bluuebunny/crossref_metadata_2025 huggingface dataset:
VELOCITY AND ATTENUATION OF SEISMIC WAVES IN TWO‐PHASE MEDIA: PART I. THEORETICAL FORMULATIONS
Authors: Kuster Guy T. , Toksöz M. Nafi
Published: October 2002

The propagation of seismic waves in two‐phase media is treated theoretically to determine the elastic moduli of the composite medium given the properties, concentrations, and shapes of the inclusions and the matrix material. For long wavelengths the problem is formulated in terms of scattering phenomena in an approach similar to that of Ament (1959). The displacement fields, expanded in series, for waves scattered by an “effective” composite medium and individual inclusions are equated. The coefficients of the series expansions of the displacement fields provide a relationship between the elastic moduli of the effective medium and those of the matrix and inclusions. The expressions are derived for both solid and liquid inclusions in a solid matrix as well as for solid suspensions in a fluid matrix. Both spherical and oblate spheroidal inclusions are considered. Some numerical calculations are carried out to demonstrate the effects of fluid inclusions of various shapes on the seismic velocities in rocks. It is found that the concentration, shapes, and properties of the inclusions are important parameters. A concentration of a fraction of one percent of thin (small aspect ratio) inclusions could affect the compressional and shear velocities by more than ten percent. For both sedimentary and igneous rock models, the calculations for “dry” (i.e.,air‐saturated) and water‐saturated states indicate that the compressional velocities change significantly while the shear velocities change much less upon saturation with water.
GAMMA‐RAY WELL‐LOGGING
Authors: Howell Lynn G. , Frosch Alex
Published: October 2002

Point‐to‐point measurements of radioactivity in bore holes were made with an ionization chamber. The correlation between the curves obtained and the electrical logs for the same holes led to the construction of a more rugged apparatus containing two Geiger counters, coupled separately to two amplifiers and two frequency meters on the surface of the ground. This instrument can be run continuously and logs taken in both cased and open holes. Correlation was obtained between two cased hole records taken several miles apart in West Texas. Remarkable correlation in many instances between radioactivity and electrical logs has been found in the Gulf Coast. The method seems to open up a broad field in cased hole well‐logging.
ON GEOCHEMICAL PROSPECTING—I
Authors: Horvitz Leo
Published: October 2002

The first type of geochemical prospecting, that of searching for and recognizing visible oil and gas seeps, is one of the oldest methods of prospecting for petroleum deposits. A second type of geochemical prospecting, that of soil gas analysis, has been of record in the literature for some ten years, and depends upon the microanalysis, for hydrocarbons, of “underground” or interstitial soft air. A third type of geochemical prospecting is described, that of soil analysis, which has been recently developed and depends upon the separation, identification and quantitative determination of significant constituents which are entrained, occluded and adsorbed by the soil particles. These significant constituents exhibit a wide range of molecular weights, from hydrogen through gaseous, liquid and solid hydrocarbons and their derivatives. All these constituents tend to show the same significant patterns, which in general fall into two classes, the narrow elongated pattern characteristic of faulting, and the localized “halo” pattern which tends to follow and define the edges of the underlying production. This “halo” pattern has been found over both structural and stratigraphic traps.
RECENT DEVELOPMENTS IN ELTRAN PROSPECTING
Authors: Klipsch Paul W.
Published: October 2002

Early difficulties encountered relative to measuring the wave form of the detected potential by means of a predistorted opposing wave have been eliminated by introducing several novelties. These comprise a new mixing circuit, novel means for synchronizing the opposing wave with the detected wave, and simplified predistorting networks. A calibration scheme is outlined to maintain the detection apparatus at a constant level of performance. A simplified method of measuring the detected wave form obviating the synthetic opposing wave, useful in certain areas, is shown. Essentially it comprises subjecting the detected wave to the further distorting action of a simple circuit, the adjustment of which produces a standard wave shape consisting of straight lines in the oscilloscope. The adjustment of this circuit necessary to bring the wave shape to this standard value constitutes the measure of the time constant of the detected wave.
ON THE DEPENDENCE OF THE ELASTIC PROPERTIES OF A POROUS ROCK ON THE COMPRESSIBILITY OF THE PORE FLUID
Authors: Brown Robert J. S. , Korringa Jan
Published: October 2002

