bluuebunny/crossref_metadata_2025 huggingface dataset:
Electromagnetic field of a dipole on a two‐layer earth
Authors: Chew W. C. , Kong J. A.
Published: October 2002

The electromagnetic field due to a horizontal electric dipole placed on top of a two‐layer earth is represented in terms of fields due to a dipole over a half‐space earth and its image source fields. Integral representations of image source fields are evaluated with uniform asymptotic approximations. Leading order ordinary saddle‐point approximation, giving rise to the geometrical optics approximation (GOA), is shown to be inaccurate. This is especially true when the angle of observation is close to the critical angle, which corresponds to the presence of a branch‐point singularity near the saddle point. In the uniform asymptotic approximation, the integrand of the image source integral is split into a branch‐point free part and another part containing the branch‐point singularity. The branch‐point free part can be approximated with a spherical wave function, while the part containing the branch point can be approximated with parabolic cylinder functions. Vertical magnetic field components and the horizontal electric field component near the surface are illustrated and compared with the geometrical optics approximation, giving the direct numerical result as well as experimental measurement. It is shown that the uniform asymptotic approximation yields excellent agreement with numerical and experimental results compared to the geometrical optics approximation.
Detectability of an intermediate layer by magnetotelluric sounding
Authors: Kumar Rakesh , Sarma S. V. S. , Narayan P. V. Sanker
Published: October 2002

The recent publication by Verma and Mallick (1979) on the detectability of an intermediate layer by time domain EM sounding provides some informative answers to a problem of practical interest. That is, an attempt has been made to probe the usefulness of the sounding system with regard to its ability to detect a subsurface layer. It is worthwhile to attempt to analyze the same problem of detectability in a three‐layer sequence by magnetotelluric (MT) sounding which is finding increasing use in recent years in exploration for minerals (Strangway and Koziar, 1979) and in prospecting for geothermal resources (Hoover and Long, 1975), particularly in the audio‐frequency range. We present results of an analysis of the problem of detectability of an intermediate layer in a three‐layer horizontal sequence with several possible combinations of the layer resistivities of practical interest covering all the four types H, K, A and Q, by the AMT sounding system. The computational approach used by Verma and Mallick (1979) has been adopted in our study.
Scale invariance of the low‐frequency electrical properties of inhomogeneous materials
Authors: Cohen Morrel H.
Published: October 2002

We show that the electrical properties of an inhomogeneous material are invariant to the scale of the inhomogeneity at low frequencies when they are determined solely from local bulk properties, Thus the pore and grain sizes of rocks cannot be ascertained by low‐frequency conductivity and dielectric constant measurements.
Error estimates for inverse modeling schemes using seismic traveltimes
Authors: Ursin Bjørn
Published: October 2002

Different methods for estimating parameters in a layered geologic model are discussed. Traveltime parameters, estimated from seismic data, are used to estimate the layer parameters defining the velocity function in each layer and the interfaces between the layers. Seismic measurement data are assumed to consist of a sum of nonoverlapping reflected pulses and additive white Gaussian noise. An estimate of the covariance of the traveltime parameters is then given by the inverse of Fischer’s information matrix. It is shown how the information matrix can be computed theoretically or directly from data. Expressions for the covariance matrix of the layer parameters are given. The results can be used to compute confidence regions for the estimated parameters. Optimal seismic measurement systems are discussed, resulting in a criterion for designing an optimal seismic pulse: The energy of the derivative of the received signal (the source pulse convolved with the impulse response of the earth and the impulse response of the instruments) should be maximized. Parameter estimation in a horizontally layered model is considered as an example, and the covariance matrix of the layer velocity and layer thickness is given explicitly.
The temperature stabilization of a borehole
Authors: Leblanc Y. , Pascoe L. J. , Jones F. W.
Published: October 2002

Analytic solutions for the temperature stabilization of both square and circular boreholes are considered. It is found that a previously published solution for a square borehole is incorrect in that it does not reproduce the initially assumed conditions. The correct analytic solution for a square well, as well as that for a circular well, indicates a much more rapid approach to the formation temperature. The temperature stabilization curves for a range of thermal diffusivity values are given.
A combination of electrical resistivity, seismic refraction, and gravity measurements for groundwater exploration in Sudan
Authors: van Overmeeren Ronald A.
Published: October 2002

