configurations. Interaction effects are significant for inter-source spacings smaller than or comparable with the wavelength—not, as is often stated, up to a distance related to the radii of the sources. The results show that potential exists for tailoring the frequency response of a source system, according to the application, by simple spatial rearrangement of units.Similar effects occur with interacting impulsive sources, but it is shown that different criteria apply for the optimum arrangements of units.

Notes: This paper deals with the practical problem of processing magnetic data in the field, and it shows how the parameters describing a geological contact can be obtained quickly and conveniently on the basis of five measurements. The complete interpretation can be performed in the field using a programmable calculator. For a small ground-party the method greatly improves the quality of the field-work and the interpretation of the magnetic data. The method has been applied to the data from a magnetic survey over the Mooki Fault (Gunnedah-Manilla, N.S.W.), and the results are discussed as an illustration of the efficacity of the method as a field procedure.

Notes: The iterative estimation process of residual static corrections published earlier is further analyzed.The convergence and convergence rate of the iterative solution are analysed for components of different relative wave length with results of both theoretical and practical value.Relative wave length components practically determinable and indeterminable are defined.One model example is presented for illustrative purposes.

Notes: The observation of shear waves is finding more interest in seismic exploration, especially for the determination of additional lithologic parameters, e.g. Vp/Vs. We demonstrate the observation of converted waves in routine seismic work by means of horizontal geophones. Field technique and data processing permit acquisition and interpretation of converted waves in connection with routine seismic measurements. A special interpretation of the recorded converted waves results in the shear wave velocity and the Vp/Vs relation.

Notes: The transient response of a conductive shell-shell model in the one-loop version was obtained analytically. The results indicate that four zones, namely early, late early, intermediate, and late zone can be identified in the total transient characteristic of the model. In case the measurements are carried out in the late early zone, a conductive target appears as a resistive one. It is suggested that the optimum time of measurement should be so selected as to fall in the intermediate zone.

Notes: A careful examination of the seismic refraction technique details the general assumptions and processes on which it is based. It is apparent that the normal interpretive process of determining velocity by hand fitting time breaks, while necessary to identify the refractors, is subject to imprecision.We describe a digital technique that calculates velocity and its precision from the time break measurements. The technique also facilitates examining for the possibility of systematic errors. Having observed the kind of imprecision that was apparent with velocity we extended our study to layer thicknesses (and thus depth) and found that the imprecision was significantly magnified.The technique and our claims for it are supported by an example of its application to a refraction survey in the Sturt Block, Western Australia.

Notes: A stacked seismic section represents a wave-field recorded at regularly spaced points on the surface. The seismic migration process transforms this recorded data into a reflectivity display. In recent years, Jon F. Claerbout and his co-workers developed migration techniques based on the numerical approximation of the wave equation by finite difference methods. This paper describes an alternative method, termed ASD (for Accurate Space Derivative), and its application to the wave equation migration problem. In this approach to the numerical solution of partial differential equations, partial derivatives are computed by finite Fourier transform methods. This migration method can accommodate media with vertical as well as horizontal velocity variations.

Notes: Qureshi and Mula have suggested a computer method for the calculation of the shape of a two dimensional body from the gravity anomaly profile associated with it. The application of the method, however, was restricted to those bodies which have their top or base horizontal and end sides vertical. In this paper study has been made to investigate the possibility of eliminating the above mentioned restrictions and has arrived at the affirmative conclusion.

Notes: Consideration is given to the form of apparent resistivity sections obtained by varying electrode array position and spacing over two dimensional features.Since basic solutions exist for horizontally layered media and for vertical or dipping single interfaces, simple rules are proposed whereby these solutions can be directly combined to give solutions for more complex sections. Substantial approximations may be involved as the rules do not fully allow for interactions between the constituents.The range of error incurred in application of the rules is explored, with particular reference to the square array system of resistivity measurement. The two extremes- of orientation of the square array with respect to the line of section are separately considered in this survey.Within appropriate limits, the rules appear extendable to a wide variety of simple structures for which rigorous solutions would be formidable. The rules are finally discussed in relation to practical applications.