An equation is derived for the dependence of the elastic properties of a porous material on the compressibility of the pore fluid. More generally, the elastic properties of a container of arbitrary shape are related to the compressibility of the fluid filling a cavity in the container. If the pore system or cavity under consideration is filled with a fluid of compressibility [Formula: see text], the compressibility κ* of the closed container is given by [Formula: see text] Here [Formula: see text] is the compressibility of the container with the fluid pressure held constant in the interconnected pore system or cavity. Fluids in other pores or cavities not connected with the one in question contribute to the value of [Formula: see text]. ϕ is the porosity, i.e., the volume fraction corresponding to the pore system or cavity in question. The equation contains two distinct effective compressibilities, [Formula: see text] and [Formula: see text], of the material exclusive of the pore fluid. When this material is homogeneous, one has [Formula: see text], and the equation reduces to a well‐known relation by Gassmann. For the other elastic properties, we also obtain expressions which generalize Gassmann’s work and which also differ from it only in the appearance of [Formula: see text] instead of [Formula: see text] in one term. Our result is intimately related to the reciprocity theorem of elasticity. Special cases are discussed.
DESTRUCTION OF POROSITY THROUGH PRESSURE SOLUTION
Authors: Sprunt Eve S. , Nur Amos
Published: October 2002

A stressed fluid‐filled porous system was modeled by hollow cylinders of St. Peter sandstone subjected to various combinations of pore and confining pressure at 270° to 280°C for up to four weeks. Large reductions in porosity, up to more than 50 percent, were produced purely by pressure solution without grain crushing. Most of the porosity reduction occurred early in the experiments and in samples with the finer of two grain sizes. Experiments with the same pore pressure, but different confining pressures, and experiments with the same effective stress, but different stress magnitudes showed that a simple effective stress law does not hold for pressure solution, and that the amount of porosity reduction depends on pore fluid pressure. However, nonhydrostatic stress appears to be necessary for rapid porosity reduction because experiments with hydrostatic pressure produced very little change in porosity. Also, experiments with the same confining pressure but different pore pressures showed that the amount of porosity loss is dependent on both pore pressure and effective stress. Pore pressure appears to place an upper limit on the rate of porosity reduction, while nonhydrostatic stress appears to be necessary for rapid porosity reduction. A dry control experiment showed that fluid must be present for porosity reduction at the temperatures and pressures in our study. The porosities of many of the samples in this study were determined both gravimetrically and by point counts on cathodoluminescent micrographs. Cathodoluminescence is useful in studying pressure solution because the intergranular relationships and pore spaces are very distinct. However, in examining natural samples caution is required when relying solely on the luminescence to determine pressure solution, because luminescent characteristics change with time.
AN ATTEMPT TO DEFINE THE CURIE POINT ISOTHERM IN NORTHERN AND CENTRAL ARIZONA
Authors: Byerly P. E. , Stolt R. H.
Published: October 2002

Magnetic total intensity anomalies in northern and central Arizona have been analyzed to locate the bases of the polarized source bodies. The base of the magnetic crust is interpreted as the position of the Curie point isotherm. Results indicate a zone of shallow Curie depth (∼10 km) in a belt, about 60 km wide, running through the center of the state. This zone, near the northern border of the Basin‐Range province, is flanked on the north and south by areas of greater Curie depth (∼20 km). The results are in agreement with regional variations in [Formula: see text] velocity in Arizona.
APPARENT ATTENUATION DUE TO INTRABED MULTIPLES, II
Authors: Schoenberger M. , Levin F. K.
Published: October 2002

In a paper with the same title published in Geophysics (June 1974), we showed that synthetic seismograms from two wells gave a frequency‐dependent attenuation due to intrabed multiples of about 0.06 dB/wavelength. This loss was 1/3 to 1/2 of the total attenuation found for field data on lines near the wells. Our data sufficed to confirm the conclusion of O’Doherty and Anstey that attenuation caused by intrabed multiples may be appreciable, but the number of wells was insufficient to establish the magnitude of that attenuation in general. To get a better feel for intrabed multiple‐generated attenuation, we have computed losses for 31 additional wells from basins all over the world. Sonic and, where available, density logs were digitized every foot and converted into synthetic seismograms with 50 orders of intrabed multiples. Using the technique of the 1974 paper of extending the logs and placing an isolated reflector 2000 ft below the bottom of the wells, we computed attenuation constants for plane seismic waves that had traveled down and back through the subsurfaces defined by the logs. Computed constants varied from 0.01 dB/wavelength to 0.22 dB/wavelength. Total traveltimes ranged from 0.7 to 2.7 sec; the average was 1.9 sec. Attenuation constants computed from surface seismic data near four of the 31 wells gave values 1.3 to 7 times the corresponding intrabed constants. Thus, attenuation due to intrabed multiples accounts for an appreciable fraction of the observed attenuation but by no means all of it.
Quasi‐static transient response of a conducting half‐space— An approximate representation
Authors: Nabighian Misac N.
Published: October 2002

For a step‐function excitation, it is shown that, to a first‐order approximation, the quasi‐static transient response in the air due to an arbitrary loop situated at the earth’s surface can be represented by a downward and outward moving current filament, of diminishing amplitude and having the same shape as the transmitter loop.
Seismological investigations at The Geysers geothermal field
Authors: Majer E. L. , McEvilly T. V.
Published: October 2002