In the savannah belt of central Sudan, near the town of Kosti, a regional geophysical survey has been carried out forming part of a groundwater project. Because of the presence of detectable and significant contrasts in physical properties of the subsoil, integrated use could be made of electrical resistivity, seismic refraction, and gravity methods. In the interpretation of multilayer electrical sounding curves, additional subsurface information such as lithological well descriptions and geophysical well logs is normally a necessity for solving the problems of equivalence. Along a profile in the eastern part of the area studied, where additional subsurface information was scarce, 16 vertical electrical soundings have been made. A preliminary simple mathematical interpretation suggested possibilities for the presence of fresh groundwater in the eastern part of the profile. In order to solve the equivalence problem, seismic refraction work was carried out at some selected places; that yielded additional information on depths to bedrock. These seismic data made possible a unique solution of the electrical sounding curves, from which it could be concluded that all groundwater in the area is saline. Subsequent test drilling confirmed these findings. A regional relative Bouguer anomaly map provided a picture of the general geologic structures and made possible rough estimates of depths to bedrock. In areas where the basement rocks are relatively close to the surface, as is the case with the profile presented, the gravity anomalies cannot be correlated with bedrock relief, because the effect is strongly influenced by lateral density variations within the bedrock itself. This is an example of a case where only an integrated application of several geophysical exploration methods can provide the desired hydrogeologic information in an acceptable balance between reliability and cost.
Transient electromagnetic calculations using the Gaver‐Stehfest inverse Laplace transform method
Authors: Knight J. H. , Raiche A. P.
Published: October 2002

Calculations for the transient electromagnetic (TEM) method are commonly performed by using a discrete Fourier transform method to invert the appropriate transform of the solution. We derive the Laplace transform of the solution for TEM soundings over an N‐layer earth and show how to use the Gaver‐Stehfest algorithm to invert it numerically. This is considerably more stable and computationally efficient than inversion using the discrete Fourier transform.
High‐resolution seismic study in the Gas Hills uranium district, Wyoming
Authors: Applegate James K. , Emilia David A. , Neitzel Edwin B. , Donaldson Paul R.
Published: October 2002

A study was undertaken to evaluate the effectiveness of the high‐resolution seismic technique for the mapping of stratigraphic and structural controls in the Gas Hills uranium district, Wyoming. The test area is one in which uranium deposits are in Tertiary sediments which unconformably overlie a Mesozoic Paleozoic section. Paleochannels on the unconformity appear to control the localization of the uranium. Drilling in the area allows an evaluation of the effectiveness of the study. Using both sonic and density logs, we computed synthetic seismograms to evaluate the feasibility of predicting the success of the seismic reflection technique and to test this prediction using surface seismic methods. The field study was undertaken utilizing primarily two energy sources—a high‐frequency vibrator (40–350 Hz), and one‐pound dynamite charges shot in 10-ft holes. A limited amount of data was also acquired using detonating cord on the surface. Some three‐dimensional (3-D) data were also acquired, and a later study acquired passive seismic data. The seismic reflection data were successful not only in delineating the unconformable surface and in mapping paleodrainages on the unconformity, but also in defining channel deposits within the Tertiary section. Correlation with the logs shows the success of the study. Several areas were delineated where one would undertake tight drilling patterns, and other areas were delineated in which one might minimize or eliminate exploratory drilling. The synthetic seismograms also could have predicted the success of the seismic work.
Plane‐wave decomposition of seismograms
Authors: Treitel Sven , Gutowski P. R. , Wagner D. E.
Published: October 2002

A point‐source seismic recording can be decomposed into a set of plane‐wave seismograms for arbitrary angles of incidence. Such plane‐wave seismograms possess an inherently simple structure that make them amenable to existing inversion methods such as predictive deconvolution. Implementation of plane‐wave decomposition (PWD) takes place in the frequency‐wavenumber domain under the assumption of radial symmetry. This version of PWD is equivalent to slant stacking if allowance is made for the customary use of linear recording arrays on the surface of a three‐dimensional medium. An imaging principle embodying both kinematic as well as dynamic characteristics allows us to perform time migration of the plane‐wave seismograms. The imaging procedure is implementable as a two‐dimensional filter whose independent variables are traveltime and angle of incidence.
Forward modeling by a Fourier method
Authors: Kosloff Dan D. , Baysal Edip
Published: October 2002

A Fourier or pseudospectral forward‐modeling algorithm for solving the two‐dimensional acoustic wave equation is presented. The method utilizes a spatial numerical grid to calculate spatial derivatives by the fast Fourier transform. Time derivatives which appear in the wave equation are calculated by second‐order differencing. The scheme requires fewer grid points than finite‐difference methods to achieve the same accuracy. It is therefore believed that the Fourier method will prove more efficient than finite‐difference methods, especially when dealing with three‐dimensional models. The Fourier forward‐modeling method was tested against two problems, a single‐layer problem with a known analytic solution and a wedge problem which was also tested by physical modeling. The numerical results agreed with both the analytic and physical model results. Furthermore, the numerical model facilitates the explanation of certain events on the time section of the physical model which otherwise could not easily be taken into account.
Wave propagation and sampling theory—Part II: Sampling theory and complex waves
Authors: Morlet J. , Arens G. , Fourgeau E. , Giard D.
Published: October 2002