Notes: In modern oil exploration layers of prospective interest with rather simple structural features are often overlain by very complicated bodies as e.g. saltdomes or other kinds of diapirs, olistostromes, or front zones of overthrusted blankets. In all these cases normal reflection seismic investigations, where downgoing and upgoing rays are rather close to each other, mostly fail, either because no reflections from underneath the complicated bodies are obtained, or because a reliable migrated depth presentation becomes practically impossible due to the inhomogeneity of the overlying bodies.The undershooting technique avoids these difficulties by using ray paths which do not traverse the complicated bodies e.g. by shooting on one side of a saltdome and recording on the other side. On account of the large shot-geophone distances in this method special considerations and computer processes were developed concerning moveout corrections for common depth point stacking and migrated depth presentation.In many cases the location of the disturbing complicated bodies is known in advance. The shooting and recording program can then be adjusted to this knowledge and thereby kept to a minimum. If the location of the complicated bodies is unknown a more extended seismic program has to be carried out encompassing a great variety of shot-geophone distances. But in this case the approximate location of the complicated bodies can be deduced from the survey too.Results are presented in order to give an idea of the efficiency of the new seismic tool.

Notes: This paper describes the procedure for interpreting the apparent resistivity data measured with the two-electrode array directly with the help of kernel function. The calculation of kernel function from the observed resistivity curve is done by the method of decomposition. In the method of decomposition the resistivity curve is approximated by a sum of certain functions, whose choice is only restricted by the requirement that the contribution to the kernel function corresponding to them should be easily computable. A few such functions are classified. These, and the standard curves for corresponding kernel functions obtained by utilising an integral expression for two-electrode array expressing the kernel explicitly in terms of the apparent resistivity functions, are plotted on log-log scale. The determination of layer parameters, that is, the layer resistivities and thicknesses from the kernel function can be carried out by a method proposed by Pekeris (1940).

Notes: A six-channel wide-band digital system for magnetotelluric measurements is described The system is designed to operate in the frequency band 10-.0001 Hz. The recording is made on a 7 track tape in an IBM compatible 12 bit format. The amplitude and phase responses of the system and sample records are presented.

Notes: Several types of multichannel filters have been introduced in the past with the purpose of rejecting, in a seismic section, coherent noise having a slope different from that of the signal.These filters, generally, tend to introduce a certain amount of mixing and therefore the output trace shows increased horizontal coherence. This is due to the model on which these filters are based, since the hypothesis is posed that the reflectors are continuous. This may be dangerous since it could lead to mistaken interpretations, for example when small faults or breaks are made to disappear in the output section.Other problems that could arise in the application of multichannel filters after-stack are space-aliasing and high-pass filtering. The former occurs when coherent noise is rejected with apparent Velocity V and frequency fa=V/X, where X is the distance between traces. In this case, the signal also is distorted since it is rejected in the same frequency range. The high pass filtering effect occurs when the multichannel filter is designed to remove low coherent noise with high apparent velocity.In the paper a family of multichannel filters is presented based on a model of the seismic section such that minimum mixing effects appear. The filters are designed to give good results even in the case of low frequency and high velocity coherent noise.Some practical examples are shown.

Notes: On seismograms recorded at sea bubble pulse oscillations can present a serious problem to an interpreter. We propose a new approach, based on generalized linear inverse theory, to the solution of the debubbling problem. Under the usual assumption that a seismogram can be modelled as the convolution of the earth's impulse response and a source wavelet we show that estimation of either the wavelet or the impulse response can be formulated as a generalized linear inverse problem. This parametric approach involves solution of a system of equations by minimizing the error vector (ΔX = Xobs– Xcal) in a least squares sense. One of the most significant results is that the method enables us to control the accuracy of the solution so that it is consistent with the observational errors and/or known noise levels.The complete debubbling procedure can be described in four steps: (1) apply minimum entropy deconvolution to the observed data to obtain a deconvolved spike trace, a first approximation to the earth's response function; (2) use this trace and the observed data as input for the generalized linear inverse procedure to compute an estimated basic bubble pulse wavelet; (3) use the results of steps 1 and 2 to construct the compound source signature consisting of the primary pulse plus appropriate bubble oscillations; and (4) use the compound source signature and the observed data as input for the generalized linear inverse method to determine the estimated earth impulse response—a debubbled, deconvolved seismogram. We illustrate the applicability of the new approach with a set of synthetic seismic traces and with a set of field seismograms.A disadvantage of the procedure is that it is computationally expensive. Thus it may be more appropriate to apply the technique in cases where standard analysis techniques do not give acceptable results. In such cases the inherent advantages of the method may be exploited to provide better quality seismograms.