Two short (4 and 6 day) recording periods at The Geysers geothermal field provided useful data on two large refraction explosions and numerous microearthquakes. The vapor‐dominated reservoir appears to be characterized by regionally anomalous high P‐ and S‐wave velocities and low attenuation, but the anomaly seems to decrease, possibly reversing, with depth. Microearthquakes occur in a diffuse pattern, with no indication of dominant throughgoing faults and an absence of activity in the main production zone. Mechanisms are generally consistent with northeast‐southwest compression. Occurrence rates indicate a slightly high incidence of smaller magnitude shocks. It is possible that the microearthquake activity is related to an expanding steam zone. While the present anomalies appear to delineate the reservoir, it is not certain that they would have been detectable during exploration prior to large‐scale exploitation of the field.
Long‐wave elastic anisotropy in transversely isotropic media
Authors: Berryman James G.
Published: October 2002

Compressional waves in horizontally layered media exhibit very weak long‐wave anisotropy for short offset seismic data within the physically relevant range of parameters. Shear waves have much stronger anisotropic behavior. Our results generalize the analogous results of Krey and Helbig (1956) in several respects: (1) The inequality [Formula: see text] derived by Postma (1955) for periodic isotropic, two‐layered media is shown to be valid for any homogeneous, transversely isotropic medium; (2) a general perturbation scheme for analyzing the angular dependence of the phase velocity is formulated and readily yields Krey and Helbig’s results in limiting cases; and (3) the effects of relaxing the assumption of constant Poisson’s ratio σ are considered. The phase and group velocities for all three modes of elastic wave propagation are illustrated for typical layered media with (1) one‐quarter limestone and three‐quarters sandstone, (2) half‐limestone and half‐sandstone, and (3) three‐quarters limestone and one‐quarter sandstone. It is concluded that anisotropic effects are greatest in areas where the layering is quite thin (10–50 ft), so that the wavelengths of the seismic signal are greater than the layer thickness and the layers are of alternately high‐ and low‐velocity materials.
Estimating crack parameters from observations of P‐wave velocity anisotropy
Authors: Crampin Stuart , McGonigle Robert , Bamford David
Published: October 2002

Cracks are a very common feature of crustal rocks, and their behavior and properties under various conditions are of growing importance to a variety of applications, including investigations of oil and water resources in cracked reservoirs, extraction of geothermal heat, and earthquake prediction by the seismic effects of dilatancy. This paper discusses mapping cracks by measurements of velocity‐anisotropy in underground refractors. The technique is demonstrated by interpreting the velocity measurements of Bamford and Nunn (1979) in shallow fractured limestone. The estimated crack distributions are found to be consistent with rose‐diagrams at neighboring outcrops, and the degree of saturation of the cracks has a major effect on velocity variations. Elastic constants can be derived for an equivalent purely elastic solid which has the same velocity variations as the cracked solid. This allows synthetic seismograms to be calculated for propagation through cracked structures, which demonstrates that use of polarization anomalies in three‐component recordings is a sensitive technique for investigating cracked solids.
Problems and interpretation of COCORP deep seismic reflection data, Wind River range, Wyoming
Authors: Zawislak Ronald L. , Smithson Scott B.
Published: October 2002

Before the Consortium for Continental Reflection Profiling (COCORP) deep crustal reflection profile across the Wind River range, Wyoming, can be understood, problems involving velocity, multiple reflections, and structural style associated with thrusting must be resolved. Measurements from boreholes to maximum depths of 7.8 km show that a strong velocity inversion is associated with overpressured zones, primarily in Cretaceous shales. One‐dimensional (1-D) synthetic seismograms generated using the detailed velocity distribution closely duplicate the seismic trace on line 1 and produce multiple reflections of significant amplitude to record times of l0 sec. Other data including auto‐correlograms demonstrate presence of abundant multiple reflection energy to times of 10 to 12 sec on lines 1 and 2 and suggest that most of the deep events on these lines are multiple reflections. Because this area has not been known as a problem area for multiples in shallow (industry) reflection surveys, we conclude that multiples are a greater impediment for deep crustal reflection studies than has previously been recognized and that the sedimentary section must be treated much like the weathered zone in shallow seismic studies. Two‐dimensional (2-D) modeling and hand migration are used to determine structure in sedimentary rocks beneath the thrust Precambrian wedge. They suggest that structural as well as velocity uplift is found under the thrust, that a wedge of overturned sedimentary rocks parallels the thrust, and that the deeper sedimentary rocks bend down into the thrust.
Depth migration of imaged time sections
Authors: Larner Kenneth L. , Hatton Leslie , Gibson Bruce S. , Hsu I‐Chi
Published: October 2002

