bluuebunny/crossref_metadata_2025 huggingface dataset:
THE INTERFACE PROBLEM IN MODEL SEISMOLOGY
Authors: Schwab Fred , Burridge Robert
Published: October 2002

Many seismic problems involve interfaces. Seismic modeling provides a means of passing from the mathematical formulation to the solution of such problems when suitable analytical techniques are not available. Accurate interface formulations are necessary if modeling is to be as effective as possible in this role. Application of improved techniques has provided more accurate and detailed results than possible in the original work (Toksöz and Schwab, 1964) on model interface formulations. The present investigation was limited to butt‐joined, two‐dimensional models constructed with metallic sheets and epoxy bonding agents. Experimental results were first compared with those predicted by the simplest of “welded‐contact” theories—that which totally ignores the bonding layer. For a layer thickness of 0.007 cm, fair agreement was noted for frequencies below 125 kHz. New theoretical results were then predicted by taking the finite thickness and elastic properties of the bonding layer into consideration. The metal‐epoxy interfaces were assumed “welded‐contacts.” Irrespective of whether the formulation specified a perfectly elastic or an anelastic bonding material, the correlation between predicted and experimental results was quite poor. The disparity was much greater, over the entire frequency range, than that obtained from the formulation which totally ignored the bonding layer. All the welded‐contact interface formulations tested in this investigation were found unsatisfactory for highly accurate work. Based on the technique used to test the welded‐contact assumption, a mathematically accurate description of the interface was developed.
NOISE ATTENUATION ON COMMON‐DEPTH‐POINT SEISMIC RECORDS BY A SEMIDETERMINISTIC APPROACH
Authors: Robinson John C.
Published: October 2002

A simple seismic record synthesis for common‐depth‐point data was examined for analytic representation in terms of its harmonic spectrum. This frequency‐domain investigation revealed that the primary‐reflection signal can be completely recovered in the absence of random noise, or it can be better recovered in the presence of random noise than normal stacking affords, especially, if the coherent‐noise‐to‐random‐noise ratio is high. The success of this technique is founded upon the principle that difference equations in the time domain become algebraic equations in the frequency domain. The technique is partially “probabilistic” because analytic solutions for the primary‐reflection signal are stacked for further attenuation of noise. The constituents of the seismic records, after static and normal‐moveout corrections, are: identical, coincident, primary‐reflection signal; identical, time‐shifted coherent noise; and random noise. The coherent‐noise time shifts must be determined for application of the semideterministic technique; methods are discussed in the Data Processing section.
CONVECTIVE FLOW AND ITS EFFECT ON TEMPERATURE LOGGING IN SMALL‐DIAMETER WELLS
Authors: Sammel Edward A.
Published: October 2002

Critical thermal gradients for the onset of convection in small‐diameter wells are computed by means of an expression given by Krige (1939) and are shown graphically for water of several salinities and for glycerol. A series of field and laboratory tests in wells with diameters of 4.8 cm and 10.2 cm showed that water columns are unstable at temperature gradients as low as 0.003 °C/m. Magnitudes of thermal oscillations at higher gradients were as large as 0.49 °C, and apparent sizes of convection cells ranged up to 210 cm in height in a 10.2 cm cylinder and to 48 cm in wells 4.8 cm in diameter. Comparison of temperatures in adjacent wells showed temperature differences as great as 3 °C when thermal gradients were greater than the theoretical critical gradients. It is concluded that temperatures in the upper zone of deep wells may depart widely from ambient temperatures in the formations penetrated.
TIME‐VARYING DECONVOLUTION FILTERS
Authors: Clarke G. K. C.
Published: October 2002

Deconvolution or spiking filters are frequently employed to sharpen the character of seismograms and hence improve resolution of the earth’s layering. In media having significant attenuation or scattering, the shape of an input swaveform will change as it propagates. On a reflection seismogram this results in a change with time in the character and frequency content of the seismic signal. Since a statistical description of this situation would be time‐dependent, the seismogram should be treated as a nonstationary random process. A spiking filter to deconvolve such a seismogram must be time‐variable. Optimum filters for nonstationary inputs can be designed using the least‐mean‐square error criterion. For it zero‐delay filter to give satisfactory results, the signal waveform must at all times be minimum phase. This will be true if the input waveform and the law governing the change of waveshape with time are both minimum phase. If these conditions are not met, a filter which has a time delay should be used. For a linear attenuation mechanism with frequency‐independent Q, there is some justification for expecting a minimum‐phase law. In the absence of a priori knowledge of the input waveform and the attenuation structure of the layered earth, it is necessary to estimate the time‐dependent autocorrelation function of the recorded seismic trace.
USE OF MONTE CARLO TECHNIQUES IN OPTIMUM DESIGN OF THE DECONVOLUTION PROCESS
Authors: Foster M. R. , Sengbush R. L. , Watson R. J.
Published: October 2002