Morlet et al (1982, this issue) showed the advantages of using complex values for both waves and characteristics of the media. We simulated the theoretical tools we present here, using the Goupillaud‐Kunetz algorithm. Now we present sampling methods for complex signals or traces corresponding to received waves, and sampling methods for complex characterization of multilayered or heterogeneous media. Regarding the complex signals, we present a two‐dimensional (2-D) method of sampling in the time‐frequency domain using a special or “extended” Gabor expansion on a set of basic wavelets adapted to phase preservation. Such a 2-D expansion permits us to handle in a proper manner instantaneous frequency spectra. We show the differences between “wavelet resolution” and “sampling grid resolution.” We also show the importance of phase preservation in high‐resolution seismic. Regarding the media, we show how analytical studies of wave propagation in periodic structured layers could help when trying to characterize the physical properties of the layers and their large scale granularity as a result of complex deconvolution. Analytical studies of wave propagation in periodic structures are well known in solid state physics, and lead to the so‐called “Bloch waves.” The introduction of complex waves leads to replacing the classical wave equation by a Schrödinger equation. Finally, we show that complex wave equations, Gabor expansion, and Bloch waves are three different ways of introducing the tools of quantum mechanics in high‐resolution seismic (Gabor, 1946; Kittel, 1976; Morlet, 1975). And conversely, the Goupillaud‐Kunetz algorithm and an extended Gabor expansion may be of some use in solid state physics.
Seismic wave velocity investigation at The Geysers‐Clear Lake geothermal field, California
Authors: Gupta Harsh K. , Ward Ronald W. , Lin Tzeu‐Lie
Published: October 2002

Analysis of P‐ and S‐waves from shallow microearthquakes in the vicinity of The Geysers geothermal area, California, recorded by a dense, telemetered seismic array operated by the U.S. Geological Survey (USGS) shows that these phases are easily recognized and traced on record sections to distances of 80 km. Regional average velocities for the upper crust are estimated to be [Formula: see text] and [Formula: see text] for P‐ and S‐waves, respectively. Poisson’s ratio is estimated at 23 locations using Wadati diagrams and is found to vary from 0.13 to 0.32. In general, the Poisson’s ratio is found to be lower at the locations close to the steam production zones at The Geysers and Clear Lake volcanic field to the northeast. The low Poisson ratio corresponds to a decrease in P‐wave velocity in areas of high heat flow. The decrease may be caused by fracturing of the rock and saturation with gas or steam.
Velocity and density profiles of a layered acoustic medium from common source‐point data
Authors: Coen Shimon
Published: October 2002

An inverse scattering theory is presented for the unique reconstruction of the density and velocity profiles of a layered acoustic half‐space from common source‐point surface data. The point source is either impulsive or is capable of vibrating at two arbitrary frequencies. An additional datum for the unique reconstruction of these profiles is an estimate of either the highest or lowest velocity within the inhomogeneous acoustic half‐space. Two direct (noniterative) inversion algorithms are developed which construct the density and velocity profiles of the inhomogeneous half‐space from these data. Analytical examples are presented in which all steps in the inversion algorithms are analytically determined. Finally, the paper discusses the potential application of the theory to real seismic data.
Magnetotelluric regional strike
Authors: Gamble T. D. , Goubau W. M. , Miracky R. , Clarke J.
Published: October 2002

A new method for determining regional strikes from the magnetotelluric impedance tensor Z and tipper T is presented. It involves the minimization of weighted sums of the squared magnitudes of elements of Z or T over all frequencies and all stations of interest. When applied to data from the Mexicali Valley, Baja California around the Cerro Prieto geothermal field for a particular weighting function, the method yielded orientations that agree to within 2.9 degrees for three lines with a total of 16 stations. The consistency of orientations can be attributed in part to the pronounced two‐dimensional (2-D) geologic characteristics of the area, but the techniques also proved stable at stations near three‐dimensional (3-D) inhomogeneities.
Measurement of rise times of seismic pulses in rock
Authors: Blair D. P.
Published: October 2002

Rise times for seismic pulses in rock are discussed for both nearly constant Q (NCQ) and constant Q (CQ) theories of pulse attenuation. The frequency content of the NCQ pulse is examined in detail. Frequencies close to the megahertz region are shown to have a significant contribution to the rise time of pulses a meter or so from an impulsive source. Hence, the measurement of such rise times is significantly influenced by the frequency response of the measurement system itself. In giving a numerical assessment of the system influence, I propose a model for a general system transfer function. The effect of such a system on the measurement of rise times of seismic pulses is then obtained by convolving the system impulse response with the given seismic pulse. For even the most broad‐band seismic measurement systems presently available, rise time measurements made especially within 10 m or so of an impulsive source show a large contribution dependent upon the rise time of the measurement system itself.
Depth of investigation studies for gradient arrays over homogeneous isotropic half‐space
Authors: Bhattacharya B. B. , Dutta Indrajit
Published: October 2002