None of the leading approaches to the migration of seismic sections—the Kirchhoff‐summation method, the finite‐difference method, or the frequency‐domain method—readily migrates seismic reflections to their proper positions when overburden velocities vary laterally. For inhomogeneous media, the diffraction curve for a localized, buried scatterer is no longer hyperbolic and its apex is displaced laterally from the position directly above the scatterer. Hubral observed that the Kirchhoff‐summation method images seismic data at emergent “image ray” locations rather than at the desired positions vertically above scatterers. In addition, distortions in diffraction shapes lead to incorrect imaging (i.e., incomplete diffraction collapse) and, hence, to further displacement errors for dipping reflections. The finite‐difference method has been believed to continue waves downward correctly through inhomogeneous media. In conventional implementations, however, both the finite‐difference method and frequency‐domain approach commit the same error that the Kirchhoff method does. Synthetic examples demonstrate how conventional migration fails to image events completely. Hubral’s solution to this migration problem is two‐ (or three‐) dimensional mapping of imaged time sections into depth. This mapping, “depth migration,” replaces simple vertical conversion from time to depth. Such depth migration can be postponed until after efficient image‐ray modeling has been performed to (1) support the final choice of velocity model, and (2) determine whether depth migration is necessary. Comparisons between depth‐migrated and conventionally depth‐converted sections of both synthetic and field data properly show that significant lateral displacement is often required to position reflectors properly. Monte Carlo studies show that the lateral corrections can be important not only in absolute terms but also in relation to errors expected from an inaccurate velocity model.
The signature of an air gun array: Computation from near‐field measurements including interactions
Authors: Ziolkowski A. , Parkes G. , Hatton L. , Haugland T.
Published: October 2002

We designed a system to enable the signature of an air gun array to be calculated at any point in the water from a number of simultaneous independent measurements of the near‐field pressure field [subject of a patent application]. The number of these measurements must not be less than the number of guns in the array. The underlying assumption in our method is that the oscillating bubble produced by an air gun is small compared with the wavelengths of seismic interest. Each bubble thus behaves as a point source, both in the generation of seismic waves and in its response to incident seismic radiation produced by other nearby bubbles. It follows that the interaction effects between the bubbles may be described in terms of spherical waves. The array of interacting guns is equivalent to a notional array of noninteracting guns whose combined seismic radiation is identical. The seismic signatures of the equivalent independent elements of this notional array can be determined from the near‐field measurements. The seismic radiation pattern emitted by the whole array can be computed from these signatures by linear superposition, with a spherical correction applied. The method is tested by comparing far‐field signatures computed in this way with field measurements made in deep water. The computed and measured signatures match each other very closely. By comparison, signatures computed neglecting this interaction are a poor match to the measurements.
Recognition of electromagnetic overburden anomalies with horizontal loop electromagnetic survey data
Authors: Villegas‐Garca C. J. , West G. F.
Published: October 2002

An analog modeling program was conducted to investigate the electromagnetic (EM) response of nonuniform conductive overburden layers with the horizontal loop technique of geophysical prospecting. Several characteristics of the response that will help to differentiate between the EM response of nonuniform overburden layers and the response of bedrock mineralized conductors are reported. To recognize these characteristics, survey data at several frequencies and coil separations are required. It was observed that the response of a ramp‐like, a ridge‐like, and a valley‐like inhomogeneity in the overburden can be mistaken as caused by bedrock conductors. In the case of the ramp and ridge inhomogeneities, the migration of the negative peak anomaly observed in profiles surveyed at different coil separations was one of its more diagnostic characteristics. Prominent positive shoulders as well as an abnormal distance between crossovers of a given detected field anomaly might be the first indication of the presence of a valley‐like inhomogeneity undernearth the overburden. It was generally found that phasor plots of the studied overburden anomalies reveal clearly their basic characteristics.
Recovery of the acoustic impedance from reflection seismograms
Authors: Oldenburg D. W. , Scheuer T. , Levy S.
Published: October 2002

This paper examines the problem of recovering the acoustic impedance from a band‐limited normal incidence reflection seismogram. The convolutional model for the seismogram is adopted at the outset, and it is therefore required that initial processing has removed multiples and recovered true amplitudes as well as possible. In the first portion of the paper we investigate the effect of substituting the deconvolved seismic trace (that is, the band‐limited version of the reflectivity function) into the standard recursion formula for the acoustic impedance. The formalism of linear inverse theory is used to show that the logarithm of the normalized acoustic impedance estimated from the deconvolved seismogram is approximately an average of the true logarithm of the impedance. Moreover, the averaging function is identical to that used in deconvolving the initial seismogram. The advantage of these averages is that they are unique; their disadvantage is that low‐frequency information, which is crucial to making a geologic interpretation, is missing. We next present two methods by which the missing low‐frequency information can be recovered. The first method is a linear programming (LP) construction algorithm which attempts to find a reflectivity function made of isolated delta functions. This method is computationally efficient and robust in the presence of noise. Importantly, it also lends itself to the incorporation of impedance constraints if such geologic information is available. A second construction method makes use of the fact that the Fourier transform of a reflectivity function for a layered earth can be modeled as an autoregressive (AR) process. The missing high and low frequencies can thus be predicted from the band‐limited reflectivity function by standard techniques. Stability in the presence of additive noise on the seismogram is achieved by predicting frequencies outside the known frequency band with operators of different orders and extracting a common signal from the results. Our construction algorithms are shown to operate successfully on a variety of synthetic examples. Two sections of field data are inverted, and in both the results from the LP and AR methods are similar and compare favorably to acoustic impedance features observed at nearby wells.
Numerical integration of related Hankel transforms by quadrature and continued fraction expansion
Authors: Chave Alan D.
Published: October 2002