The deconvolution process is widely used to enhance seismic data by suppressing distortions of the shot pulse caused by such things as reverberations and ghosts. The process consists of estimating the correlation function from the data, determining the inverse filter using the Levinson algorithm, and applying the inverse filter to the data. This paper is concerned with the estimation problem. Certain conclusions about the estimation problem are suggested by the theory of power spectra developed by Tukey and others. By means of a Monte Carlo simulation of the deconvolution process, we have tested these conclusions: (1) Severely distorted data should be prewhitened. (2) Tructors (lag windows) with the same number of degree of freedom yield the same error. (3) There is an optimum number of degree of freedom for a fixed data window. (4) Due to time variance in the data, there is an optimum length of data window. Monte Carlo simulation can be used to estimate the optimum values (3) and (4) and so improve the performance sof the deconvolution process.
ESTIMATION OF SEISMIC NOISE STRUCTURE USING ARRAYS
Authors: Lacoss R. T. , Kelly E. J. , Toksöz M. N.
Published: October 2002

A theoretical study of the use of arrays for the analysis of seismic noise fields has been completed. The frequency‐wavenumber power spectral density [Formula: see text] is defined and techniques for estimating it are given. The estimates require that the auto‐ and crosspower spectral densities be estimated for all elements in the array. Subject to certain asymptotic properties of these auto‐ and crosspower spectral density estimates, expressions for both the mean and variance of the estimates of [Formula: see text] have been obtained. It has been demonstrated that if [Formula: see text] is estimated by the Frequency Domain Beamforming Method, then the estimate has the same stability as the estimates of auto‐ and crosspower spectral density. [Formula: see text] has been estimated from both long‐ and short‐period noise recorded by the Large Aperture Seismic Array in Montana. At frequencies higher than 0.3 Hz, a compressional body‐wave component which correlates with atmospheric disturbances over distant oceans has been detected. In the frequency range of 0.2 and 0.3 Hz both body waves and higher mode Rayleigh waves are observed. At frequencies below 0.15 Hz the organized vertical component of microseisms consists primarily of fundamental mode Rayleigh waves. Appreciable amounts of fundamental mode Love wave energy may also be present on horizontal instruments at these low frequencies.
A LEAST‐SQUARES METHOD OF INTERPRETING MAGNETIC ANOMALIES CAUSED BY TWO‐DIMENSIONAL STRUCTURES
Authors: Johnson William W.
Published: October 2002

The equations relating the magnetic anomalies to the shape and susceptibility of a body are nonlinear with respect to the coordinates describing the shape. Therefore, iterative procedures must be used to obtain least‐squares estimates of the body coordinates. One method in general use for obtaining nonlinear least‐squares estimates is the Gauss method. This method often fails when the initial values for the structures and susceptibilities do not adequately account for the magnetic anomalies. Another method known as the steepest descent method generally converges to a solution; however, a large number of iterations are required. A method suggested by Marquardt (1963) incorporates the best features of the previous methods. In this paper the Marquardt method is applied to the interpretation of magnetic anomalies. For this purpose the two‐dimensional formulas derived by Talwani and Heirtzler (1964) are used to relate the geometry of a body to the resulting magnetic anomalies. The procedure efficiently controls the amount of change made to an interpreted structure at each iteration, assuring rapid convergence to a solution which satisfies the observed data better in the least‐squares sense than does the initial solution. The method is applied to representative problems.
AN INVERSE METHOD OF MAGNETOTELLURIC ANALYSIS FOR A MULTILAYERED EARTH
Authors: Nabetani S. , Rankin D.
Published: October 2002

In the inverse method of analysis, the model for the resistivity structure is deduced from the data. An iterative process is developed wherein the maximum residual between the measured data and the theoretically deduced values for a successively increasing number of layers is reduced to a value less than the scatter in the data. In carrying out this procedure the parameters for each successive layer are determined and the number of layers required in the interpretation is determined by both the spectral range of the data and the scatter.
THREE‐DIMENSIONAL SEISMIC DEPTH COMPUTATION USING SPACE‐SAMPLED VELOCITY LOGS
Authors: Sattlegger J. W.
Published: October 2002

Due to the large amount of velocity information provided through adequate signal processing of multicoverage seismic data, approaches for depth computation presuming the velocity to be described by some simple analytic function may no longer be considered adequate. Three approaches to depth computation, are applied to cases of arbitrarily complicated velocity distributions. When we use these approaches, accuracy may be increased to any desired degree or to any degree which seems reasonable with respect to the velocity information available.
COLOR MIMICRY IN GEOLOGY AND GEOPHYSICS
Authors: Grossling B. F.
Published: October 2002

The polychromatic drawings of Paleolithic age in the Altamira Caverns, Santander Province, Spain, reveal man’s early interest in color, not merely to attain a faithful reproduction of what he sees, but by adding the dimensions of chroma to that of tone, to differentiate better in graphic representation.
HAMMER REFLECTION SEISMICS IN ENGINEERING GEOPHYSICS
Authors: Meidav Tsvi
Published: October 2002

A major problem in exploiting the reflection method in engineering geophysics lies in the difficulty of separating the various superimposed arrivals at short record times. Velocity filtering is used in the present study as a means of identifying the reflection arrivals by removing the undesirable waves and leaving a substantially usable reflection record, even at very short record times. Special circuitry has been developed to sense the time lag of positive zero crossings of the signal at two separate geophones, and to record only those arrivals whose phase shift is smaller than an arbitrarily set amount. This circuitry has been incorporated into a standard hammer‐type engineering seismograph. Fundamentals of analysis of an expanding reflection spread are reviewed, and field examples are shown to demonstrate the abilities and limitations of the present technique.
OPTIMUM SECOND‐DERIVATIVE AND DOWNWARD‐CONTINUATION FILTERS
Authors: Clarke Garry K. C.
Published: October 2002