Notes: According to data presented by YU.A. Kosigin, 84% of all endogenous mineral deposits are in some direct or indirect relation with the fractures of the earth's crust. Therefore the discovery and the study of the spatial disposition of the fractures is the most important object for geophysicists. Abyssal fractures are of particular interest.By geophysical methods one can find the geometrical parameters of abyssal fractures such as their extent, the depth of formation, the breadth of the zones, and the amplitude of the relative displacement of separated blocks.The methods determining these parameters are widely known. A calculation of the difference in the levels of the erosion cuts of the blocks are of particular interest under shield conditions. A method to calculate this difference by gravity interpretation of “step” anomalies and by using the gradient model of the earth's crust is proposed.A comparision of the results of gravimetry and magnetometry with those of deep seismic soundings shows that the fractures of the first and the second order in the Ukrainian shield cut the earth's crust and part of the upper mantle so they can be qualified as abyssal fractures.In the Ukrainian shield the spatial regularities of the fractures determined by geophysical methods can be used for the prognosis of the ore deposits.

Notes: The interpretation of electrical sounding data for a subsurface with monotonic continuous variation of the resistivity with depth is becoming increasingly necessary. The contribution of this article is the derivation of the solution for the Wenner and the Schlumberger apparent resistivity functions for a resistivity varying as a real power of a linear positive function of the depth. The interpretation of sounding data in these cases can be used to estimate the variation of the porosity or the salt content of the pore water with depth.

Notes: During the past four or five years, Vertical Seismic Profiles have been run in a large number of wells and in a variety of geological provinces with the object of assisting the seismic data processor and improving the geological interpretation.The special properties of the Vertical Seismic Profile, which allows the separation of the upward and downward travelling components of the recorded waveform, provides a means of studying the acoustic response of the earth in detail. Deconvolution of the data in particular gives a clearer understanding of the mechanics of multiple reflections and the way in which they may obscure primary reflections in the vicinity of the well.The primary reflection response of the earth can be observed with greater resolution than conventional seismic data permits, making correlation with lithology more precise, and allowing a good estimate of the reflection coefficient series to be determined. Inversion of the seismic traces to produce an acoustic impedance log leads to better definition of the sedimentary sequence and is of particular interest in predicting lithologic variations ahead of the drilling bit.In addition, Vertical Seismic Profile data can be used to assess parameters in areas such as deconvolution and signal band width for the evaluation of conventional seismic data.

Notes: An analysis of the equivalence phenomenon, analogous to that encountered in resistivity sounding, has been made for electromagnetic (frequency) sounding with the following systems: horizontal coplanar coils, perpendicular coils, vertical coplanar coils, and vertical coaxial coils. Cases analyzed are three-layer H and K type resistivity distributions. The theoretical responses for the EM sounding systems have been computed by the digital linear filter method using short filters. An analysis has been made of the resolution by the four EM systems considered f the equivalence effect. It is concluded that from the equivalence point of view electromagnetic (frequency) sounding has relatively better resolution compared to resistivity sounding for the H type three-layer cases. For the K type three-layer cases electromagnetic (frequency) sounding provides a serious problem in resolution similar to that encountered in resistivity sounding. Empirical relationships have been established for the H and K type cases respectively in order to numerically quantify the equivalence involved in electromagnetic (frequency) sounding.

Notes: The normal moveout velocity of a reflecting bed is a function of the dips and curvatures of all overlying velocity interfaces. Now let the (N– 1)th velocity interface be a non- (or badly) reflecting bed, whereas the other interfaces, including the base of the Nth layer, reflect satisfactorily, and let the velocities UN– 1 and UN of the (N– 1)th and Nth layer, respectively, be known. Then the normal moveout velocity for the base of the Nth layer, if known in one direction at a certain part of the surface of the earth, provides a second order differential equation in the horizontal coordinates x and y for the depth ZN – 1(x, y) of the unknown interface.The mathematics becomes rather simple in the case of two-dimensional geological structures. For this case and N= 2 the differential equation mentioned can be solved by stepwise integration or by iteration. One of the many possible applications of the new concept is the determination of the structure of the base of an overthrusting sheet.