An algorithm is presented for the accurate evaluation of Hankel (or Bessel) transforms of algebraically related kernel functions, defined here as the non‐Bessel function portion of the integrand, that is more widely applicable than the standard digital filter methods without enormous increases in computational burden. The algorithm performs the automatic integration of the product of the kernel and Bessel functions between the asymptotic zero crossings of the latter and sums the series of partial integrations using a continued fraction expansion, equivalent to an analytic continuation of the series. The integrands may be saved to allow the rapid computation of related transforms without recalculating the kernel or Bessel functions, and the integration steps use interlacing quadrature formulas so that no function evaluations are wasted when it is necessary to increase the order of the quadrature rule. The continued fraction algorithm allows very slowly divergent or even formally divergent integrals to be computed quite easily. The local error is controlled at each step in the algorithm, and accuracy is limited largely by machine resolution. The algorithm is written in Fortran and is listed in an Appendix along with a driver program that illustrates its features. The driver program and subroutine are available from the SEG Business Office.
Comparison of apparent resistivity functions for transient electromagnetic methods
Authors: Raiche A. P.
Published: October 2002

The use of transient electromagnetic (TEM) methods is increasing throughout the world because of their success in finding conductive anomalies in regions previously thought inappropriate for EM techniques. Most TEM systems now in use (SIROTEM UTEM, Crone Pulse EM, etc.) employ voltage measurements, i.e., measurements of the time derivative of the magnetic field. However, the success of SQUID based receiving systems in many fields has led research organizations (such as the Bureau of Mineral Resources, Australia) to investigate the use of SQUIDs in TEM systems to obtain direct measurements of the magnetic field.
An updated Bouguer anomaly map of south‐central West Africa
Authors: Hastings David A.
Published: October 2002

A new Bouguer gravity anomaly map compiled for western Africa adds data for Ghana, Guinea, and Liberia. The new data add detail to a key part of the Eburnean shield and assist in the development of a model of rifting at the time of the Eburnean orogeny, 2000 million years ago. This model includes a framework for the deposition of the region’s mineral deposits. The model and existing field data can be used to guide future minerals exploration in the region.
Crustal structure of the continental shelf off northwest Britain from two‐ship seismic experiments
Authors: Jones E. J. W. , White R. S. , Hughes V. J. , Matthews D. H. , Clayton B. R.
Published: October 2002

Two‐ship multichannel seismic profiles, using expanding spread and constant offset source‐receiver configurations, were shot with explosive charges and a 16.4 ℓ air gun to investigate the structure of the continental shelf off northwest Britain. A long‐range (69 km) expanding spread profile reveals that the crystalline basement off northern Scotland is covered by sedimentary sections up to 2.5 km thick, and is divisible into two seismic units with velocities of 6.1 km/s and 6.6 km/s. Prominent supercritical Moho reflections indicate a crustal thickness of 26.7 km. Strong sedimentary and basement refractions, together with oblique reflections from the vicinity of the Moho, have been profiled at a constant air gun‐receiver offset of 10 km across a sedimentary basin west of the Orkney Islands. On the Outer Hebridean shelf to the west of mainland Scotland, the metamorphic basement lies within 250 m of the sea floor. P- to S-wave conversion occurs at the basement surface; [Formula: see text] gives a Poisson’s ratio of 0.27–0.31 at depths of 300–1 000 m. Marked changes in mode conversion efficiency are observed on constant offset profiles and are attributed to variations in the velocity structure of an uppermost low‐velocity (4.9 km/s) layer of weathered basement. The deeper crustal velocity appears uniform with depth, although there is some evidence of significant lateral velocity changes (6.28–6.61 km/s). In contrast to the shelf north of Scotland, reflections from within the basement and from near the base of the crust are recorded only sporadically on constant‐offset profiles. A strong event at 10.4 s two‐way reflection time appears to have arisen from a seismic discontinuity within the upper mantle. The differences in seismic character of the basement on the two‐ship profiles suggest significant variations in crustal structure within the Caledonian foreland of northern Britain.
The ratio Vp/Vs as a discriminant of composition for siliceous limestones
Authors: Wilkens Roy , Simmons Gene , Caruso Lou
Published: October 2002