Second‐derivative and downward‐continuation filtering are often employed to enhance gravity and magnetic maps. Noise due to aliasing, measurement errors, and near‐surface sources can be greatly amplified and lead to erratic filter outputs which produce spurious anomalies. To prevent this undesirable occurrence, it is often necessary to smooth the data, or equivalently, to modify the response of the applied filter. By means of the Wiener filter theory it is possible to derive optimum second‐derivative and downward‐continuation filters in either the wavenumber or space domain. Application of the theory involves separating the power spectrum into signal and noise components. A white noise assumption is realistic if the noise is due to small random near‐surface sources, random measurement errors, and random errors in corrections for terrain and elevation. As a striking demonstration of the superiority of optimum filters, the effects of optimum and “ideal” filters on a synthetic gravity map are compared.
SEISMIC ATTENUATION OF GULF COAST SEDIMENTS
Authors: Tullos Frank N. , Reid Alton C.
Published: October 2002

Previous efforts to measure the attenuation of seismic energy as it propagates vertically through the earth have been restricted to thick, isotropic, homogeneous sections of material. Values have now been obtained from normally layered Gulf Coast sediments. After normalizing with respect to the shot, the spectra of many traces over a small interval in depth can be averaged to minimize reflection interference and to yield a frequency response function associated with a given depth. Except for the measurements in the low velocity layer (LVL), a cemented array of geophones 1000 ft deep was used. The LVL measurements were made using individually cemented geophones. Data were taken on a digital recorder using a 0.5 ms sampling rate, and the processing was performed on a digital computer. Attenuation was found to vary exponentially with frequency to the first power in the range from 50 to 400 Hz. The 1000‐ft section of earth, made up largely of clay and sand layers, was separated into four sections at depths of 10, 100, and 500 ft. Attenuation in db/wavelength was found to be 13.1, 0.1508, 0.3641, and 0.2004 in the respective sections.
UNDERGROUND APPLICATIONS OF SEISMIC MEASUREMENTS IN A SASKATCHEWAN POTASH MINE
Authors: Gendzwill D. J.
Published: October 2002

The seismic refraction method is used underground in a Saskatchewan potash mine to monitor the thickness of the salt formation over the mine. Frequencies over 100 Hz characterize the seismic records. Mining machines create noise problems. Records are picked with 0.1 ms precision and a computer used to make the calculations. The statistical random error in the interpretation ranges from ±4 ft to ±15 ft for typical thicknesses of about 130 ft. Seismic techniques have aided in locating a nearly completed mine shaft with respect to existing underground workings. The geophysical work was originally intended as a verification and check against gross errors in the conventional surveying. Preliminary tests showed that the method would work with acceptable accuracy. Interpretation was made using only the relative time differences between geophones. The predicted position of the shaft center was 340±2 ft northeast and 235±10 ft northwest of a reference point. This compares with the actual position of 342.4 ft northeast and 228.5 ft northwest of the reference position determined upon completion of the shaft connection.
On: “Estimation of seismic noise structure using arrays” by R. T. Lacoss, E. J. Kelley, and M. N. Toksöz (GEOPHYSICS, vol. 34, no. 1, p. 21–38, February, 1969)
Authors: Sax Robert L. , Lintz Paul R.
Published: October 2002

Our comments (Geophysics, October, 1969, p. 793) on the paper of Lacoss et al were not concerned with possible semantic misinterpretation (see authors’ response in same issue) on our part of the authors’ usage of the term ‘phase velocity,’ but with whether or not the formulas given by the authors are correct. The authors explicitly state (p. 21) that [Formula: see text] is the “frequency‐wavenumber power spectral density,” so that [Formula: see text], and [Formula: see text] are components of wavenumber; on page 22, line 3, [Formula: see text] and [Formula: see text] are explicitly described as “phase velocity components.” Then equations (3) and (5) as given by the authors are simply incorrect: Correct equation reads: Equation (3) [Formula: see text] Equation (5) [Formula: see text] Lacoss et al have [Formula: see text].
APPLICATIONS FOR BOREHOLE GEOPHYSICS IN GEOPHYSICAL EXPLORATION
Authors: Pickett G. R.
Published: October 2002

Most geophysicists are familiar with the use of well logs for stratigraphic correlation and perhaps for estimating volumes of oil and gas in place. Over the years, additions to the array of available borehole measurement techniques have led to additional capabilities perhaps not as well known. There are several dozen borehole measurements currently available. Problems involved in extracting useful data under practical conditions with acceptable costs from these measurements pose constraints on complete utilization. Nevertheless, potential applications for such measurements include estimation of recoverable hydrocarbons from petroleum reservoirs, identification of geological environments, derivation of compressional and shear‐wave velocities and attenuations, quantitative measurements of lithology, identification of “flushed” hydrocarbon reservoirs and fluid migration paths, and identification of potential reservoirs. These and other borehole measurement capabilities have important ramifications toward making surface exploration methods more effective. It is concluded that a better marriage of borehole geophysics to surface exploration techniques should be rewarding both to the borehole specialist and to the surface explorationist.
WAVELET MAPS: A NEW ANALYSIS TOOL FOR REFLECTION SEISMOGRAMS
Authors: Morgan Nabil A.
Published: October 2002