Notes: The asymptotic approximation of Pekeris is replaced by two new procedures referred to as the two-point method and the multilayer method, other steps in the direct interpretation remaining unmodified. The new methods are based on the assumption that there are at least one or two consecutive sample points of the kernel curve containing the information on a particular layer and containing no information on the deeper layers. In any step, the identified covering layers are accumulated and the interpretation progresses to the successive deeper layer.The multilayer method is oriented towards interpretation of data severly contaminated by noise. The elimination of noise with simultaneous averaging of layer parameters is performed in the domain of Dar Zarrouk parameters.

Notes: Multiple sea-floor reflections in deep water often are not effectively suppressed by either CDP stacking nor standard predictive deconvolution methods. These methods fail because the reflection coefficient varies markedly with angle of incidence and also because of the variation of arrival time with offset and because of dip. For a reasonablly flat sea-floor, multiples of various orders and the primary sea-floor reflection which have all been reflected at nearly the same angle lie along a straight line through the origin in time-offset space. This line is called the “radial direction.” The multiples which lie along this line show a systematic relationship because they all experience the same water-bottom reflection effect. In other words, multiples behave in a stationary manner along the radial directions on multi-trace seismic records. A technique of multi-channel predictive deconvolution, called “Radial Multiple Suppression,” utilizes this aspect to design Wiener operators for the prediciton and suppression of water bottom multiples.The effectiveness of the technique is demonstrated by the study of field records, autocorrelations, velocity analyses, and stacked sections before and after Radial Multiple Suppression processing.

Notes: A new technique is developed for generating a short seismic pulse from the bubble pulses which are radiated by an air-gun. The new technique, which is useful in well velocity surveys and vertical seismic profiling, can be implemented by firing a single air-gun several times at the same depth but with different chamber pressures.A record obtained by this procedure from a well-geophone clamped at a depth of 2450 m gave a maximum peak-to-peak amplitude within the first 100 ms of the effective seismic pulse at least ten times any later peak-to-peak amplitude.

Notes: A seismic source array is normally composed of elements spaced at distances less than a wavelength while the overall dimensions of the array are normally of the order of a wavelength. Consequently, unpredictable interaction effects occur between element and the shape of the far field wavelet, which is azimuth-dependent, can only be determined by measurements in the far field. Since such measurements are very often impossible to make, the shape of the wavelet—particularly its phase spectrum—is unknown.A theoretical design method for overcoming this problem is presented using two scaled arrays. The far field source wavelets from the source arrays have the same azimuth dependence at scaled frequencies, and the far field wavelets along any azimuth are related by a simple scaling law. Two independent seismograms are generated by the two scaled arrays for each pair of source-receiver locations, the source wavelets being related by the scaling law.The technique thus permits the far field waveform of an array to be determined in situations where it is impossible to measure it. Furthermore it permits the array design criteria to be changed: instead of sacrificing useful signal energy for the sake of the phase spectrum, the array may be designed to produce a wavelet with desired amplitude characteristics, without much regard for phase.

Notes: Man's engineering activities are concentrated on the uppermost part of the earth's crust which is called engineering-geologic zone. This zone is characterized by a significant spatialtemporal variation of the physical properties status of rocks, and saturating waters. This variation determines the specificity of geophysical and, particularly, geoelectrical investigations.Planning of geoelectric investigations in the engineering-geologic zone and their subsequent interpretation requires a priori) geologic-geophysical information on the main peculiarities of the engineering-geologic and hydrogeologic conditions in the region under investigation. This information serves as a basis for the creation of an initial geoelectric model of the section. Following field investigations the model is used in interpretation. Formalization of this a priori) model can be achieved by the solution of direct geoelectric problems. An additional geologic-geophysical information realized in the model of the medium allows to diminish the effect of the “principle of equivalence” by introducing flexible limitations in the section's parameters. Further geophysical observations as well as the correlations between geophysical and engineering-geologic parameters of the section permit the following step in the specification of the geolectric model and its approximation to the real medium. Next correction of this model is made upon accumulation of additional information. The solution of inverse problems with the utilization of computer programs permits specification of the model in the general iterational cycle of interpretation.