The depth of investigation of gradient arrays using point, finite, and infinite line sources over homogeneous isotropic ground has been studied. The depth of investigation depends for all cases on the radial distance of the plotting point (i.e., the midpoint of the line joining the potential probes) and separation between the current electrodes. For point electrode systems, it also depends upon azimuth of the plotting point, whereas for finite line electrode systems, it depends upon the azimuth and the length of the line electrode. The depth of investigation at the center of the array is maximum (0.145 L) for infinite line electrodes, decreases to 0.135 L for finite line electrodes of length L, and becomes least (0.125 L) for the point source, where L is the separation between the current electrodes. The depth of investigation for finite line electrodes of unit length L is practically independent of the y‐coordinate which is mathematically the case for infinite line electrode systems. The depth of investigation is least toward the current electrode and increases as one moves away from the current electrode; it ultimately reaches the maximum value of 0.135 L at the center of the system. The depth of investigation for point electrode systems is also minimum near the current electrode and increases with the increase of azimuth for any radial distance.
Acoustic modes of propagation in the borehole and their relationship to rock properties
Authors: Paillet F. L. , White J. E.
Published: October 2002

Acoustic waveform measurements in boreholes have important applications in fracture hydrology and radioactive waste disposal, but ambiguities in existing interpretation techniques remain a problem. We have addressed the problem by using residue theory to predict the relative excitation of various modes contained in experimental waveforms. A plane‐geometry model involving a layer of fluid between two elastic half‐spaces is shown to provide velocity dispersion curves for propagating modes that are very similar to those for the fluid‐filled borehole. We use the plane‐geometry model to illustrate the effects of the confined borehole fluid on surface and body waves traveling along the borehole in the elastic solid. We also computed excitation functions for some of the lowest‐order symmetric modes, calculated the time‐domain response of the trapped modes following the shear head waves, and compared them to waveforms recorded in boreholes through several homogeneous formations. The insight into the mode composition of the experimental waveforms obtained in these formations is used to construct amplitude logs that should be especially sensitive to variations in the presence of fluid‐filled fractures in the borehole wall. Initial tests show the technique is most successful when the waveform is dominated by the fundamental tube wave, and yet frequencies remain relatively high. The model analysis indicates these conditions can only be obtained when the borehole diameter is not much larger than that of the logging tool.
Response characteristics of coincident loop transient electromagnetic systems
Authors: Weidelt P.
Published: October 2002

The occasional occurrence of persistent sign reversals in coincident loop transient electromagnetic (TEM) measurements stimulates an investigation of possible causes for this effect. By examining the response in the complex frequency plane near the spectrum of freely decaying current modes, it is shown that for any physically reasonable frequency‐independent distribution of electrical conductivity and magnetic permeability the voltage response to a step function driving current is of one sign only. Moreover, under the conditions mentioned above, the logarithm of the induced voltage is a decreasing convex function of time. These characteristics are retained for more general time functions of the driving current. The conservation of sign for frequency‐independent material parameters supports the assumption of IP effects as a possible mechanism for sign reversals. The latter point is illustrated by a simplified example.
On: “Fields of view of airborne gamma‐ray detectors” by R. L. Grasty, R. S. Foote, and K. L. Kosanke (GEOPHYSICS, August 1979, p. 1447–1457) and “Design parameters for aerial gamma‐ray surveys” by J. A. Pitkin and J. S. Duval (GEOPHYSICS, September 1980, p. 1427–1439).
Authors: Kellogg William C.
Published: October 2002

In March, 1971, I presented a paper entitled “Calculation of airborne radioactivity survey responses: Theory, method, and field test,” before the AIME at its annual meeting in New York. I note that two recent publications in GEOPHYSICS reference it: “Fields of view of airborne gamma‐ray detectors,” by Grasty et al (August 1979), and “Design parameters for aerial gamma‐ray surveys,” by Pitkin and Duval (September 1980). The recognition in each case is appreciated.
Radiation patterns of a shear‐wave vibrator in near‐surface shale
Authors: Robertson James D. , Corrigan Dennis
Published: October 2002

Two shallow, surface‐to‐borehole field tests were conducted to investigate the radiation patterns of a shear‐wave vibrator in near‐surface shale. In the in‐line direction, for which baseplate motion is transverse to the source‐geophone raypath, the vibrator produces a broadband, high‐amplitude signal of the SH type and virtually no signal of the SV or P types. The amplitude of the SH radiation is approximately constant as a function of polar angle, but it falls off as the cosine of the azimuthal angle measured with respect to the in‐line direction. In the broadside direction, the vibrator produces a strong, uncontaminated signal of the SV type. The radiation pattern of the SV signature is lobate in the polar plane and peaks at an incident angle of 30 to 35 degrees. In the horizontal plane, the SV radiation varies as the sine of the azimuthal angle measured with respect to the in‐line direction. The field tests were conducted on a Permian shale in Oklahoma and an Eocene shale in East Texas. Comparison between SH and SV wave surfaces indicates that both shales behave approximately like transversely isotropic solids with a vertical axis of symmetry. Theoretical wave surfaces are fit to the observed data by using elastic moduli determined from the field measurements and by making the assumption that the near‐surface shale at each field site is a single, homogeneous, inherently transversely isotropic material. The analyses indicate that horizontal SH group velocity is about 30 percent greater than horizontal SV group velocity in the Permian shale and about 25 percent greater in the Eocene shale.
Scattering theory of wave propagation in a two‐phase medium
Authors: Mehta C. H.
Published: October 2002