Wavelet maps are special displays of reflection seismograms. Seismic wavelets from a reflecting horizon are gathered and displayed in each of 4 data organizations: common depth point, common shot position, common receiver position, and common offset. In each of these organizations, the wavelets are aligned relative to their estimated traveltimes, thereby removing the structural and the hyperbolic normal moveout effects. By suitable averaging and analysis of the wavelets, we may extract information from each reflector relating to (1) the behavior of amplitude and waveform as a function of common depth point, offset and shot and receiver locations, and (2) the residual traveltime, referred to hyperbolic normal moveout, as a function of offset, shot position, and receiver position. This information can be used to provide a basis for (1) amplitude control and corrections as functions of time and space, (2) surface‐consistent static corrections, (3) shot characteristics, (4) indication of thin‐bed, complex, interface, and lithological changes, and (5) nonhyperbolic moveout interpretation and correction to minimum paths for velocity determination. General results of the applications of this analysis tool to several prospects are shown to demonstrate its potential for increasing our understanding of the reflection seismic process.
GEOPHYSICAL STUDIES OF THE CRIPPLE CREEK MINING DISTRICT, COLORADO
Authors: Kleinkopf M. Dean , Peterson Donald L. , Gott Garland
Published: October 2002

Integrated geophysical, geochemical, and geological interpretations expand the knowledge about the localization of the ore deposits in the Cripple Creek district, Colorado. The principal gold deposits occur in a Tertiary volcanic subsidence basin within Precambrian granite, gneiss, and schist. The basin is filled with volcanic breccia and is intruded by dikes and irregular masses of phonolite, latite‐phonolite, syenite, trachydolerite, and basalt. The volcanic complex gives rise to a broad 10 mgal gravity minimum anomaly upon which are superimposed local minima believed to be related to deep mineralized fissure zones. A negative magnetic anomaly over the volcanic subsidence basin probably reflects the degree of alteration of rocks in the subsurface. Two local closed magnetic lows may represent highly altered volcanic centers in the bottom of the basin. The gravity and magnetic anomalies of the basin correlate geographically with positive geochemical anomalies for gold, silver, and tellurium. Just east of the volcanic basin, a prominent negative magnetic anomaly and a corresponding gravity low may represent an altered zone in the granite subsurface.
STATISTICAL AUTOMATIC STATICS ANALYSIS
Authors: Disher David Alan , Naquin Paul J.
Published: October 2002

From theoretical considerations and extensive experience, we show that proper weathering statics can be computed by use of a systematic analysis of correlation statistics. Time jitter on individual traces due to weathering variations, variations in shot depth, and trace reversals can be determined and corrected for in the presence of interference due to noise, dip, and improper normal‐moveout corrections. Four independent sets of statistics, requiring two time windows for shot‐oriented data and two time windows for receiver‐oriented data, are used to determine static corrections at the shot and at the receiver. To determine shot statics, we correlate pairs of traces from the same receivers and consecutive shots. Pairs of traces from consecutive receivers and the same shots are correlated to determine receiver statics. These two sets of correlation functions are viewed statistically to determine the two subsets of functions needed for the ensuing analysis. The functions remaining after rejection of those deviating greatly from the average values are summed in groups by receiver and by shot order. The resultant peaks yield two sets of differential statics. A cumulative total of the differential statics is computed. Subtraction of the low wavenumber part of the cumulative total, which is the dip, from the cumulative total yields residual shot and receiver weathering statics.
ELECTROMAGNETIC FIELDS ABOUT A LOOP SOURCE OF CURRENT
Authors: Ryu Jisoo , Morrison H. Frank , Ward Stanley H.
Published: October 2002

Integral expressions for the electromagnetic field components produced by a horizontal loop, carrying a current [Formula: see text] and placed on or above the surface of an n‐layered half‐space, are deduced in a form such that numerical integration can be performed easily. The expressions are free of approximations and completely general for all frequencies. They are constrained only to the uniformity of current around the transmitting loop. The resulting computed electromagnetic fields are valid for arbitrary values of the electrical parameters σ, μ, and ε. The quasi‐static approximation for the region above the half‐space, wherein the wave equation is replaced by the Laplace equation, can be avoided. Measurements outside the loop constitute induction depth sounding. Induction depth sounding curves of field components and magnetic polarization parameters show good resolution of subsurface layering. In particular, it is suggested that the measurements of tilt angle and/or ellipticity of the magnetic polarization ellipse should be made to determine earth layering because of the rapidity and ease of these measurements in field operation. It is shown that the radius of the loop should, in the general case, be taken into account in theoretical computations. Measurements at the center of the loop constitute central induction sounding. Central induction sounding responses are diagnostic only for layered earth models in which conductivity increases with depth. Measurement of the quadrature part of the vertical magnetic field is particularly promising. Theoretical curves for earth models consisting of one layer overlying a half‐space are given for the quasi‐static case for induction depth sounding, and for the nonquasi‐static (general) case for central induction sounding. In another application, the response from a homogeneous, conductive, magnetic half‐space with the central induction method at low frequencies reveals the feasibility of in‐situ determination of static magnetic permeability. In a final application, it is shown that the effect of ground conductivity should be included in making the normal correction to Turam data whenever the apparent conductivity of the ground is greater than [Formula: see text].
OPTIMIZATION AND IMPLEMENTATION OF MARINE SEISMIC ARRAYS
Authors: Schoenberger Michael
Published: October 2002

