ALBERT

Notes: Dipole-dipole induced polarization (IP) data are displayed typically as multi-level profiles, or as contours on vertical sectional plots referred to as pseudo-sections. The dipole-dipole array tends to yield IP anomalies in which the most anomalous values are displaced laterally from the source body. The data patterns are fairly interpretable on pseudo-sections or on multi-level profiles but are sufficiently complex to discourage the contouring of the data in plan.A method was developed for the presentation of dipole-dipole IP data on a contour map. The method consists of a simple averaging of data which can be performed manually if desired. It yields a single output value per station which reflects all levels of the pseudo-section, and is suitable for contouring in plan. The advantage of the technique is that it provides a quantitative picture of IP anomalies in their background or regional setting.

Notes: Constant offset sections can be mapped to a fixed offset and compared in order to provide a method of velocity analysis. The direct mapping to zero offset prior to stack might provide an alternative processing procedure to NMO and stack. The main advantage of such a procedure would lie in the correct treatment of cross-dips, but interpretational advantages might also follow from the performance of partial stacks biased to either high or low offset information.

Notes: Induced polarization and resistivity model studies over thin dykes for varying resistivity contrasts, depth of burial, and dip angles show striking parallelism of the surface apparent resistivity contours with the boundary of the body. This effect may be utilized for the estimation of strike length of the body. Results show that intermediate values of the electrode spacing is satisfactory for detection under widely varying conditions of resistivity contrast and depth. The percentage frequency effect (P.F.E.) and the metal factor (M.F.) responses are found to be more sensitive to the variation in the depth of burial than the resistivity responses. Pseudosections for P.F.E. and M.F. are concentrated much closer to the body than the resistivity pseudo-sections.

Notes: A direct interpretation scheme is developed which is capable of determining most of the geological features of a ground which can be assumed to be two dimensional in structure. This scheme extends the earlier work of Pekeris (1940) and Koefoed (1968) to the case where the basal layer of a ground is undulating. It also has a limited use for finding the parameters of a dipping dyke in the lower medium. Though the top and dip of the dyke can be determined, this is not true for the thickness.

Notes: Laboratory studies of absorption-frequency behavior in rocks often use spectral ratios of digitally recorded ultrasonic signals which have been transmitted through a rock sample and a reference sample of very low absorption, respectively. It is proposed to treat the digitally recorded signals as an autoregressive-moving average (ARMA) process which, using recursive filter concepts, can be represented as a ratio of two polynomials in the z-transform variable z. The numerator polynomial contains only that part of the signal that is modified by anelastic effects, whereas the denominator contains the elastic effects of the physical apparatus such as reverberations. Examples are given which show that this separation of the recorded signal greatly facilitates the laboratory investigation of loss mechanisms and absorption-frequency behavior based on spectral ratios.

Notes: The generalized integral equation for the electric potential governed by a quasi-harmonic equation can be derived via a variational formulation. For surface current distributions it is not always a Fredholm integral equation of the second kind. Numerical solutions of the general heterogeneous problem can be obtained with the “reciprocal averaging technique”, where the solution is obtained a second time after exchange of source and field points.

Notes: A method to calculate the resistivity transform of Schlumberger VES curves has been developed. It consists in approximating the field apparent resistivity data by utilizing a linear combination of simple functions, which must satisfy the following requirements: (i) they must be suitable for fitting the resistivity data; (ii) once the fitting function has been obtained they allow the kernel to be determined in an analytic way.The fitting operation is carried out by the least mean squares method, which also accomplishes a useful smoothing of the field curve (and therefore a partial noise filtering). It gives the possibility of assigning different weights to the apparent resistivity values to be approximated according to their different reliability.For several examples (theoretical resistivity curves in order to estimate the precision of the method and with field data to verify the practicality) yield good results with short execution time independent of shape the apparent resistivity curve.

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 method is given for solving the dc electric field problem of a point current source in an anisotropic 2 1/2-dimensional structural model. The surface integral equation of the field strength is given. Parallel to the strike the field strength is represented by a Fourier series. On the plane perpendicular to the strike each term of the field strength series is solved by means of the method of sub-sections, where linear behaviour of field strength over the sub-sections is assumed. Some numerical examples for different galvanic effects are given.