A theory is developed for the propagation of pressure waves in a two‐phase medium where one phase consists of spherical inclusions distributed randomly in the second phase. The theory is based on an integral equation of Foldy (1945) and Twersky (1970) for the average wave which includes almost all multiple scattering processes, but it ignores correlations among inclusions. In the low‐frequency limit, this equation is solved exactly for an analytical expression for the refractive index of compressional waves in terms of elastic parameters of the matrix and the inclusions. The theory is then applied to fluid‐solid suspensions and to fluid‐saturated porous rocks. In the former case, velocities measured by Kuster and Toksöz (1974b) as a function of the concentration of inclusions are compared with theoretical predictions of seven different models. The closest agreement is obtained for the present theory. This is attributed to systematic inclusion of multiple scattering effects including near‐field scattering interactions. Theoretically computed attenuation also agrees well with experiments. In the case of fluid‐saturated porous rocks, comparison between theoretically computed velocities and observed velocities in sandstones (Wyllie et al, 1962) suggests the importance of microcracks and nonspherical inclusions, factors which are not included in the present model. Attenuation caused by viscosity of inclusions is shown to arise in two different ways: losses caused by generation of shear waves in the fluid, and those caused by Darcy‐type flow of the fluid relative to the matrix. The former increases with viscosity, while the latter decreases. The sum, however, remains negligible at frequencies relevant to seismic prospecting and earthquakes.
Acoustic estimation of deep sea floor nodule densities
Authors: Tolstoy Ivan
Published: October 2002

A particularly simple method of calculating sound scatter from planar distributions of small bodies was devised some years ago by Biot (1968) for a type of rough surface model pioneered by Twersky (1957) consisting essentially of spheroidal or hemispheroidal bumps on a rigid plane. The Biot theory has been generalized recently by Tolstoy (1979, 1980, 1981, 1982a, b) to scatterers of arbitrary shapes and impedance contrasts at interfaces between arbitrary fluids. It applies to the case [Formula: see text], (1) where k is the wavenumber, a the mean height of the scatterers, and h the spacing between their centers (Figure 1). The theory deals with the coherent part of the multiple scatter and predicts phenomena not adequately described by conventional stochastic models of rough surface scattering of acoustic waves, whose usefulness is restricted by the assumption that the slopes of the irregularities are everywhere small (Bass and Fuks, 1979; Wenzel, 1974; Kuperman, 1975).
Deep reflection experiments in northeastern Australia, 1976–1978
Authors: Mathur S. P.
Published: October 2002

Between 1976 and 1978 the Australian Bureau of Mineral Resources (BMR) recorded deep crustal reflection data at seven sites in northeastern Australia over continuous profiles up to 15 km long by simply extending the recording time to 16 sec during normal sedimentary basin surveys. The record sections show many events with variable strength, continuity, dip, and spatial distribution. By comparing the sections from the longer and the shorter perpendicular traverses, it is possible to discriminate between primary reflections and diffractions, multiples, and other noise events. Based on their character the reflections can be grouped into zones which are interpreted in terms of the nature and structure of the crust. Most of the reflection sections show, below the sedimentary reflections, a thin (2–3 sec) reflection‐free zone underlain by a thick (9 sec or more) zone of numerous reflection segments which varies in thickness and the distribution of reflection segments. The data thus suggest that the upper crust under the sediments is similar in seismic character throughout northeastern Australia. On the other hand, the deeper crust under the Georgina and Drummond basins is significantly different in seismic signature and thickness from that under the Bowen basin and the northern margin of the Galilee basin. It is concluded that good quality deep reflections can be recorded with little extra effort during sedimentary basin surveys using modern multiple‐fold common‐depth‐point (CDP) techniques, and that the data recorded on long traverses, cross‐spreads, and expanded spreads provide information on the structure and composition of the crust and upper mantle with a resolution greater than has been possible before. Such information is valuable in studying the evolution of mineral and petroleum provinces and the lithosphere in general.
Spectral analysis of gravity and magnetic anomalies due to a vertical circular cylinder
Authors: Soto A. , Singh S. K. , Flores C.
Published: October 2002

Expressions for the spectra of gravity and magnetic anomalies due to a vertical right circular cylinder can be written in terms of a Bessel function and the sum of two exponentials. From the zeros of the amplitude spectra, which are the zeros of the Bessel function, an estimate of the radius of the cylinder can be obtained. The depths to the top and to the bottom enter as exponents of the exponential terms and can be evaluated by taking ratios of the spectra at several frequencies. The density or the intensity of magnetization can then be easily estimated. For the magnetic case the epicenter of the cylinder can be obtained from the slope of the phase spectra. The method has been tested on anomalies of various cylinders and was found to give good results.
A case for larger offsets
Authors: Schultz Philip S. , Pieprzak Andrew W. , Loh Eddie K. L.
Published: October 2002