The ratio of the velocity of compressional waves, [Formula: see text], to the velocity of shear waves, [Formula: see text], is an important parameter for interpreting geophysical field data. Recent studies have emphasized the role played by pore geometry in controlling [Formula: see text] in homogeneous rocks. We measured the carbonate content of a set of siliceous limestones of varying proportions of carbonate and silica and observed the pore structures of these samples using a scanning electron microscope. The range of [Formula: see text] at 1.0 kbar is from 1.6 to 2.0. The behavior of [Formula: see text] of individual samples during increasing confining pressure is consistent with crack‐closure theory. However, the value of [Formula: see text] within the sample set as a whole is dominated by its carbonate content. Variations in [Formula: see text] due to total porosity and pore geometry are around 0.1, whereas the change due to composition is 0.4. Values of pore aspect ratios gained from comparison of the velocity‐porosity‐composition data with theory are in good agreement with the electron microscope observations.
SH-wave propagation in heterogeneous media: Velocity‐stress finite‐difference method
Authors: Virieux Jean
Published: October 2002

A new finite‐difference (FD) method is presented for modeling SH-wave propagation in a generally heterogeneous medium. This method uses both velocity and stress in a discrete grid. Density and shear modulus are similarly discretized, avoiding any spatial smoothing. Therefore, boundaries will be correctly modeled under an implicit formulation. Standard problems (quarter‐plane propagation, sedimentary basin propagation) are studied to compare this method with other methods. Finally a more complex example (a salt dome inside a two‐layered medium) shows the effect of lateral propagation on seismograms recorded at the surface. A corner wave, always in‐phase with the incident wave, and a head wave will appear, which will pose severe problems of interpretation with the usual vertical migration methods.
Migration of seismic data by phase shift plus interpolation
Authors: Gazdag Jeno , Sguazzero Piero
Published: October 2002

Under the horizontally layered velocity assumption, migration is defined by a set of independent ordinary differential equations in the wavenumber‐frequency domain. The wave components are extrapolated downward by rotating their phases. This paper shows that one can generalize the concepts of the phase‐shift method to media having lateral velocity variations. The wave extrapolation procedure consists of two steps. In the first step, the wave field is extrapolated by the phase‐shift method using ℓ laterally uniform velocity fields. The intermediate result is ℓ reference wave fields. In the second step, the actual wave field is computed by interpolation from the reference wave fields. The phase shift plus interpolation (PSPI) method is unconditionally stable and lends itself conveniently to migration of three‐dimensional data. The performance of the methods is demonstrated on synthetic examples. The PSPI migration results are then compared with those obtained from a finite‐difference method.
The joint use of coincident loop transient electromagnetic and Schlumberger sounding to resolve layered structures
Authors: Raiche A. P. , Jupp D. L. B. , Rutter H. , Vozoff K.
Published: October 2002

One‐dimensional earth models consisting of uniform horizontal layers are useful both as actual representations of earth structures and as host models for more complex structures. However, there are often inherent difficulties in establishing layer thicknesses and resistivities from one type of measurement alone. For example, the dc resistivity method is sensitive to both conductive and resistive layers, but as these layers become thin, nonuniqueness becomes a severe problem. Electromagnetic (EM) methods are good for establishing the parameters of conductive layers, but they are quite insensitive to resistive layers. The use of both coincident loop transient EM (TEM) and Schlumberger methods, together with a joint inverse computer program, can vastly improve interpretation of layered‐earth parameters. The final model is less dependent upon starting guesses, error bounds are much improved, and nonuniqueness is much less of a problem. These advantages are illustrated by interpretation of real field data as well as by a theoretical study of four different types of earth models.
Minimum entropy deconvolution and simplicity: A noniterative algorithm
Authors: Cabrelli Carlos A.
Published: October 2002

Minimum entropy deconvolution (MED) is a technique developed by Wiggins (1978) with the purpose of separating the components of a signal, as the convolution model of a smooth wavelet with a series of impulses. The advantage of this method, as compared with traditional methods, is that it obviates strong hypotheses over the components, which require only the simplicity of the output. The degree of simplicity is measured with the Varimax norm for factor analysis. An iterative algorithm for computation of the filter is derived from this norm, having as an outstanding characteristic its stability in presence of noise. Geometrical analysis of the Varimax norm suggests the definition of a new criterion for simplicity: the D norm. In case of multiple inputs, the D norm is obtained through modification of the kurtosis norm. One of the most outstanding characteristics of the new criterion, by comparison with the Varimax norm, is that a noniterative algorithm for computation of the deconvolution filter can be derived from the D norm. This is significant because the standard MED algorithm frequently requires in each iteration the inversion of an autocorrelation matrix whose order is the length of the filter, while the new algorithm derived from the D norm requires the inversion of a single matrix. On the other hand, results of numerical tests, performed jointly with Graciela A. Canziani, show that the new algorithm produces outputs of greater simplicity than those produced by the traditional MED algorithm. These considerations imply that the D criterion yields a new computational method for minimum entropy deconvolution. A section of numerical examples is included, where the results of an extensive simulation study with synthetic data are analyzed. The numerical computations show in all cases a remarkable improvement resulting from use of the D norm. The properties of stability in the presence of noise are preserved as shown in the examples. In the case of a single input, the relation between the D norm and the spiking filter is analyzed (Appendix B).
Distortion of magnetotelluric sounding curves by three‐dimensional structures
Authors: Park Stephen K.
Published: October 2002