Notes: It is proposed that the vertical resolving power of a seismic signal is controlled by three aspects: the width of the central lobe, the side lobe ratio, and the side-tail oscillations. A comparative study of zero-phase signals covering the same frequency range shows that improvement of any one of these aspects inevitably leads to deterioration of one of the other aspects.An analytical simulation model is proposed of zero-phase signals free from side-tail oscillations, in which both the width of the central lobe and the side lobe ratio are adjustable. Analysis of the spectra of this model shows that, while the high frequency content of the spectrum is essential for obtaining a small width of the central lobe, the low frequency content of the spectrum plays an essential part in causing a low value of the side lobe ratio.

Notes: The objective of this study is to generate the separation-distance-domain (r-domain) transformation of the theoretically calculated wave number domain (m-domain) electromagnetic induction field component Bz(m, ω) of a stratified medium and to search for interpretive information which has been absent in the previously achieved numerical solutions of the problem.The r-domain kernel R̃(r, ω) function defining the induction field appears to adequately reflect the layering and electrical properties of the medium if it is expressed as a function of the frequency if the source-receiver separation r is small with respect to the thickness of the first layer. However, exact values of the conductivity cannot be distinguished from those of the neighboring values unless a resistive basement layer is present. This feature is the result of the truncation in series representation of the kernel function R̃(m, ω). However, this truncation is regarded as significant in the case of a conductive first layer. In m-domain static-zone studies, a conductive first layer slightly influences its r-domain correspondent.Although the computational cost of obtaining the kernel B(r, ω) by evaluation of the convolution in a cylindrical coordinate system is high, this semi-analytic solution is still superior to those based on the asymptotic assumptions.

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: Les différentes sources d'erreurs de la mesure gravimétrique sont examinées. Leur connaissance a une importance particulière dans les prospections de surface, dites “microgravimétriques”.Les auteurs démontrent, expériences à l'appui, que toutes précautions prises, la source la plus fréquente d'erreurs de mesure en microgravimétrie est une mauvaise estimation de la dérive.Les auteurs exposent alors un processus de mesure et d'interprétation dont le but est une meilleure estimation de la dérive. La justification théorique et expérimentale du processus est donnée. La méthode implique une prise de mesure suivant une répartition spatiale aléatoire ou semi-aléatoire. Un cas réel est décrit.

Notes: A number of time-domain IP traverses were carried out across two parallel mineralized sheets in the Lower Pillow Lavas, near Mitsero, Cyprus with Huntec Mark III equipment using the pole-dipole array. In one sheet the mineralization was disseminated (2%S), and in the other it was massive (30%S). The transients were recorded at separation n= 2 at a number of points to give the complete shape of the curves. The normalized time integrals were anomalous over the two sheets, but were not significantly different; the highest values being observed over the disseminated sheet. Both sheets were also associated with high electromagnetic components of the decay curve. The chargeability and resistivity values obtained over the disseminated body were considerably higher. The metal factor was also of value in discriminating between massive ore, disseminated mineralization, and barren rock. The values of P2 and P3 for the two bodies were also compared (P2 and P3 are defined by〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR906:GPR_906_mu1"/〉where M1 to M4 are the amplitudes of the decay curve at 55, 130, 280 and 580 ms respectively). For the massive ore, P was inversely related to M, but for the disseminated ore P was independent of M. Four simple parameters from the decay curves show that indices of curve shape offer the best prospect of grade discrimination.

Notes: Large gravity platforms are often used as alternatives to the more conventional pilesupported structures in hydrocarbon exploitation. A gravity structure, as opposed to the piled structure, is sitting on the sea floor by virtue of its weight and base width; as such it poses considerable problems for the site investigation engineer. One such problem is the calculation of the settlement of the structure and its time history; these depend upon the permeability and compressibility of the soil and its drainage conditions. The required data are usually obtained by sampling for subsequent laboratory testing. The collection of an undisturbed sample is beset by problems so that the consolidation behavior of the foundation material can only be inadequately assessed by laboratory testing. However, a series of laboratory consolidation experiments during which seismic velocities have been measured on the sample as consolidation proceeds shows that it is possible to reconstruct the stress-strain and time-dependent curves from the seismic data, once the initial void ratio and permeability of the soil are known. This leads the way to an in situ technique for predicting settlement using a combination of geophysical techniques (electrical resistivity and seismic velocities) to obtain the required engineering properties.