Notes: The computation of the electrical potential created by a source of direct current in a horizontally stratified earth is easy, and it is now a common practice to interpret, by manual or automatic procedures, the maps of apparent resistivity or of mise-à-la-masse surveys.The study of 3-D cases requires a computer cost too high for a general use, and the available techniques usually refer only to an anomalous body embedded in a stratified medium. In fact, it often happens that the surface of the ground cannot be regarded as a plane, an assumption which can cause large discrepancies between the observed and the calculated potentials. A first estimate of these discrepancies can be made by assuming that the earth's surface makes a dihedron and the underground consists either of one homogeneous medium or of several media whose plane interfaces pass through the edge of the ground surface dihedron. Although very schematic, this approximate model can provide a useful information on the effect of the relief.

Notes: Alfano L. 1980, Dipole-Dipole Deep Geodectric Soundings over Geological Structures, Geophysical Prospecting 28, 283–296.The dipole-dipole array is used for deep vertical geoelectric soundings for practical reasons. However, the data obtained are often too scattered and the quality is lower than that of a Schlumberger sounding. The mathematical transform from these fields data to the corresponding Schlumberger ones is needed. It is demonstrated that for more general underground structures different from plane parallel stratifications, only the continuous polar dipole-dipole array permits a general and reliable transform of this type. It follows that any other dipole-dipole array, (for instance the azimuthal, equatorial, parallel, perpendicular, etc.), are useless over complex structures, or in the presence of irregularities on the ground surface.

Notes: A new method of Vibroseis deconvolution has been recently proposed by the authors. This discussion describes the effects of noise on the application of this method. The initial deconvolution step involves estimating the spectrum of the Vibroseis wavelet by homomorphic filtering. It is shown that noise causes problems with phase estimation. Hence, the Vibroseis wavelet is assumed to be zero phase. Examples demonstrate that zero phase cepstral filtering is a robust wavelet estimation approach for noisy data. The second step of the deconvolution method forms an impulse response model by a spectral extension method. Although this step can improve the resolution of seismic arrivals, it must be applied with caution in view of the deleterious effects of noise.

Notes: Geophysical interpretation consists of the identification of geological parameters carried out in the state of uncertainty. From this follows that the identificative model must correspond to the degree of uncertainty. As uncertainty measure of the surveyed material the informative distance between different interpretive models is introduced. The influence of the measurement noise and the accuracy of measurement devices as well as the number of measurement sets worked out simultaneously for this survey is analyzed. Numerical examples indicate that the material considered to be not interpretable from the point of view of a certain accurate model may be interpreted by the use of a less accurate model.

Notes: Sub-bottom profilers achieve high resolution but limited penetration beneath the seabed. Marine seismic surveys with long streamers and conventional sources suffer from an incomplete CDP stack and an unnecessarily low signal frequency in the early part of the section. Consequently there is a depth interval over which the optimum resolution of the seismic reflection method is not achieved. This paper describes the design, conduct, and results of an experimental survey made to obtain high resolution sections (predominant frequency about 200 Hz) with reflection times up to one second in the northern North Sea. The prime motivation for the experiment was to assess the possibility of mapping a shallow gas sand which had been encountered by the drillers.The design concept of the survey was to keep all the benefits of conventional marine seismic data gathering and processing, but to reduce their dimensions and time scales by a factor of five to ten. The survey in 1972 recorded a total of twenty-four lines using twenty-four fold cover with 5 m spacing between the reflector points, and a separation of 50 m between adjacent lines. Multi-electrode sparkers were used with a shallow purpose-built twenty-four channel 240 m hydrophone streamer. The recording sample interval was 1 ms. The final sections, obtained after conventional data processing, were of good quality. The results of velocity analysis helped to distinguish primary and multiple energy. Reflections with large negative reflection coefficients were seen in some parts of the survey area, and these are thought to indicate thin gas sands.