Traditionally, when field acquisition parameters are chosen, an underlying consideration is the ability to process and image the data to be recorded. For the choice of the length of the receiver spread, a limiting factor is the root‐mean‐square (rms) restriction: for reflections from the depth of interest, one need not record data for which the propagation angle is so large that it cannot safely be included in an rms velocity analysis. This restriction has led to various criteria for the determination of the largest useful offset which can be recorded. For example, the farthest offset should be less than the depth of interest. Recent advances in analysis of wide‐angle arrivals compel us to re‐evaluate such criteria.
Applications of operator separation in reflection seismology
Authors: Brown David L.
Published: October 2002

The principle of operator separation, a generalization of operator splitting, is applied to some problems in reflection seismology. In particular, the examples of wave‐equation migration of seismic data in a three‐dimensional medium and accurate depth migration in a laterally varying medium are considered in light of this theory. For the case of a stratified three‐dimensional medium, the standard dimensional splitting technique used in the downward‐continuation step of the migration process can be replaced with full dimensional separation. The computational implications of this result are that the wave field array need only be transposed once during the downward continuation rather than 2n times, where n is the number of finite‐difference steps taken in the calculation. For the example of downward continuation in a laterally varying medium, the ideas of operator separation can be used to split the downward continuation operator into two parts, one that looks like the conventional downward‐continuation operator for a stratified medium, and a second that represents the correction for the effects of lateral variation.
Electromagnetic soundings in the sedimentary basin of southern Ontario—A case history
Authors: Gómez‐Trevino E. , Edwards R. N.
Published: October 2002

The results of electrical and electromagnetic (EM) soundings conducted in the sedimentary basin of southern Ontario are presented. The sounding sites are located strategically to take advantage of the dipping nature of the sediments, a progressive study being undertaken from shallow to deep sections. The vertical magnetic field transfer function, estimated with a pseudonoise source EM system, and conventional Schlumberger apparent resistivity are jointly inverted. For each site, the layered earth model containing the minimum number of layers is fitted to the data. The joint inversion enables up to eight distinct layers to be identified at some sites. The nonuniquenesses or ambiguities in each model, for example S (conductivity‐thickness product) equivalence of a deep thin conductive layer, are revealed through an eigensolution analysis. The intrinsic ambiguities of the models of the deeper sections are resolved by a systematic, progressive site‐to‐site correlation of electrical units across the basin. For example, the conductivity of a conductive unit is measurable when it is at a shallow depth. In a deeper section, if the unit appears as a thin layer, it is assigned this value of conductivity removing the S‐equivalence ambiguity. The individual inversions combined with the site‐to‐site correlation produce an overall electrical model of the basin consistent with the known geologic section.
Numerical analysis of the 45‐degree finite‐difference equation for migration
Authors: Brysk Henry
Published: October 2002

Migration is now most commonly performed by means of a finite‐difference solution of the wave equation in the space‐time domain (although alternative approaches such as f-k, Kirchhoff, finite‐difference in the space‐frequency domain have strong adherents). Claerbout’s derivation of the 15‐degree paraxial ray equation and its iteration to the 45‐degree equation are well documented. On the other hand, the transcription of the differential equation to a finite‐difference scheme has accreted with practical computing experience and is only mentioned piecemeal (when at all) in the literature. The full expression is reviewed here, as used in a typical production code. A numerical stability analysis of the von Neumann type is applied to the complete finite‐difference equation. It proves that the computer algorithm is stable, at least for the values of the computational parameters in normal use (the sensitivity to the values of these parameters is illustrated.) Thus, any perceived noisiness of migrated sections cannot be blamed on computational precision. The shortcomings are entirely caused by deficiencies in the analytic framework and the modeling.
Reflection of spherical seismic waves in elastic layered media
Authors: Krail Paul M. , Brysk Henry
Published: October 2002

The solution of the elastic wave equation for a plane wave incident on a plane interface has been known since the turn of the century. For reflections from reasonably shallow beds, however, it is necessary to treat the incident wave as spherical rather than plane. The formalism for expressing spherical wavefronts as contour integrals over plane waves goes back to Sommerfeld (1909) and Weyl (1919). Brekhovskikh (1960) performed a steepest descent evaluation of the integrals to attain analytic results in the acoustic case. We have extended his approach to elastic waves to obtain spherical‐wave Zoeppritz coefficients. We illustrate the impact of the curvature correction parametrically (as the velocity and density contrasts and Poisson’s ratios are varied). In particular, we examine conditions appropriate to “bright spot” analysis; expectedly, the situation becomes less simple than in the plane‐wave limit. The curvature‐corrected Zoeppritz coefficients vary more strongly (and in a more complicated manner) with the angle of incidence than do the original ones. The determination of material properties (velocities and densities) from the reflection coefficients is feasible in principle, with exacting prestack processing and interpretation. For orientation, we outline the procedure for the simple case of a separated single source and detector pair over a multilayered horizontal earth.
A practical method for the inversion of magnetotelluric data for a layered earth
Authors: Rankin D. , Pascal F.
Published: October 2002