Notes: An underground gravity study was carried out under extreme conditions of the Alpine regions. The lead–zinc mine Bleiberg, Carinthia, was selected as an example to show the possibilities and limitations of the subsurface gravity method. For in situ density determinations, gravity measurements were made in two vertical mine shafts passing through Triassic sedimentary rocks of the Bleiberg Unit. The main prblem in gravity data reduction in extremely rugged topography is the accurate calculation of the terrain effect on underground stations. A general discussion of the various corrections required for the gravity measurements in the mine is presented. The mean interval densities in the two shafts, in limestone, dolomite, and schists formations, were determined as 2.76 and 2.77 g/cm3, respectively, with an accuracy of better than 0.01 g/cm3 for a depth interval of 50 m. The interval densities provide valuable information about the lithological and structural changes in the shaft surroundings and also agree well with the representative hand sample densities.In the second part, the applications of subsurface horizontal gravity surveys in exploration are discussed. Since the influence of topography is less underground because of the greater distance to the surface, subsurface surveys have definite advantages over surface surveys and can be very helpful in locating anomalous density zones in the mines. An example of gravity survey with a station spacing of 10 m at a depth of about 540 m is presented.

Notes: Lateral inhomogeneities generate fluctuations in the traveltime of seismic waves. By evaluation of these traveltime fluctuations from different source and receiver positions, lateral inhomogeneities can be located using a pseudo inverse matrix method (Aki, Christoffersson and Husebye 1977). The formulation of the problem is possible for transmitted waves as well as for reflected and refracted waves. In reflection seismics this method is of importance, if no reflections from the inhomogeneities themselves, but only reflections from lower boundaries can be observed.The basic assumptions for the mathematical formulation are (1) the average velocities and depths of the reflecting horizons are known already from standard processing methods, and (2) the traveltime residuals are due to lateral velocity changes between different reflectors or between reflectors and the surface. The area of the earth to be considered is divided into layers and the layers into rectangular blocks. The parallel displacement of a ray after passing a disturbed block is neglected, only the traveltime residual is taken into account.In this paper the method and its application to data obtained with two-dimensional models are described.

Notes: The electric and magnetic fields generated by horizontal electric and vertical magnetic dipoles lying on the surface of a conducting medium with horizontal anisotropy are investigated. Full expressions of their Fourier transforms are given, and the fields for a vertical magnetic dipole are calculated numerically. The radial and vertical magnetic components are found to be independent of the receiver-transmitter direction, whereas the other magnetic and electric components strongly vary with this direction. These results give useful criteria for defining the direction and amplitude of anisotropy from ground data; a ground experiment on fissured limestone was found to confirm the expected variations of the various field components. It is believed that this electromagnetic method can be used in order to provide information about the direction and amplitude of electric anisotropy.

Notes: On the basis of known relationships between various elastic moduli and porosity in a porous medium and of various parameters from well-logs, the reflection coefficient for normal incidence of P-waves is compared to that of S-waves. If pores contain gas, the reflection coefficient in S is much smaller than that of P but shows large differences for different gas concentration in one of the two layers while the reflection coefficient in P is insensitive to the gas concentration. It is found that the ratio of the two reflection coefficients provides a powerful tool for discriminating between layers of different degrees of gas concentration and for the extension of the sensitivity of the bright-spot technique to greater depths.

Notes: The laterites in Burundi, which are formed by weathering of ultrabasic rocks, show a complete profile with the following horizons: canga, the ferruginous crust capping, ferralite, consisting essentially of iron hydroxides, and saprolite, which contains a large quantity of hydrosilicate minerals. Nickel bearing minerals occur in the saprolite and the lower portion of ferralite.Resistivity well-logging and resistivity sounding indicated that the electrical properties of rocks depend upon their composition: Canga and ferralite showed high resistivities of 6,500 Ωm and 800 Ωm, respectively. The resistivity of saprolite was found to be much lower, between 10 Ωm and 20 Ωm. The laterite is underlain by resistive peridotite. The chargeability of saprolite was found to be lower than that of the upper horizons and the bedrock.Electrolytic conductivity of laterite, which depends on the geometry of the deposit, was found to be low, because the laterite contains moisture and ground water, which are highly resistive. The relatively high conductivity of saprolite is caused by nickeliferous hydrosilicates, which exhibit the electrical properties of clay minerals, with an apparent maximum conductivity of 0.25 S/m. The conductivity of saprolite corresponds to a concentration between 30% and 50% of conductive silicate minerals distributed in the pore space of deposit. A nickel enrichment of up to 6% was estimated from the resistivity of the saprolite.Prospecting for laterites by electrical sounding showed that the development of laterite horizons in a nickel deposit correlates with the surface morphology of weathered ultrabasic massif. Thus the method can be used in preliminary exploration of such deposits.