The objective in array design is the rejection of bands of wavelengths which contain noise. In marine exploration, where the coupling between receiver element and water does not vary significantly along the array, element gains can be chosen to maximize this rejection. For a fixed number of elements and no limitations on array length, a Chebyshev array results. The solution to the more relevant problem of a fixed length array with a variable number of elements is presented here. Upon implementation, element gains cannot be realized exactly, but only to within a specified tolerance. Corresponding to this specified tolerance, an array design procedure presented in this paper provides the best possible array. Naturally, the smaller the tolerance, the better the array. Examples of various array designs are compared for gain tolerances of one percent and five percent; the effect of inexact placement of the array elements is also considered.
ELECTROMAGNETIC DEPTH SOUNDING APPLIED TO MINING PROBLEMS
Authors: Duckworth K.
Published: October 2002

A simplified approach to electromagnetic depth sounding in the variable coil separation mode is described. The method was developed by scale model studies and consideration of the geometry of the dipole magnetic field. Its use is limited to nonmagnetic, highly conductive plane structures or nonmagnetic thin sheets of moderate to high conductivity. Field tests indicate the method to be capable of providing good depth estimates over quite steeply dipping structures. The effect of conductivity anisotropy proved to be readily recognizable in the field tests.
ELECTROMAGNETIC SCATTERING FROM CYLINDERS OF ARBITRARY CROSS‐SECTION IN A CONDUCTIVE HALF‐SPACE
Authors: Parry J. R. , Ward S. H.
Published: October 2002

A general numerical technique is presented for solving the problem of electromagnetic scattering by conducting cylinders of arbitrary cross‐section located in a conductive half‐space. Solutions to the electromagnetic wave equation are required for the free space above the half‐space, for the half‐space surrounding the cylinder, and for the cylinder. The problem is formulated by choosing an integral representation for the electromagnetic fields in each of the three homogeneous regions. By enforcing the boundary conditions on tangential E and H, we obtain a set of coupled integral equations which can be solved numerically for the unknown equivalent surface current densities on the interface bounding each homogeneous region. Once these current densities have been estimated, the fields can be calculated at any point from the general integral representations. The following conclusions are among those of importance to AFMAG and VLF surveys: 1) the ratio of Re (H) to Im (H) is a function of traverse position and of ground conductivity, as well as of cylinder conductivity and of survey frequency; 2) in no case was a zero phase observed, even for perfectly conducting cylinders; and 3) reverse crossovers in Im (H) can occur in the field scattered by a single conductor whenever the radius of curvature on the upper portion of a “poor” conductor is small.
SEISMIC STRATIGRAPHIC EXPLORATION—PART I
Authors: Marr John D.
Published: October 2002

The basic problem to be solved in stratigraphic exploration always has been the same—how to develop and use practical techniques which have the capability of finding large stratigraphic oil reserves at a profit. If the petroleum industry in the United States is going to discover in domestic areas the huge reserves which are obviously required for the future, seismic stratigraphic exploration will have to be accepted by the industry and play a major role in the discovery. Seismic stratigraphic exploration must, therefore, be described in such a way that management can visualize it as practical and potentially profitable with proven past accomplishments, with important new capability not yet in application, and with significant future potential. Past seismic stratigraphic exploration capabilities, which found large amounts of oil with crude tools from 1938 to 1962, are illustrated with three case histories covering the probable direct detection of a hydrocarbon‐saturated sand, the discovery of saturated lenticular sands over the area of a tilted out ancestral structure, and the delineation of a flank type stratigraphic trap. Three additional case histories will be presented in Part II in the next issue of Geophysics.
CRUSTAL ELECTRICAL CONDUCTIVITY ANOMALIES IN THE GREAT PLAINS PROVINCE OF THE UNITED STATES
Authors: Porath H. , Dziewonski A.
Published: October 2002

Magnetic disturbance fields were recorded during the spring and fall of 1969 with two magnetometer arrays in the Great Plains province of the United States. The purpose of these studies was to map magnetic variation anomalies arising from inhomogeneities of crustal electrical conductivity; we wished to find regions where plane layered models yield apparent resistivity curves that are adequate approximations to curves determined from magnetotelluric measurements. Variation anomalies were found to be related to lateral changes in electrical conductivity of the upper crust, changes associated with sedimentary features. In southeast Oklahoma, induced currents are concentrated in the conductivity sediments of the deep Anadarko basin. These currents give rise to attenuated vertical variation fields to the west and south of the basin and to enhanced vertical fields to the north and northeast. Reversed vertical fields are observed for stations in north central Texas, close to the Ouachita tectonic belt which separates Paleozoic sediments in West Texas from younger sediments in the Gulf Coast plains. This distribution of fields indicates concentration of induced currents in the highly conductive coastal plains sediments. A small variation anomaly is associated with the region of the midcontinent gravity high in the northern Great Plains. The anomaly is probably caused by currents in the sedimentary troughs on the steep flanks of the Precambrian basalts, which give rise to the gravity anomaly.
On: “Hammer Reflection Seismics in Engineering Geophysics,” by Tsvi Meidav (GEOPHYSICS, June 1969, p. 383–395)
Authors: Kristjansson Leo , Wright J. A.
Published: October 2002