A numerical one‐dimensional magnetotelluric inversion technique based on the Nabetani‐Rankin algorithm for a layered earth is presented and illustrated with a noise‐free theoretical model and two examples with real field data. The inversion of noise‐free data is for practical purposes unique. The method is computationally efficient and removes most of the subjective biases which may be introduced into the interpretation of more or less real noisy data. A very satisfactory fit of the inverted result to field measurements is achieved using the least‐squares criterion applied to the real part of the Nabetani‐Rankin function V. The advantages of this function over others which have been suggested lie in its simplicity, its whiteness, and its relative freedom from noise. The Marquardt algorithm for the estimation of nonlinear parameters used for fitting the V curves overcomes the frequent failure of convergence in the Taylor series method and the slow convergence of the gradient method.
COCORP: New York — New England and Kansas Areas
Authors: Kaufman S.
Published: October 2002

The Consortium for Continental Reflection Profiling (COCORP) announces the availability of the data packages and tapes for the New York‐New England area and the Kansas area for the cost of reproduction and shipping. These data were produced by COCORP whose operation is part of the U.S. Geodynamics Project sponsored by the National Academy of Sciences and funded by the National Science Foundation. The executive group of the consortium consists of members from Cornell University, Dartmouth College, Princeton University, Rice University, and the University of Wisconsin. Cornell University is the operating institution.
Electrode configuration influence on resistivity measurements about a spherical anomaly
Authors: Lytle R. J. , Hanson J. M.
Published: October 2002

The trade‐offs involved with subsurface resistivity probing are studied for the case of a spherical anomaly. In particular, two‐, three‐, and four‐electrode configurations are investigated. The three‐ and four‐electrode configurations have similar results and have significantly better remote detection capabilities than does a two‐electrode configuration. Cross‐borehole probing is capable of detecting anomalous conditions at a greater range than is single‐borehole probing.
Enhancement of electromagnetic anomalies—A circuit theory approach
Authors: Bhattacharya B. B. , Mukherjee D. S. , Chatterjee D.
Published: October 2002

The physical consequences of a grounded conducting target with realistic leakage path between itself and the host are discussed from a circuit theory approach. The real and imaginary components of the response of a conductor with leakage are enhanced when both the “leakage factor” and “leakage parameter” are positive. Pure galvanic contact cannot cause enhancement in both real and imaginary components of the response. The model results with so‐called “galvanic contact” in all probability would give even qualitatively misleading results because leakage factor and leakage parameter for model experiment and field conditions are expected to be widely different.
On: “The signature of an air gun array: Computation from near‐field measurements including interactions”, by A. Ziolkowski, G. Parkes, L. Hatton, and T. Haugland (GEOPHYSICS, 47, p. 1413–1421.)
Authors: Wielandt Erhard
Published: October 2002

I wish to put forward a few arguments in favor of the after‐flow pressure term which Keller and Kolodner (1956) retain in their calculation of bubble oscillations and which Ziolkowski et al consider as “absolutely negligible.”
A comparison of gravity prediction methods on actual and simulated data
Authors: Morrison F. Foster , Douglas Bruce C.
Published: October 2002

A comparison was made between Shepard’s method (inverse‐distance weighting) and collocation (linear filtering) for the purpose of predicting gravity anomalies. Tests were made with actual data from southern California and with simulated data created from buried point masses generated by a random number generator. The autocorrelation functions of the simulated and actual gravity data behaved very much alike. In general, the sophisticated collocation method did produce better results and very good variance estimates, compared with Shepard’s method, for simulated data. The advantage was less for actual data. The cost of the better results is the use of more computer time. The most important scientific conclusion of this study is that careful trend removal must be done and an adequate data sample obtained to produce truly optimal results from collocation. The variance estimates are much more sensitive to the form and calibration of the model autocorrelation function than are the prediction results.
Born inversion with a variable background velocity
Authors: Foster Douglas J. , Carrion Philip M.
Published: October 2002

Direct, or Born, inversion has been presented as an approximate solution of the multidimensional seismic‐acoustic inverse problem (e.g., Cohen and Bleistein, 1979; Phinney and Frazer, 1978; Raz, 1981; Clayton and Stolt, 1981). The most basic assumption of the Born model is that variations, or perturbations, of some reference model remain small. This requirement of smallness is due to the fact that errors are directly related to the value of the perturbations. Both the local and overall values of the perturbation variable contribute to these errors, which are reduced if the known reference model, or background velocity, closely matches the actual medium velocity.
Optimum seismic velocity estimators
Authors: Kirlin R. L. , Dewey Lois A. , Bradley Jonathan N.
Published: October 2002