Notes: Thirty-eight gravity method estimates of the depth to the pre-Cenozoic surface under Yucca Flat are used to determine the statistical accuracy associated with the gravity method. Results indicate that the gravity method tends to overestimate the depth to the pre-Cenozoic surface, on the average, by 3.5 m with a standard deviation of 75.2 m. No significant change of this statistical estimate was observed with (1) depth, (2) location, or (3) date when the gravity-method estimate was made.

Notes: Since its development some thirty years ago, the airborne electromagnetic (AEM) method has been primarily used as a tool for mineral prospecting. However, advanced AEM systems are capable of other tasks, such as geological mapping and groundwater exploration. Excellent correlation between maps of apparent conductivity and geological maps was observed in several regions of Brazil where AEM surveys were performed. The degree of correlation seems to depend on the local climate. In humid and subhumid tropical regions, a weathered layer develops whose thickness and conductivity depend upon bedrock lithology. Therefore certain lithological types can be recognized from their conductivity signature; e.g., granites and Precambrian coarse clastic rocks are resistive, metavolcanic (particularly mafic) and volcanic rocks are conductive, Phanerozoic sediments are generally highly conductive.Two geophysical surveys are analyzed in the paper. The first was conducted with the time-domain, towed-bird AEM system in the Itapicuru greenstone belt in the state of Bahia. The apparent conductivity map correlated better with the local lithology than the magnetic map. Results of the AEM survey were successfully used to improve the regional geological map. A helicopter EM system was used in the second survey, which covered a portion of the Precambrian shield of Rio Grande do Sul. Also in this region ground checks confirmed the usefulness of conductivity surveys in geological mapping.The technique outlined in the paper holds great promise for countries of humid tropical climate, where few outcrops exist and access is often difficult. The tests performed in Brazil indicate that by executing AEM/aeromagnetic surveys during initial stages of mapping and exploration programs, time and expenditure required for geological field work can be considerably reduced. The resulting geological maps are more accurate and the inventory of mineral occurrences becomes more complete.

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: The examination of apparent resistivity space sections over two-dimensional targets requires the accumulation of large amounts of data, if the resistivity field is to be adequately described.Whilst such data may be obtained from an intensive sounding traverse in the field, it is desirable for interpretation purposes to be able to generate such space sections for a range of model variations.Within their limitations, tank analogs can be used to provide such interpretation material, but the collection of data can itself be time-consuming. In this paper, an account is given of the development of an automated tank analog, where an entire space section can be scanned and the output obtained in paper tape format for later processing on a digital computer. The resistance measurement accuracy attained is comparable with normal field measurement accuracy.A practical example of the use of this analog in investigating the problem of resolving and discriminating between two horizontal cylindrical tunnels is given. This problem is basic to an understanding of the minimum size and disposition of targets which can be observed on a space section. The square array has been used in this example because of its good resolution properties in general prospecting rather than its particular suitability for the targets investigated. The directional response of the array is also illustrated and discussed.