We wish to point out errors noticed by us in a recent paper by Meidav (1969) for seismic reflection from dipping interfaces. A correct graphical solution for the perpendicular depth to the interface and dip follows from the equations given in Heiland (1946, p. 562).
TOWARD A UNIFIED THEORY OF REFLECTOR MAPPING
Authors: Claerbout Jon F.
Published: October 2002

Schemes for seismic mapping of reflectors in the presence of an arbitrary velocity model, dipping and curved reflectors, diffractions, ghosts, surface elevation variations, and multiple reflections are reviewed and reduced to a single formula involving up and downgoing waves. The mapping formula may be implemented without undue complexity by means of difference approximations to the relativistic Schroedinger equation.
MULTIPLE‐CONSTRAINT ADAPTIVE FILTERING
Authors: Booker Aaron , Ong Chung‐Yen
Published: October 2002

An algorithm is derived for multichannel time‐series data processing, which maintains specified initial multiple filter constraints for known signal or noise sources while simultaneously adapting the filter to minimize the effect of the unknown noise field. Problems of implementing the technique such as convergence, determination of a starting filter, and comparison of results with conventional filters are discussed and illustrated with data from a vertical seismic array. The procedure is shown to be stable and obtains approximately 3–4 db gain in S/N improvement over conventional Wiener filtering in the band 1 to 3 hz.
APPLICATION OF RATIONAL APPROXIMATION IN CALCULATION OF THE SECOND DERIVATIVE OF THE GRAVITY FIELD
Authors: Agarwal B. N. P. , Lal Tarkeshwar
Published: October 2002

A rational approximation method has been introduced to increase the convergence of the Taylor series, which is the fundamental basis for calculation of the second derivative of the gravity field or any field satisfying Laplace’s equation. Six weight coefficient sets, three each using rational and Taylor series approximations for the same number of rings, have been developed. The frequency responses of the proposed weight coefficient sets establish the superiority of rational approximation over Taylor series approximation. The amplitude responses of all derived coefficient sets, along with those of some of the existing coefficient sets, are also presented.
RADIUS OF INVESTIGATION IN DC RESISTIVITY WELL LOGGING
Authors: Roy A. , Dhar R. L.
Published: October 2002

The contribution to the measured signal of any desired portion of the ground (as distinct from that of the rest of the ground) in a direct current (dc) well logging system can be computed by using the equivalence between dc and electrostatic fields. Considering a thin cylindrical shell having its axis coincident with that of the sonde, we find that the contribution of the shell usually begins with a small value for small values of shell radii and goes through a few extrema before falling to zero at large radii. In this paper, the radius of investigation of a sonde is defined to be that radius at which the contribution of the cylindrical shell is a maximum and has the same sign as the total measured signal. With this definition, the radii of investigation of the various sondes come out approximately as follows: Wenner 0.19L Schlumberger 0.20L Normal 0.60L Lateral 0.40L Laterolog [Formula: see text] 0.30L [Formula: see text] 0.26L [Formula: see text] 0.16L [Formula: see text] 0.15L, where L is the distance between the extreme active electrodes. Note that, spacing for spacing, the radius of investigation for the unfocused normal sonde seems to be much larger than that for the focused laterolog device.
ELASTIC WAVE SOLUTIONS IN STRATIFIED MEDIA
Authors: Richards Paul G.
Published: October 2002

Classical Thomson‐Haskell methods are proven applicable to the asymptotic wave solution in a stratified elastic medium which has both first and second order discontinuities in ρ, λ, and μ. This proof removes a weakness of the original method, which made it unsatisfactory for modeling velocity gradient anomalies. The generalized method, simple in application for a stack of inhomogeneous layers, is used here to derive P-SV reflection/conversion/transmission properties for a transition region in which ρ, [Formula: see text], and [Formula: see text] vary linearly. Although the solution method is approximate, its accuracy is confirmed by comparison with exact solutions.
HIGH RESOLUTION BATHYMETRY, AN AID TO GEOPHYSICAL PROSPECTING
Authors: Van Der Linden Willem J. M.
Published: October 2002

A hydrographic survey carried out for navigational purposes has been used for the construction of a detailed bathymetric chart. The chart resolves morphological features with an elevation of only a few meters. As in the case shown, such morphological features may accurately define subsurface structural anomalies.
CRUSTAL SECTION FROM SEISMIC REFRACTION MEASUREMENTS NEAR VICTORIA, TEXAS
Authors: Dorman J. , Worzel J. Lamar , Leyden R. , Crook T. N. , Hatziemmanuel M.
Published: October 2002