Notes: This paper deals with a case study on the application of auto-correlation and spectral analysis methods to mineral assay data taken along seven drives and two winzes concerning the McTaggart's (West) lode of Kolar gold fields. The general model conceived in this study is: measured (estimated) ore grade at jth location =true value + error at jth location. Employing an auto-correlation function of the form C e- a |k| for signals, the respective contributions of signals and noise to the total logarithmic variances for the data along drives and winzes are analysed. Smoothed spectral density estimates and their 90% confidence limits are computed for the series of data.

Notes: Methods and typical case histories of EM and IP surveys are compared in order to check their compatibility for the investigation of large areas for base metal sulphides. It is demonstrated that the fast, low cost EM may miss sulphide concentrations which cause no reduction of apparent resistivity, or which act like horizontal slabs, where EM anomalies occur marginally. In such cases only IP can recognize the whole extent of the mineralization. The misleading role of graphite exists for both methods.The conclusion is that EM remains the only economical method to survey whole ore districts, but that the shortcomings should always be taken into account in the interpretation. They can be overcome by employing geological, geochemical or other geophysical indicators in selecting promising targets for follow-up IP. Even if less than 20% of the area is covered by the expensive IP, there is a fair chance that all sulphide bearing rocks will be found. Therefore, the question is not whether to apply EM or IP methods, but how to combine them best.

Notes: The paper deals with the prerequisites of application, specific peculiarities and methods of electrometric and thermometric investigations aimed at the solution of certain engineering-geological problems in offshore areas. Practical examples are supplied.

Notes: The voltage induced in a horizontal loop on a layered ground has been calculated for the case where the loop is excited by a step current and measurements are made during the off-cycle.The expressions derived for a uniform ground show that for large time t the induced voltage E(t) is approximately given by E(t)≃— (Ibαμ/20t) (σμ2/t)3/2 where σ is the conductivity of the ground, μ the permeability, b the loop radius, and I the amplitude of the current step. For small times the corresponding result is E(t)≃—Ibμ/2t.When the ground is composed of a number of layers a numerical procedure for calculating the induced voltage is described.The calculated responses of various multilayered structures show that at short times the induced voltage is asymptotic to that produced in the case of a uniform ground of conductivity equal to the top layer.Interference effects in the top layer can lead to anomalous decay curves which may result in the underestimation of the conductivity of a buried layer.

Notes: Marine geophysical work requires accurate navigation on a continuous basis. A repeatability of 150 m CEP (circular error probable) with sequential positioning of 15 m CEP is usually acceptable. Quoted figures for many presently available navigation systems yield nearly the required accuracy. In actual operations, however, such accuracies may not be achieved, and usually the performance actually realized cannot be determined for want of independent measurements for comparison. If more redundancy in navigation measurements were available on an integrated basis, the limitations of individual systems would no longer be so critical and the accuracy of measurements could be assessed in real time. Failures in navigation continue to occur. Such failures usually result from ignorance of the capabilities of the navigation system and limitations and consequent choice of a system which is not appropriate to the demands of a particular survey. The points to be covered in work standards are listed.

Notes: The acceptance of articles in Geophysical Prospecting is strictly based on the originality and relevance of the contents. In order to be published a paper has to satisfy additional requirements on its external form and on its style and language: it should be written preferably in English though articles in French and German are permitted. A paper should consist of (i) a title page, (ii) an abstract, (iii) the text, (iv) list of references, (v) captions to illustrations, if any, (vi) tables, if any, and (vii) illustrations, if any. These seven parts should be mailed together but be physically separable and should be prepared according to rules which are either based on printing necessities or on the editorial style of the Journal.Failure to comply with these rules may result in delay in further processing of the article. Since Geophysical Prospecting is edited with a minimal budget correspondence with authors is kept to a minimum.

Notes: Depths of investigation for normal (bipolar) and focusing (unipolar) linear electrode arrays have been computed following the method given earlier (Roy and Apparao 1971) both in homogeneous and layered earth. The focusing arrangement is found to be superior to normal arrangement both in regard to depth of investigation and zone of uniform depth of investigation. This analysis holds good in layered media too. Further, the depth of investigation increases with the increase in the length (2M) of the electrode and reaches a limit, 0.29L for normal and 0.50L for focusing, when the electrode attains an optimum length to satisfy the infinite condition. This optimum length of the electrode is six times the distance L of the observation point from the electrode for normal and about ten times for focusing. A contour diagram for contributions of individual ground elements to the total signal measured at the centre of focused system is also discussed.