Notes: The “Autorité des amenegements des valées des Voltas (AVV)” is establishing new rural settlements in the Volta valleys. First, a survey of available water supplies is performed. Economic aquifers in Precambrian terrains are deep (15–50 m) and usually occur in fractured zones accompanying faults. Such zones can be identified on aerial photographs, but their precise location on the ground is virtually impossible by visual means. Because of the small size of the aquifers, a location error of 5 m can make the difference between a productive well and a dry hole.Traditionally, resistivity profiling has been used as the means of locating the fractured zones in the field. Our studies suggest that the task can be performed faster, cheaper and more accurately by VLF and EM methods. Because of the limited choice of transmitting stations reccivable in Upper Volta, the VLF method is not sufficiently sensitive to detect conductors with a strike between 45° and 105°. The results obtained with a multifrequency, horizontal-loop EM (HLEM) system were satisfactory in all investigated areas. During the 1980 field season, 35 target areas were surveyed. Of the 24 holes drilled so far, 23 are productive.The weathered layer is a source of distinctive HLEM anomalies, which are characteristic of the underlying rocks. Therefore, different interpretational procedures had to be developed for granitic and volcano-sedimentary areas. Despite the high background level of in-phase and quadrature components, which varied with thickness and conductivity of the weathered layer, aquifers could be detected at a depth greater than 30 m. Attempts were made to interpret the HLEM results quantitatively using two models: a three-layer medium and a valley discontinuity. The latter model is more realistic, but more scale modelling will have to be performed to permit development of viable interpretational procedures. Meanwhile, phasor diagrams based on drilling and resistivity sounding data can be used to estimate the aquifer depth.

Notes: A type of iterative deconvolution that extracts the source waveform and reflectivity from a seismogram through the use of zero memory, non-linear estimators of reflection coefficient amplitnde is developed. Here, we present a theory for iterative deconvolution that is based upon the specification of a stochastic model describing reflectivity. The resulting parametric algorithm deconvolves the seismogram by forcing a filtered version of the seismogram to resemble an estimated reflection coefficient sequence. This latter time series is itself obtained from the filtered seismogram, and so a degree of iteration is required. Algorithms utilizing zero memory non-linearities (ZNLs) converge to a family of processes, which we call Bussgang, of which any colored Gaussian process and any independent process are members. The direction of convergence is controlled by the choice of ZNL used in the algorithm. Synthetic and real data show that, generally, five to ten iterations are required for acceptable deconvolutions.

Notes: The magnetic anomaly due to a uniformly magnetized vertical rectangular prism and that due to an arbitrary structure which can be divided into a number of such prisms are expressed in forms suitable for rapid computation. Both two-dimensional and three-dimensional cases are considered. The simplified expressions will find use in interpretation techniques where repeated computations have to be made of the anomaly due to prisms as in automated fitting of prism anomalies to observed magnetic anomalies using non-linear optimization techniques or related methods.

Notes: The determination of the nature of reservoirs containing hydrocarbons is approached via a pattern-recognition method with prior learning. This method consists of comparing the nature of a reservoir that has been drilled into with an unknown reservoir. The known reservoir plays the part of a monitor for the learning process. To this end an algorithm is compiled using the Burg method of the features represented by different portions of traces contained in the reservoirs. An analysis of the dots representing these different features serves as a criterion for deciding whether the two reservoirs have identical or different natures.

Notes: In this paper we design a non-linear filter to suppress surface multiples in a non-normal incidence plane wave seismogram of a horizontally-layered elastic (or acoustic) earth model. Our filter is optimal in a least-squares sense and is very efficient in suppressing surface multiples, especially for small incidence angles. The design is based on an extension of earlier work by Mendel on normal incidence Bremmer series decomposition to the case of non-normal incidence, and relies heavily on work by Aminzadeh on a non-normal incidence state space model.

Notes: The radiation distribution of a single vibrator can be described using the formulas given by Miller and Pursey. From these the displacement characteristic for the radial component and also for horizontal component can be derived. This horizontal component is strengthened by adding another vibrator with opposite polarity near the first one. When this horizontal component is oriented perpendicular to the X-Z plane (plane spanned by the direction of the spread and the vertical axes), an SH-wave can be generated. Survey results indicate that this method works efficiently.

Notes: High-frequency electromagnetic probing is used to monitor the rate and direction of flow of fluids injected into the ground. This method shows the potential for providing more detailed information than procedures presently used. The experimental technique and the test-of-concept experimental results are discussed. This technique has applications in oil-reservoir engineering and in hydrology studies concerning storage of chemical wastes.

Notes: Vertical velocity gradients can be readily accommodated in seismic refraction interpretations by using simple mathematical idealizations of curved raypaths entailed by certain analytic representations of these gradients. Computation procedures are formulated for velocity gradients in the overburden or an intermediate layer of a multilayer section. The former is demonstrated for an overburden velocity gradient manifest in published time-distance data.

