bluuebunny/crossref_metadata_2025 huggingface dataset:
A model study of a thin plate in free space for the EM37 transient electromagnetic system
Authors: Gallagher Peggie R. , Ward Stanley H. , Hohmann G. W.
Published: October 2002

The computer program PLATE, developed at the University of Toronto, models the electromagnetic (EM) response of an inductively thin plate in free space. We used PLATE to compute two components of the time derivative of the magnetic field for a range of models for the EM37 fixed‐source transient system ([Formula: see text] loop). Analysis of the response curves produced methods of interpretation for obtaining plate geometry and conductance. The overall width of an anomaly, the distance between peaks and the width of the updip lobes, can provide an estimate of depth. Dip has the dominant effect on the ratio of the peak amplitudes. A rough estimate of plate size and the position in time (early or late) of the currents is essential before proceeding with interpretation. Strike length is not obviously reflected in the shape of the curves, but depth extent is indicated by the rate at which the downdip tail returns to the baseline, except for vertical plates. For vertical plates, curve matching may be the only method of obtaining an estimate of depth extent. Varying conductance for a particular model in free space affects whether a channel represents an early, intermediate, or late time response. The shape of a profile varies with the time of measurement. The estimated time constant can be used to calculate the conductance, provided an estimate of the shortest dimension of the plate is available. Extinction angles appear frequently for plates of small depth extent but do not occur for plates which are of infinite strike and depth extent with respect to the size of the transmitting loop.
On the detectability of crustal magma chambers using the magnetotelluric method
Authors: Newman Gregory A. , Wannamaker Philip E. , Hohmann Gerald W.
Published: October 2002

We utilized resistivity models of silicic magma chambers to explore effects that layering can have on three‐dimensional (3-D) magnetotelluric (MT) responses. Model simulations show that MT detection of magma may depend strongly on its one‐dimensional host. The 3-D responses of a model juvenile magma body which is connected electrically to deeper, less resistive crust of regional extent are very subdued. However, intermediate and mature magmatic systems, leaving magma no longer in contact with lower, less resistive crust, may be detectable with the MT method. Further, the release and ascent of volatiles from crystallizing melt may lead to fracturing above the chamber, thereby establishing electrical contact of the magma with shallow, conductive crust and amplifying its MT response.
Approximate computation of radial gravity profiles for sources with circular symmetry
Authors: Paul M. K.
Published: October 2002

Computation of the radial gravity profile due to a source body with circular symmetry about a vertical axis is normally accomplished by a complex computational evaluation of elliptic integrals or lambda functions. To solve this problem, an alternative method is proposed which first obtains the easily computed gravity values at points on the axis of the source body and then finds an appropriate linear combination of these values which approximates the gravity value at a given point on the radial profile to an acceptable degree of accuracy. Sets of coefficients in the linear relationship for each point of computation on the radial profile need be evaluated only once and then can be used repeatedly for different assumptions on the shape and size of the source body and its density distribution. A simple iterative scheme allows selection of a small set of equidistant points on the vertical axis, consistent with a desired accuracy for the computed values along the radial profile. In the two examples given, errors in the computed anomalies are everywhere less than 0.01 percent of the true peak anomaly values.
A bias in amplitude measurements
Authors: Powell James A.
Published: October 2002

Measurements based on the amplitude of seismic events have been proposed as a means of determining bed thickness (Widess, 1973), composition of facies (Lindseth, 1979), contents of pores (Sherwood et al., 1983), and rock density (Carrion et al., 1983). In this note a systematic error in empirical amplitude measurements is described, its magnitude is estimated, and some of its implications are discussed.
On: “A sum autoregressive formula for the reflection response” by P. Hubral, S. Treitel, and P. R. Gutowski (GEOPHYSICS, 45, 1697–1705, November 1980).
Authors: McClary W. K.
Published: October 2002

Hubral et al. considered the reflection response of a set of horizontal interfaces to a downgoing pulse as a sum of generalized primaries (GPs). The GP asscociated with interface n is [Formula: see text] where [Formula: see text] is the reflection response of the first i interfaces only. Their formula for the GPs may be understood by the argument illustrated in Figure 1.
Phase‐coherency filtering of reflection seismic data
Authors: McGlynn John D. , Ioup George E.
Published: October 2002

In addition to the standard techniques of stacking and digital band‐pass filtering for enhancing signal‐to‐noise (S/N) ratio for common‐depth‐point (CDP) reflection seismic data, a number of alternative or supplementary methods are available: (1) weighted mixing of adjacent traces, (2) semblance weighting of multichannel data based upon interchannel semblances (Neidell and Taner, 1971), and (3) filtering with the output energy filter (Robinson and Treitel, 1980). Each approach has advantages and disadvantages.
Gravity interpretation using the Mellin transform
Authors: Mohan N. L. , Anandababu L. , Rao S. V. Seshagiri
Published: October 2002

The Mellin transform of the gravity effect of a buried sphere and two‐dimensional horizontal circular cylinder, and the first horizontal derivative of the gravity effect of a two‐dimensional thin fault layer are derived. The transformed functions are bounded by two asymptotes. They are analyzed and procedures are formulated excluding the asymptotic regions for the extraction of the body parameters. The application of the Mellin transform is tested on simulated models as well as on two field examples: (1) the Humble Dome gravity anomaly near Houston, USA; and (2) the Louga gravity anomaly, USA.
Estimates of velocity dispersion between seismic and ultrasonic frequencies
Authors: Winkler Kenneth W.
Published: October 2002