Notes: The authors generalize a method expounded in a previous paper (1971, Geoph. Prosp. 18, 786-799) to the case of a local conductivity σ(M) of the infinite medium satisfying the relation 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR246:GPR_246_mu1"/〉 where the Ri's are the distances from the point M to n fixed points Si (i= 1,. n), k is a positive real constant and Ci, Cii are constants ensuring the condition α 〉 O.The sub-surface conductivity distributions (half-spaces) complying with (1) provide a wide variety of conducting structures, which can fit quite successfully the rather complicated distributions of conductivity occurring in natural ore bodies.An exact algebraic calculation of the apparent resistivity for these grounds, valid for any dc electrical prospecting devices (Wenner, Schlumberger, dipole, etc.) leads to a set of simultaneous linear equations, with a matrix which is invariant with respect to the position of the quadrupole being used. This greatly simplifies the numerical computation.We also present some examples of cross sections for the real and apparent resistivity obtained by this method.

Notes: Section migration after stack has been widely accepted by the industry. From a theoretical point of view, section migration before stack should provide superior results, the improvement warranting the drastically increased cost is not realized in most cases.There are a number of reasons that explain the discrepancy between actual and theoretically expected quality: Long period statics, refraction of rays, two-dimensional treatment of an actually three-dimensional problem.The section migration package subject to this paper allows(i) to take refraction into account,(ii) to discriminate against noise with a variety of statistical and geometrical criteria,(iii) to adapt processing time to problem complexity by a special process called SEMI-STACK.A number of examples will demonstrate the effects of section migration.

Notes: A seismic trace after application of suitable amplitude recovery may be treated as a stationary time-series. Such a trace, or a portion of it, is modelled by the expression 〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR627:GPR_627_mu1"/〉 where j represents trace number on the record, t is time, αj is a time delay, α (t) is the seismic wavelet, s(t) is the reflection impulse response of the ground and nj is uncorrelated noise. With the common assumption that s(t) is white, random, and stationary, estimates of the energy spectrum (or auto-correlation function) of the pulse α(t) are obtained by statistical analysis of the multitrace record. The time-domain pulse itself is then reconstituted under the assumption of minimum-phase. Three techniques for obtaining the phase spectrum have been evaluated: (A) use of the Hilbert transform, (B) Use of the z-transform, (C) a fast method based on inverting the least-squares inverse of the wavelets, i.e. inverting the normal time-domain deconvolution operator. Problems associated with these three methods are most acute when the z-transform of α(t) has zeroes on or near the unit circle. Such zeroes result from oversampling or from highly resonant wavelets. The behaviour of the three methods when the energy spectra are perturbed by measurement errors is studied. It is concluded that method (A) is the best of the three. Examples of reconstituted pulses are given which illustrate the variability from trace-to-trace, from shot-to-shot, and from one shot-point medium to another. There is reasonable agreement between the minimum-phase pulses obtained by this statistical analysis of operational records and those estimated from measurements close to the source. However, this comparison incorporates a “fudge-factor” since an allowance for absorption has to be made in order to attenuate the high frequencies present in the pulse measured close to the shot.

Notes: The implementation of a stacking filter involves the filtering of each trace with an individual filter and the subsequent summing of all outputs. The actual position of a trace in space as well as certain simultaneous shifts of traces and filter components in time do not influence the process. The resulting output is consequently invariant to various arbitrary coordinate transformations. For a certain useful class of ensembles of non-linear moveout arrival times for signals a particular transformation can be found which transforms a given ensemble into one consisting only of straight lines. It is thus possible to reduce, for instance, the analysis of a stacking filter designed for hyperbola-like moveout curves to the analysis of a velocity filter with linear moveout curves. As the (f—k) transform is a very useful concept to describe a velocity filter, it can consequently be applied to characterize a stacking filter in regard to its performance on input signals with non-linear moveout.

Notes: The technique of linear digital filtering developed for the computation of standard curves for conventional resistivity and electromagnetic depth soundings is applied to the determination of filter coefficients for the computation of dipole curves from the resistivity transform function by convolution. In designing the filter function from which the coefficients are derived, a sampling interval shorter than the one used in the earlier work on resistivity sounding is found to be necessary. The performance of the filter sets is tested and found to be highly accurate. The method is also simple and very fast in application.