Notes: A laboratory instrument was developed to investigate the electrical properties of rock samples with respect to changes of frequency, temperature and pressure. The instrument can be used to obtain general trends and typical values for geological media. It should be of particular interest in geothermal studies and research in the geophysical properties of rocks.The design intervals for quantities under investigation were 20–300°C, 105-4 × 107 Pa and 5 × 10−4-103 Hz. Certain limitations exist on the simultaneous use of the highest values of temperature and pressure.The main features of the instrument are: analog electrical outputs recorded by an x-y recorder or observed on a scope with an attached camera (according to the frequency range); pressures produced by an oil hydraulic system in order to ensure electrical insulation of the sample; temperatures obtained by placing the pressure vessel into a thermostatically controlled room. Thus the monitoring instrumentation is directly accessible during the experiment. Information is also given about calibration procedures and examples of rock sample data are given.

Notes: Optimum multichannel filters can be designed to process seismic events falling on hyperbolic moveout curves using the conventional least-squares method. Contrary to the linear moveout filters, autocorrelation and crosscorrelation functions inherent in the normal equations have to be computed numerically. However, computation times of filter coefficients are comparable to linear moveout operators.For a given source-receiver geometry and assuming straight ray-path, relative moveout of a seismic reflection event is dependent on the two way arrival time and rms velocity. Consequently, to avoid overlapping of pass and reject moveout windows, hyperbolic moveout filters have to be designed over time gates rather than for the whole record lengths. Hyperbolic and hyperbolic-linear moveout filters applied to synthetic and field seismic reflection traces show good signal-to-noise (S/N) ratio improvements. Results of some combined synthetic and field data examples are presented.

Notes: A simple theory is presented to derive explicit recursive migration schemes in three dimensions which are suitable for situations with lateral velocity variations. The proposed schemes can be realized by one-dimensional convolutions along the x-axis and y-axis. An investigation is made on the errors of each scheme. For each frequency component the amplitude error and the phase error are computed as a function of the immergence angle (dip). Based on the error analysis a critical discussion is given on the stability of explicit schemes.

Notes: Due to non-linear effects, the swept frequency signals (sweeps) transmitted into the subsurface by vibrators are contaminated by harmonics. Upon correlation of the recorded seismograms, these harmonics lead to noise trains which are particularly disturbing in the case of down-sweeps. The method described in this paper—which can be regarded as a generalization of Sorkin's approach to the suppression of even order harmonics—allows elimination, from the final vibratory source seismogram, of harmonics of the sweep up to any desired order. It requires that not one single signal but rather a series of M signals is employed where each signal has an initial phase differing from that of the previous one of the series by the phase angle 2πM. Prior to stacking, the seismograms generated with the different signals have to be brought into the form they would have if they had been generated with the same signal.The method seems also to be capable of reducing the correlation noise if sign-bit recording techniques are used.

Notes: Six thousand three hundred IP measurements made in central and southern Germany have been statistically evaluated. Shapes of IP decay curves obtained in the course of routine prospecting for sulfides were characterized in the following way: three chargeabilities were recorded during the 2 s current-off time. By dividing the last by the first chargeability an “IP decay coefficient’ was calculated and statistically evaluated by means of histograms. When the histograms were compared with the statistics of apparent resistivity and chargeability, no relationship could be detected. Therefore, the histograms of M3/M1 values represent a characteristic property of distinct areas with certain geological features, mineral assemblage and tectonics. Weathering does not alter this geophysical “fingerprint”, which depends solely on geology.

Notes: An iterative stacking algorithm (superstack) has been applied in velocity analysis as a velocity filter prior to the coherency measurements. The effect of this filtering is demonstrated on both synthetic and real data using the following three methods of velocity analysis: Constant velocity stack, constant velocity gather, and velocity spectrum. The experimental results indicate that the velocity analysis can be improved by this approach.

Notes: A nomogram has been devised for situations, in which the source of a self-potential anomaly can be approximated by an obliquely polarized sphere or horizontal cylinder embedded in a homogeneous half space. The nomogram can be used for rapid determination of three parameters of the target: (1) depth to the centre, (2) angle between the axis of polarization and the horizontal, (3) shift of the point vertically above the centre of the body from zero potential value.The nomogram has been tested and the parameters determined for SP results obtained over ore bodies Weiss and Süleymanköy in the Ergani Copper district, Turkey. The curves computed for the estimated parameters match the field curves well.