Microearthquake equipment was used in the Texas Gulf Coast area to measure noise levels, monitor natural earthquakes, and to make seismic refraction measurements. There is a small correlation of the noise level with the distance from the Gulf of Mexico. Three horizons within the sedimentary section were successfully observed by seismic refraction measurements to the northeast along the strike. Beneath these is a 5.22 km/sec layer at a depth of 10 km, overlying a 6.45 km/sec layer at 16 km, which in turn overlies the mantle at 8.41 km/sec at a depth of 30 km. The observed velocities and depths correlated well with those of Cram (1961) about 40 km farther inshore. Refraction reception to the northwest was much poorer, with signal amplitudes about 15 times smaller than those to the northeast. A composite crustal structure southeast from the Llano Uplift, across the Gulf of Mexico is presented and discussed. More work is required to delineate the structure between our new profile and the Sigsbee Scarp, and the deeper structure towards the Llano Uplift.
A PHYSICALLY OPERATIONAL FORMULATION OF CAGNIARD’S PROGRESSIVE WAVE THEORY
Authors: Dix C. Hewitt
Published: October 2002

The mathematical details of the theory of progressive seismic waves as presented in Cagniard’s book (1962) are assumed to be reasonably well understood. A simplification can be achieved by a minor change of viewpoint. This alternative view is illustrated by a reconsideration of Cagniard’s 8th chapter, “The Static Problem.” The mathematical tools apply as well to the other chapters but are not of vital interest for exploration problems, so the problem of further development is left to able readers.
On: “Geophysical Analysis in Central Indiana using Potential Field Continuation,” by A. J. Rudman, Judson Mead, Joseph F. Whaley, and Robert F. Blakely (GEOPHYSICS, October 1971, p. 878–890)
Authors: Guion Douglas J.
Published: October 2002

I read with interest the article concerning modeling the Hamilton County, Indiana, gravity and magnetic anomaly. The authors’ method for outlining the igneous body by downward continuation aroused my curiosity to the point that I decided to study the results in detail. My investigation revealed that the calculated gravity effect of the model did not satisfy the observed gravity anomaly. In fact, the amount of mismatch is quite serious.
ESTIMATION OF A TIME‐VARYING SEISMIC AUTOCORRELATION FUNCTION
Authors: Thompson David D. , Cooper George R.
Published: October 2002

The autocorrelation function of a seismic trace provides information about the generating wavelet needed for optimal processing. The classical time‐averaging technique used to estimate the autocorrelation, however, fails for the commonly encountered time‐varying autocorrelation resulting from progressive wavelet distortion. To estimate a time‐varying autocorrelation, an iterative computational procedure is proposed from which a sequence of progressively improved estimates of the autocorrelation is obtained. In the time‐invariant case, the algorithm reduces to the usual time‐average procedure applied to several different “windows” along the trace, and convergence occurs on the first step. For a “slowly” varying autocorrelation, however, the procedure tends to iteratively correct the bias error resulting from time averaging. It is proven that if the time variation for each “lag” value can be modeled by a polynomial of degree N, the sequence of estimates converges (in expected value) to the solution in no more than the integer part of [Formula: see text] steps. Examples are included to illustrate the procedure.
VECTOR MAGNETIC ANOMALIES DERIVED FROM MEASUREMENTS OF A SINGLE COMPONENT OF THE FIELD
Authors: Lourenco José Seixas , Morrison H. Frank
Published: October 2002

Three‐component magnetic data are derivable from measurements of one single component of the magnetic field over a plane. The technique involves computation of the double‐Fourier‐series coefficients of the measured magnetic anomaly, multiplication of the coefficients by a filter operator, and, finally, evaluation of the magnetic components by taking the inverse Fourier transform. The desired filter operator is obtained from a simple relationship between the components of a potential field. The scheme has been tested with excellent results on the fields of a vertical prismatic model.
INDUCED CURRENT DISTRIBUTION IN A CONDUCTIVE TWO‐LAYER SPHERICAL BODY
Authors: Gupta Chandra P. , Raval Upendra , Negi Janardan G.
Published: October 2002

Under complex geologic situations the analysis of induced current distribution, rather than of the scattered field, may provide a useful physical insight into the electromagnetic response characteristics of a conducting ore body. Influence of a conducting cover and inhomogeneity in the conductivity on the currents induced in aspherical conductor excited by a uniform alternating magnetic field has, therefore, been investigated. The analysis shows (a) reduction of the current‐density amplitudes in the core by the cover, (b) occurrence of current‐density maxima inside the conducting system for some characteristic frequencies, (c) enhancement of the in‐phase component in some cases, and (d) reduction of current‐density in the shell with increase in the core conductivity and significant influence of the inhomogeneity in conductivity at low frequencies. Since there is a direct correspondence between the electromagnetic response of a target and the currents induced in it, these results are expected to aid in the interpretation of data over ore deposits having a halo‐zone of disseminated mineralization.
TELLURIC ANOMALIES ASSOCIATED WITH ISOLATED REEFS IN THE MIDLAND BASIN, TEXAS
Authors: Yungul S. H. , Hembree M. R. , Greenhouse J. P.
Published: October 2002

It appears that strong but irregular positive telluric anomalies are geographically associated with three major, isolated, known, and deeply buried reefs. These are the Millican, Jameson, and IAB Reefs, covered by a telluric survey in the Midland Basin Texas. Dipole resistivity sounding and E‐log analyses give information about the resistivity distribution in the post‐reef sediments. The Millican Reef telluric anomaly was interpreted quantitatively by two‐dimensional modeling. This anomaly apparently is almost totally due to lateral variations in resistivity within most of the “layer‐cake” type post‐reef sediments. This is possibly related to the unusual sedimentational and geochemical processes brought about by the presence of the reef.
ON THE MINIMUM‐LENGTH PROPERTY OF ONE‐SIDED SIGNALS
Authors: Berkhout A. J.
Published: October 2002