Notes: A case history is presented for the exploration of barite with the electrical resistivity method. Altogether eight locations were recommended out of which six correspond to barite bodies. In the present case the gravity method, which is commonly used for the location of barite because of its high density contrast with the host rocks, has failed, perhaps due to small size of the ore bodies.

Notes: A correct derivation of rms, average and interval velocities from one another and from common depth point stacking velocities requires a clear understanding of the relationships between these velocities. We relate the average velocity to the rms velocity through a “heterogeneity factor” which is a quantity that gives a measure of the degree of velocity heterogeneity in the ground. The interval velocity is a quantity which varies according to the method of its derivation. The difference between rms and stacking velocities depends on the heterogeneity factor and on the length of the spread. Unless allowed for, this difference can reverse the advantages of long spreads and cause large errors in interval velocity determinations. It may be removed through a number of techniques. The accuracy of stacking velocities in the presence of random “noise” is independent of the heterogeneity factor. Relevant expressions can be broken down into simple formulae which give the accuracy quickly and with good precision.

Notes: Tracers are used widely to determine the direction and velocity of ground-water movement. Failures of tracer tests are most commonly a result of incorrect choice of tracers, insufficient concentrations of tracers, and a lack of an understanding of the hydrogeologic system being tested. Some of the most useful general tracers are bromide chloride, rhodamine WT, and various fluorocarbons. For certain purposes, dyed clubmoss and baker's yeast have proved valuable. Many radionuclides including 3H, 82Br, and 198Au are almost ideal for numerous purposes, but radiation hazards associated with their use together with local, State, and Federal regulations have discouraged widespread field applications in recent years within the United States.

Notes: The Tucson, Arizona, metropolitan area has 450,000 inhabitants and is expected to have nearly 800,000 inhabitants by the year 2000. Tucson is totally dependent on ground water drawn from two basin aquifer systems for its water supplies, as are agricultural, mineral and industrial operations in the area.Municipal, agricultural, mineral and industrial ground-water withdrawals in the two basins amount to some 376,000 acre-feet per year (AFY). Dependable ground-water supplies in the two basins amounts to about 80,000 AFY. Thus, the two aquifer systems are overdrafted by approximately 296,000 AFY, 80 percent of which is by irrigation agriculture.In Arizona, ground water belongs to the owner of the land overlying the aquifer. To ensure adequate ground-water supplies, the City of Tucson has been purchasing and retiring farmlands in one of the basins. However, litigation that reached the Arizona Supreme Court led the Court to rule that the City could pump only 2.4 AFY per acre of farmland retired. The City has retired about 12,000 acres in the basin and in 1978 withdrew some 20,000 AFY of ground water for municipal use.Retiring these farmlands to secure water rights impacts on area economy and creates weed problems for farmers who own land near the retired lands. The City of Tucson budgets about $50,000 annually for weed control.A possible alternative to retiring farmlands and to cultivating crops that require heavy irrigation is cultivating arid-adapted vegetation that has economic potential. Jojoba (Simmondsia chinensis) is a shrub native to the Sonoran Desert that appears to be an economically viable arid-land crop. It needs about 1.5 AFY per acre compared with traditional crops grown in the Southwest that have average needs of 4 AFY or more.The economic value of jojoba is based on the oil extracted from its seeds. It is a unique, unsaturated oil composed of nonglyceride esters consisting almost entirely of straight-chain acids and alcohols. Such oils are difficult to synthesize in commercial quantities, and the only known natural source is the sperm whale, an endangered species.If farmers in the basin cultivated jojoba, water use could be reduced by about 2.5 AFY per acre, from 4 AFY per acre for traditional crops to 1.5 AFY for jojoba. Even if the City of Tucson had to subsidize farmers at a rate of $40 per acre for the 10 years it takes jojoba to produce economically feasible yields, the City would save more than 50 percent of the cost to purchase and retire farmlands and still be able to draw water from the basin for municipal uses.This dual use of water in the basin would permit agriculture to continue its contribution to area economy while the City could continue meeting its water needs by piping water out of the basin into the metropolitan area. However, implementing this plan would require changing Arizona ground-water laws.