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: 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: 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: Book reviews in this article:Gray Area W. Kip Viscusi, Welfare of the Elderly: An Economic Analysis and Policy Prescription.A Soft Futur Walter A. Rosenbaum, Coal and Crisis: The Political Dilemmas of Energy Management.Putting out Fires Malcolm Getz, The Economics of the Urban Fire Department.Inequities Continue Elizabeth McTaggart Almquist, Minorities, Gender, and Work.The Federal Physician J. H. U. Brown, The Politics of Health Care.A Method to the Masses Leslie Corsa and Deborah Oakley, Population Planning. Ann ArborConservative Innovations Alan Altshuler with James P. Womack and John R. Pucher, The Urban Transportation System: Politics and Policy Innovation.Why, and Whither? David P. Varady, Ethnic Minorities in Urban Areas: A Case Study of Racially Changing Communities.Undermining Authority Susan Rose-Ackerman, Corruption: A Study in Political Economy.A Question of Power Robert Lawrence, ed., New Dimensions to Energy Policy.Briefer Mention What Works, What Doesn't William H. Whyte, The Social Life of Small Urban Spaces.

Notes: Book reviews in this article:Straight Talk from Our Former Editor U.S. Department of Labor, Employment and Training Administration (prepared by Lawrence R. Klein and Susan Ghozeil), A Popularized Version of 21 Doctoral Dissertations, R & D monograph.The Well-Tempered Caveat Benjamin Chinitz, ed., The Declining Northeast: Demographic and Economic Analyses..George Sternlieb and James W. Hughes, eds., Revitalizing the Northeast: Prelude to an Agenda..The Economic Solution William J. Baumol and Wallace E. Oates, Economics, Environmental Policy, and the Quality of Life.The No-Free-Lunch Bunch Harold Sprout and Margaret Sprout, The Context of Environmental Politics: Unfinished Business for America's Third Century.Of Flora, Fish, and Titmice Ian C. Laurie, ed., Nature in Cities: The Natural Environment in the Design and Development of Urban Green Space.An Array of Options David J. Bartholomew and Andrew F. Forbes, Statistical Techniques for Manpower Planning.Reusing Resources David W. Pearce and Ingo Walter, eds., Resource Conservation: Social and Economic Dimensions of Recycling.Once More with Fueling Wallace E. Tyner, Energy Resources and Economic Development in India.Left-of-Center Viewpoint Jeannine Swift, Economic Development in Latin America.Edward J. Blakely, ed., Community Development Research: Concepts, Issues, and Strategies.Elchanan Cohn, The Economics of EducationP. W. Daniels, ed., Spatial Patterns of Office Growth and Location.Douglas Evans, Western Energy Policy: The Case for Competition.R. A. French and F. E. Ian Hamilton, eds., The Socialist City: Spatial Structure and Urban Policy.D. A. Kirby, Slum Housing and Residential Renewal: The Case in Urban Britain.Thomas D. Lynch, Public Budgeting in America.Ragaei El Mallakh, Qatar: Development of an Oil Economy.Roberta Balstad Miller, City and Hinterland: A Case Study of Urban Growth and Regional Development.Rakesh Mohan, Urban Economic and Planning Models: Assessing the Potential for Cities in Developing Countries.Joseph P. Newhouse, The Economics of Medical Care: A Policy Perspective.John L. Palmer, ed., Creating Jobs: Public Employment Programs and Wage Subsidies.V. Kerry Smith, ed., Scarcity and Growth Reconsidered.

Notes: Book Review in this Article.Richard A. Easterlin, ed., Population and Economic Change in Developing Countries.John F. McDonald, Economic Analysis of an Urban Housing Market.Thomas A. Clark, Blacks in Suburbs: A National Perspective.Stephen Merrett, State Housing in Britain.Lloyd C. Irland, Wilderness Economics and Policy.Richard E. Lonsdale and H. L. Seyler, eds., Nonmetro-politan IndustrializationDonald N. Rothblatt, Daniel J. Garr, and Jo Sprague, The Suburban Environment and Women.Glenn V. Fuguitt, Paul R. Voss, and J. C. Doherty, Growth and Change in Rural America.Chia-ling Kuo, Social and Political Change in New York's Chinatown: The Role of Voluntary Associations.Frank Cancian, The Innovator's Situation: Upper-Middle-Class Conservatism in Agricultural Cornrnunities.

Notes: Book Review in this Article.Norman J. Glickman, The Growth and Management of the Japanese Urban System.Thomas J. Espenshade and William J. Serow, eds., The Economic Consequences of Slowing Population Growth.Phillip L. Clay, Neighborhood Renewal: Middle-class Resettlement and Incumbent Upgrading in American Neighborhoods.Juliet Saltman, Open Housing: Dynamics of a Social Movement.Herman Kahn, World Economic Development: 1979 and Beyond.Werner Sichel, ed., Public Utility Rate Making in an Energy-Conscious Environment.Russian Research Carol W. Lewis and Stephen Sternheimer, Soviet Urban Management: With Comparisons to the United States.Gene F. Summers and Arne Selvik, eds., Nonrnetropolitan Industrial Growth and Community Change.Tony Killick, Development Economics in Action: A Study of Economic Policies in Ghana.Glynn Cochrane, The Cultural Appraisal of Development Projects.Meryl Aldridge, The British New Towns: A Programme without a Policy.Edmond M. Burke, A Participatory Approach to Urban Planning.

Notes: Book reviewed in this article: Urbanization and Labor Markets in Developing Countries, by Stuart W. Sinclair. Urban Housing Markets: Recent Directions in Research and Policy, by Larry S. Bourne and John R. Hitchcock, (eds.) with the assistance of Judith M. Kjellberg. A National Model of Fuel Allocation—A Prototype by E. W. Henry and S. Scott. Spatial Development Planning: A Dynamic Convex Programming Approach, M. Fujita.