Distortions of magnetotelluric fields caused by three‐dimensional (3‐D) structures can be severe and are not predictable using one‐dimensional or two‐dimensional modeling. I used a 3-D modeling algorithm based upon an extension of a generalized thin sheet analysis due to Ranganayaki and Madden (1980) to examine field distortions in crustal environments. Three major physical mechanisms cause these distortions. These mechanisms are resistive coupling between the electrical mantle and upper crust, resistive coupling between conductive features within the upper crust, and local induction of current loops within good conductors. Each mechanism produces different spatial and frequency effects upon the background field, so identification of the dominant mechanism can be used as an interpretational aid. I finally use this analysis to identify distortion mechanisms seen in magnetotelluric data from Beowawe, Nevada to aid in an interpretation of that area.
Tomographic determination of velocity and depth in laterally varying media
Authors: Bishop T. N. , Bube K. P. , Cutler R. T. , Langan R. T. , Love P. L. , Resnick J. R. , Shuey R. T. , Spindler D. A. , Wyld H. W.
Published: October 2002

Estimation of reflector depth and seismic velocity from seismic reflection data can be formulated as a general inverse problem. The method used to solve this problem is similar to tomographic techniques in medical diagnosis and we refer to it as seismic reflection tomography. Seismic tomography is formulated as an iterative Gauss‐Newton algorithm that produces a velocity‐depth model which minimizes the difference between traveltimes generated by tracing rays through the model and traveltimes measured from the data. The input to the process consists of traveltimes measured from selected events on unstacked seismic data and a first‐guess velocity‐depth model. Usually this first‐guess model has velocities which are laterally constant and is usually based on nearby well information and/or an analysis of the stacked section. The final model generated by the tomographic method yields traveltimes from ray tracing which differ from the measured values in recorded data by approximately 5 ms root‐mean‐square. The indeterminancy of the inversion and the associated nonuniqueness of the output model are both analyzed theoretically and tested numerically. It is found that certain aspects of the velocity field are poorly determined or undetermined. This technique is applied to an example using real data where the presence of permafrost causes a near‐surface lateral change in velocity. The permafrost is successfully imaged in the model output from tomography. In addition, depth estimates at the intersection of two lines differ by a significantly smaller amount than the corresponding estimates derived from conventional processing.
Analysis of temperatures in sedimentary basins: the Michigan Basin
Authors: Speece Marvin A. , Bowen Timothy D. , Folcik James L. , Pollack Henry N.
Published: October 2002

We develop an analytical and numerical methodology for the analysis of large bottom‐hole temperature (BHT) data sets from sedimentary basins, and test the methodology using temperature, stratigraphic, and lithologic data from 411 boreholes in the Michigan Basin. Least‐squares estimates of temperature gradients in the formations and lithologies present are calculated as solutions to a large system of linear equations. At each borehole the temperature difference between the bottom and top of the hole is represented as a sum of temperature increments through the various formations or lithologies penetrated by the borehole. Quadratic programming techniques enable bounds to be placed on the gradient solutions in order to suppress or exclude improbable gradient estimates. Numerical experiments with synthetic data reveal that the estimates of temperature gradients for a given formation or lithology are sensitive to the degree of representation of that unit; well represented units have more stable gradient estimates in the presence of noise than do poorly represented units. The estimates of temperature gradients obtained for lithologies are more stable than those for formations and are believed to be good estimates of actual lithologic temperature gradients in the Michigan Basin. Formation temperature gradients obtained as a weighted sum of the estimates of the component lithologic temperature gradients appear to be good estimates of the average temperature gradients for the formations of the basin. At each borehole a temperature residual exists corresponding to the difference between the observed BHT and the BHT predicted by the estimated interval temperature gradients. Residuals are far more stable than estimated temperature gradients. The values of residuals change little regardless of whether lithology, formation, bounded, or unbounded gradient estimates are used to calculate them. Maps of residuals indicate well‐defined and spatially coherent patterns of positive and negative temperature residuals. Filtered subsets of large‐magnitude residuals alone show a pattern of negative residuals coinciding with the mid‐Michigan gravity high, a geophysical feature thought to delineate a Precambrian (Keweenawan) rift zone in the crust beneath the basin. Thermal models of the Michigan Basin and the crust and upper mantle beneath the basin indicate that the suspected rift beneath the basin can cause a variation in basement heat flow sufficient to produce temperature residuals of the magnitude observed in the sediments, with negative temperature residuals over the area of the rift.
Experimental determination of elastic anisotropy of Berea sandstone, Chicopee shale, and Chelmsford granite
Authors: Lo Tien‐when , Coyner Karl B. , Toksöz M. Nafi
Published: October 2002