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: The amplitude and phase response of a simple model is compared with the performance of a real vibrator working in the field. The field results show a characteristic phase response which confirms that the real drive force applied to the baseplate and its load impedance is faithfully represented by the acceleration of the reaction mass. It follows that all the parameters necessary to calculate the load impedance and the true power dissipated in the earth can be measured at the output of the vibrator. It also follows that the current method of baseplate phase compensation should be reconsidered.

Notes: The induction problem for an inhomogeneous two-dimensional conductor presenting a vertical contact between two media of diverse conductivities is considered. The general solution of the Helmholtz equation in the atmosphere is constructed for a simple induction mechanism. It is found that in the E-polarization case the anomalous field behavior in the boundary region and beyond differs from the generally assumed one. The conclusion of this paper is that the boundary conditions widely utilized in numerical computations have to be modified.

Notes: The “Laterolog 7′’and the “Microlaterolog’ have been studied theoretically for the case of a conducting halfspace containing a single overburden, using a technique based on the method of images. The results have shown these focussed arrays to be more sensitive to the lower medium (i.e., having greater depth of investigation) than unfocussed ones of the same dimensions, when the “correct’ geometric factor is used. The geometric factor of a focussed electrode array is somewhat involved, and is explained with reference to an ideal focussed array; such an array would pass a measuring current of constant intensity into a fixed geometrical shape of conducting material, irrespective of any layering or any other heterogenities that may be present, using auxiliary current sources of variable magnitude. This concept of a constant amount of current flowing in a beam of fixed geometry and current density, is the basis of focussed arrays, and it is shown that the geometric factor, used to calculate the apparent resistivity, is the one derived when considering the homogeneous case. The value of the constant measuring current, alone, is used to convert the measured potential difference into a resistance, the ratio between this value and the combined intensities of the auxiliary current sources, for the homogeneous case, being incorporated into the geometric factor.Surprisingly good agreement was found between the theoretical models and practical experiments using a focussing seabed resistivity probe which is a substantial modification of the “Microlaterolog”. Both show similar deviations from the ideal case which are explained in terms of refraction at the overburden interface. All experiments indicated that focussed arrays have a greater depth of investigation than similar unfocussed ones for a single overburden, whether it be resistive or conductive.

Notes: A forward solution for the reflection response of a parallel stratified lossless medium characterized by discrete reflection coefficients and unequal layer delays, for a normally incident pressure source signal, is presented. The notation, which details the reflection history of each wavelet in a response record, facilitates systematic enumeration of all terms in the reflection impulse response model, the determination of compact closed form expressions for amplitudes and delays of multiply reflected wavelets, and the aggregation of dynamic analog groups. An equal delay time constraint on layer thicknesses leads then to the reflection sequence or synthetic seismogram structure as an infinite sum of wavelets by their order of reflection.

Notes: It is advantageous to postulate the phenomenological equivalence of chargeability with a slight increase in resistivities rather than a similar reduction in the conductivities. Substitution of these increments in the expression for the total differential of apparent resistivity leads directly to Seigel's formula. Included also are (i) an equally simple demonstration that, for a homogeneously chargeable ground with arbitrary resistivity distribution, the apparent chargeability ma, equals the true homogeneous value m, and (ii) a direct derivation of the completely general resistivity relation〈displayedItem type="mathematics" xml:id="mu1" numbered="no"〉〈mediaResource alt="image" href="urn:x-wiley:00168025:GPR432:GPR_432_mu1"/〉where the symbols have the usual meanings.

Notes: One of the most troublesome problems in resistivity sounding is caused by the spurious effects of near-surface lateral resistivity variations. It has been found that the effects can be strongly reduced by measuring earth resistances at two electrode array positions such that in one position the lateral effect is a positive contribution to the total measured signal and in the other the contribution is negative. The subsequent combination of the two measurements virtually eliminates the lateral effect.The same technique can also result in a significant reduction in the total number of necessary electrode positions. Consequently the method can be used with a multicore cable system. In this way, in addition to improving the accuracy of the measured results, time and manpower are considerably reduced.Details of the method, examples and comparisons with traditional sounding techniques are given.

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.