Six “optimum” estimators for the root‐mean‐square (rms) seismic velocity are given and analyzed by simulation for rms error. Two of the estimators are used to test use of a priori velocity information in a Kalman‐type improvement on the time measurements. Parameters varied include center‐point depth (time), a priori velocity variance, and interdelay‐estimate correlation. The maximum likelihood estimator is shown to be best when a priori information is relatively good, but a least‐mean‐square estimator is equally good otherwise.
Synthetic electric sounding surveys over known oil fields
Authors: Garg N. R. , Keller G. V.
Published: October 2002

The possibility of using various types of electrical methods to locate oil or gas fields has been proposed in recent years. In an effort to quantify the anomaly to be expected with electrical sounding methods, average geoelectrical parameters have been determined by studying electrical well logs from several oil fields characterized by different geoelectrical sections. The dc resistivity anomaly due to the presence of an oil‐bearing layer at depth depends upon the sequence of resistivities above and below and the electrode array employed. The radial dipole array gives the largest anomaly values, and is followed by other arrays such as the Schlumberger and Wenner arrays. The maximum anomaly in apparent resistivity is observed when the resistivity beneath the target zone is lower than that above; the relative anomaly in apparent resistivity is almost the same as the contrast ratio of the transverse resistance of the oil‐bearing layer to the overlying beds. When the radial dipole array is used, a limited areal extent of the oil‐bearing layer does not cause a significant change from the anomaly value due to a layer of infinite lateral extent. In that case the least dimension is about four times the depth. Use of one buried current electrode in the vicinity of the oil‐bearing layer increases the amplitude of the anomaly; the maximum anomaly appears at a separation comparable to the depth. Typical anomalies in apparent resistivity caused by these oil fields range from less than 0.1 percent to more than 10 percent. Such anomalies would be detectable only with an order of magnitude improvement in the capabilities of electrical sounding methods, or with considerably larger oil field targets.
Magnetic‐terrain anomalies from arroyos in an alluvial fan
Authors: Mahrer Kenneth D. , Bradley Chris , Newsom Sylvia
Published: October 2002

Gupta and Fitzpatrick (1971) remark that very little has been published on the correlation of topography and ground magnetic studies, specifically, magnetic‐terrain effects. Plouff (1976) discusses modeling of gravity and magnetic fields using polygonal prisms and the application to magnetic‐terrain anomalies. In both of these articles magnetic‐terrain anomalies from crystalline rocks are discussed. By contrast, this note discusses magnetic‐terrain anomalies identified in a ground magnetic survey within a sedimentary environment, specifically, across alluvial fans.
The hidden‐layer problem revisited
Authors: Won I. J. , Bevis Michael
Published: October 2002

Analysis of refraction seismic data falls into two classes: traditional head‐wave analysis, in which discrete “first arrivals” are mapped in terms of traveltime and distance, and modern waveform analysis, in which the time series recorded at each seismometer is considered in its entirety. Although head‐wave analysis, which makes no use of amplitude information, is clearly the more primitive and less effective approach, its application is still widespread, particularly in the field of geotechnical engineering. This note is addressed to practitioners of head‐wave analysis.
Ray equations in retarded Snell midpoint coordinates
Authors: González‐Serrano Alfonso , Yedlin Mathew J.
Published: October 2002

Group velocity (ray) equations describe the dynamic behavior of wave‐equation extrapolators in the high‐frequency limit. They are found in general from the dispersion relation of an arbitrary acoustic wave equation. Wave‐equation operators require a background extrapolation velocity. As an application of the group velocity equations, a sensitivity analysis to the background‐operator velocity illustrates the trade‐off between uncertainty in velocity and precision in imaging. Exact wave extrapolators are most useful when the exact velocity function is known. Wave‐equation imaging for velocity analysis in Snell midpoint coordinates requires velocity‐insensitive extrapolation operators. In this frame of reference, approximations of the exact acoustic wave equation are referenced to an arbitrary angle of propagation. Group velocity equations show that in Snell midpoint coordinates, using wide‐reference propagation angles, the fifteen‐degree wave equation gives satisfactory velocity‐independent images. The forty‐five degree wave equation does not appreciably improve the image.
True and apparent spectra of buried polarizable targets
Authors: Guptasarma D.
Published: October 2002

If the chargeability of a buried target is not infinitesimal, the popularly used low chargeability approximation formulated by Seigel (1959) can produce large errors in the computation of apparent polarizability spectra. A more accurate alternative approximation, based on a complex, frequency dependent “dilution factor” is presented. It turns out that for dispersions of the minimum phase shift type this approximation can be somewhat simplified and that for targets with such a dispersion, buried in a nondispersive host rock, the apparent log‐phase spectrum is only slightly different from a vertically shifted version of the true phase spectrum of the target. These results should be useful for the computation of apparent polarizabilities in numerical modeling for IP, and in attempts for mineral discrimination through field measurements of phase spectra.