We used the ultrasonic transmission method to measure P-, SH-, and SV-wave velocities for Chelmsford granite, Chicopee shale, and Berea sandstone in different directions up to 1 000 bars confining pressure. The velocity measurements indicate these three rocks are elastically anisotropic. The stiffness constants, dynamic Young’s moduli, dynamic Poisson’s ratios, and dynamic bulk moduli of the three rocks were also calculated. The elastic constants, together with velocity measurements, suggest that: (1) elastic anisotropy is due to the combined effects of pores or cracks and mineral grain orientation, and (2) elastic anisotropy decreases with increasing confining pressure. The residual anisotropy at higher confining pressure is due to mineral grain orientation.
Seismic attenuation spectra in rock mass characterization; a case study in open‐pit mining
Authors: Young R. P. , Hill J. J.
Published: October 2002

The application of engineering geophysics to the characterization of rock masses is exemplified through a case study of three phases of a research project into the design of efficient blasting systems in open‐pit mining. Seismic experiments are used before and after mine blasting to monitor the efficiency of explosions in terms of rock fragmentation. Spectral analysis of seismic signals, after they have been used to interrogate rock masses, is used to compute preblast and postblast attenuation and velocity parameters. The results show that fragmentation efficiency of a mine blast and fracture anisotropy of a rock mass can be quantified in terms of three‐dimensional (3-D) attenuation spectra and polar anisotropy diagrams. These seismic data are correlated with the blast design and the energy used by the excavating dragline machine to dig to rock mass. An overview of the seismic attenuation technique and instrumentation used in the project (phases I and II) is given. A case study from phase III highlights the scope and interpretation of the relationship between excavation parameters and seismically characterized blasting efficiency.
A plane‐wave decomposition for elastic wave fields applied to the separation of P‐waves and S‐waves in vector seismic data
Authors: Devaney A. J. , Oristaglio M. L.
Published: October 2002

We describe a method to decompose a two‐dimensional (2-D) elastic wave field recorded along a line into its longitudinal and transverse parts, that is, into compressional (P) waves and shear (S) waves. Separation of the data into P-waves and S-waves is useful when analyzing vector seismic measurements along surface lines or in boreholes. The method described is based on a plane‐wave expansion for elastic wave fields and is illustrated with a synthetic example of an offset vertical seismic profile (VSP) in a layered elastic medium.
Geophysical results in archaeology in Hungary
Authors: Pattantyús‐Á. M.
Published: October 2002

Several archaeologic sites containing different artifacts were investigated by magnetic and geoelectric measurements. Kilns of medieval semisubterranean houses, ruins of a Roman brick building, and pits of a Copper Age settlement were discovered by magnetic methods. The ground plan of a Roman fortress was determined by resistivity measurements at a location where excavation was impossible because of the high groundwater level. Resistivity measurements made of a Roman homestead to determine the location of a building are discussed in detail. By correlating characteristic maxima of filtered resistivity data, the placement and orientation of walls could be determined. From the measurements, the position and extension of a group of buildings were defined. Prehistoric mining trenches can be located on the basis of anomalously low resistivities. We determined the exact location of a 50 000 year old flint mine on the outskirts of Budapest by geoelectric measurements and defined the location of the excavation on the basis of geophysical measurements. A three‐dimensional picture constructed from apparent resistivities associated with different penetration depths agrees fairly well with the shape of the ancient mine trenches excavated later.
A single apparent resistivity expression for long‐offset transient electromagnetics
Authors: Sheng Yang
Published: October 2002

Early‐time and late‐time apparent resistivity approximations have been widely used for interpretation of long‐offset transient electromagnetic (LOTEM) measurements because it is difficult to find a single apparent resistivity over the whole time range. From a physical point of view, Dr. C. H. Stoyer defined an apparent resistivity for the whole time range. However, there are two problems which hinder its use: one is that there is no explicit formula to calculate the apparent resistivity, and the other is that the apparent resistivity has no single solution. A careful study of the two problems shows that a numerical method can be used to calculate a single apparent resistivity. A formula for the maximum receiver voltage over a uniform earth, when compared with the receiver voltage for a layered earth, leads to the conclusion that, in some cases, a layered earth can produce a larger voltage than any uniform earth can produce. Therefore, our apparent resistivity definition cannot be applied to those cases. In some other cases, the two possible solutions from our definition do not merge, so that neither of them is meaningful for the whole time range.