Apart from a visual inspection, the length property of a signal is mostly judged by its amplitude spectrum (e.g., bandwidth or “roughness” of the spectrum). However, due to the important influence of the phase spectrum. a sensible yardstick for signal length should consider both amplitude and phase. In addition, a complete investigation should also include evaluation of the length of the (partly) deconvolved signal. In this paper, signal duration and signal length are introduced as two different concepts. Unlike signal duration, giving the minimum time interval outside of which the signal equals zero, signal length gives some information as to how the signal energy is distributed within this interval. An objective yardstick for signal length is proposed, and it is shown how signal length depends on both the amplitude and phase spectrum. The minimum‐length signal is introduced and it is shown that for one‐sided signals the minimum signal‐length property implies the minimum‐phase property and vice‐versa. The efficiency of causal least‐square inverse filtering on minimum‐length and nonminimum‐length signals is evaluated. An investigation scheme is given which enables the user to determine whether a one‐sided signal has the minimum‐length (minimum‐phase) property. The theory is applicable to complex signals. For real signals the * (symbol for complex conjugate) and absolute value marks may be omitted: [Formula: see text] and [Formula: see text].
A METHOD FOR THE DIRECT INTERPRETATION OF ELECTRICAL SOUNDINGS MADE OVER A FAULT OR DIKE
Authors: Lee Terry , Green Ronald
Published: October 2002

The potential function for a point electrode in the vicinity of a vertical fault or dike may be expressed as an infinite integral involving Bessel functions. Beginning with such an expression, two methods are presented for the direct analysis of resistivity data measured both normal and parallel to dikes or faults. The first method is based on the asymptotic expansion of the Hankel transform of the field data and is suitable for surveys done parallel to the strike of the dike or fault. The second method is based on a successive approximation technique which starts from an initial approximate solution and iterates until a solution with prescribed accuracy is found. Both methods are suitable for programming on a digital computer and some illustrative numerical results are presented. These examples show the limitations of the methods. In addition, the application of resistivity data to the interpretation of induced‐polarization data is pointed out.
ROBUST MODELING WITH ERRATIC DATA
Authors: Claerbout Jon F. , Muir Francis
Published: October 2002

An attractive alternative to least‐squares data modeling techniques is the use of absolute value error criteria. Unlike the least‐squares techniques the inclusion of some infinite blunders along with the data will hardly affect the solution to an otherwise well‐posed problem. An example of this great stability is seen when an average is, determined by using the median rather than the arithmetic mean. Algorithms for absolute error minimization are often approximately as costly as least‐squares algorithms; however, unlike least‐squares, they naturally lend themselves to inequality or bounding constraints on models.
MODEL RESULTS AND FIELD CHECKS FOR A TIME‐DOMAIN, AIRBORNE EM SYSTEM
Authors: Nelson Philip H.
Published: October 2002

The airborne EM system known as Input was calibrated by applying theoretical homogeneous earth response curves to the response obtained on a flight over a large lake of known resistivity. The calibrated response curves for the conductive overburden case agree with field results in that 1) overburden resistivity in excess of 100 ohm‐m produces negligible deflection on the receiver channels, and 2) the maximum channel response occurs between 1 and 10 ohm‐m overburden resistivity. The calibrated response curves for scale model vertical sheets show fair to good agreement with the response to steeply dipping conductors which have been confirmed with ground‐based EM and drilling. The calibrated scale model results also show: 1) The system possesses a “passband” in conductivity‐thickness, with the first channel peaking around 10 mhos and the later channels at progressively higher values, with the sixth channel peaking at 25 mhos. 2) If a conservative detection cutoff is applied, a vertical conductor will not produce a four‐channel anomaly if it is much deeper than 200 ft subsurface for an aircraft elevation of 400 ft. 3) Channel ratios are constant with depth and also fairly constant over the 10–100 mhos range in conductivity‐thickness.
POLLUTION—ENVIRONMENTAL VERSUS MORAL
Authors: Brant Arthur A.
Published: October 2002

Demonstration: (1) Take 1 gm of sulfur and burn it on a metal gauze screen in the lecture room. At Anaheim that was [Formula: see text] or [Formula: see text] m. This will give you 2 gm of [Formula: see text] m or 300 μgm/cu m, i.e., four times the allowable average federal permissible level of 80 μgm/cu m, and six times the allowable average Arizona level. The 300 μgm of [Formula: see text] m is about 1/4 ppm by weight of air. The allowable federal level is 1/15 ppm. Level of smell is about 20 ppm [Formula: see text]. You cannot smell the sulfur burning 20 ft away. (2) Take a 200‐cc glass beaker of water, about that held by a smallish coffee cup, and add 1/2 gm of 5 percent standard commercial DDT wettable powder. This gives 125 ppm of DDT in the glass. This is some 10,000 times the average DDT concentration in river muds and about 25 times that in fish from Lake Erie. It is a little more than the 100 ppm in Herring gulls from Lake Erie, the highest concentration in living species.