It is generally accepted that acoustic velocities in fluid‐saturated rocks vary with frequency. Evidence comes from experimental measurements and from theoretical causality arguments. We have developed a simple analysis technique that gives estimates of total velocity dispersion between zero frequency and any measurement frequency. The technique requires compressional (P) and shear (S) wave velocity measurements on dry and fully saturated rock. Assuming that the dry velocities are independent of frequency, the Biot‐Gassmann equations are used to calculate the zero‐frequency velocities in the fully saturated rock. Any difference between the measured velocities and the calculated zero‐frequency velocities is interpreted as evidence of dispersion. Application of this analysis technique to a variety c ultrasonic data sets gives consistent results. In many rocks, dispersion between zero frequency and ultrasonic frequencies is on the order of 10 percent at low effective stress, and it decreases to only a few percent at higher stresses. Dispersion varies with degree of saturation and with fluid viscosity in the same way as do low‐frequency attenuation measurements. The results are readily interpreted in terms of the same local‐flow absorption/dispersion mechanism that has been used to explain recent laboratory attenuation measurements. This apparent dispersion places upper bounds on seismic‐to‐sonic velocity differences. It also points out possible discrepancies between seismic velocities and ultrasonic laboratory measurements.
On: “The electrochemical mechanics of sulfide self‐potentials” by M. Sato and H. M. Mooney (GEOPHYSICS, 25, 226-249, February 1960)
Authors: Burr S. V.
Published: October 2002

I was recently introduced to this very important paper on the self potential. Realizing the paper is 25 years old, additional field information is now available, and that others have probably responded with critiques, nevertheless, I choose to report my experiences with this trustworthy, sorely neglected, geophysical method.
Zero‐offset reflections from a curved interface
Authors: Ursin Bjørn
Published: October 2002

Dynamic ray theory is used to compute the reflection response from a curved surface when the source and receiver are located at the same point. This response has also been computed by Cohen and Bleistein from the Helmholtz formula using the Kirchhoff approximation and the method of multidimensional stationary phase. The same approximation has been derived by Hilterman, and it may also be computed from a simple formula given by Hubral. Ray methods may be applied to the approximate computation of the reflection response from inhomogeneous media with complicated structure. This is not so easily done with methods based on the Kirchhoff approximation of the Helmholtz integral.
Three‐dimensional mise‐à‐la‐masse modeling applied to mapping fracture zones
Authors: Beasley Craig W. , Ward Stanley H.
Published: October 2002

A numerical scheme applying the method of volume integral equations has been developed for borehole‐to‐borehole and borehole‐to‐surface modeling of the apparent resistivity response of a thin conductive body in a half‐space; the inhomogeneity simulates a fracture zone in a geothermal system. The algorithm is applicable for the direct‐current case when the buried electrode is either inside (mise‐à‐la‐masse) or outside (near‐miss) the body. In implementing the scheme, the integral equation is transformed into a matrix equation as a result of discretizing the inhomogeneity into rectangular cells. All physical properties are assumed constant within each cell. The rectangular cells are used through‐out execution of the algorithm. The computed surface and subsurface apparent resistivity responses are examined for bodies of similar shape and size but with different orientations: (1) vertical, (2) horizontal, (3) dipping at 60 degrees, and (4) dipping at 30 degrees. The four bodies produce apparent resistivity cross‐section plots which differ little from each other except in orientation. Varying the depth to the top of a body does not significantly alter the subsurface apparent resistivity response in the vicinity of the body. In both section and plan views, estimates of orientation, areal extent, and dip can often be made. The maximum depth at which a body can be located and still produce a detectable surface anomaly is dependent upon the position of the buried electrode and upon the contrast in conductivity. Locating the buried electrode just outside the body does not significantly alter the results from those when the electrode is embedded in the inhomogeneity. However, the similarity between the results of these two cases decreases as the distance between the electrode and the body is increased.
The altitude dependence of terrestrial gamma‐ray spectra: A simple model
Authors: Bailey R. C.
Published: October 2002

Accurate airborne multichannel gamma‐ray surveys require accurate knowledge of the spectral shapes of the natural radioelements and their variation with height. Simple physical considerations suggest a model with two spectral components for each radioelement, in which the first component decays into the second with increasing height. The two spectral components are approximately identified with gamma rays that have been scattered and those that have not been scattered since entering the atmosphere, although this interpretation is irrelevant to the applications of the model. The model’s analytic representation of spectral dependence on height yields an explicit formula for the effective height of the detector as deduced from spectral shape. Atmospheric radon is shown to produce a negative effective height, which implies a possible method for estimating atmospheric radon directly rather than from spectral shape. An extension of this approach gives an approximate formula for estimating the spectral contribution of an arbitrarily stratified distribution of radon.
Nomogram for the direct interpretation of magnetic anomalies due to long horizontal cylinders
Authors: Rao T. K. S. Prakasa , Subrahmanyam M. , Murthy A. Srikrishna
Published: October 2002

One of the widely used geometrical configurations for magnetic interpretation is the long horizontal circular cylinder. Gay (1965) provides a set of master curves for the interpretation of magnetic anomalies of these bodies. Rao et al. (1973) formulates functions of the anomaly at several distances from an arbitrary point, and the linear equations thus formed are solved for coefficients related to the parameters of the causative body. Prakasa Rao and Murthy (1976) propose an empirical method for rapid interpretation. Atchuta Rao and Ram Babu (1980), Mohan et al. (1982), and Sampath Kumar and Prakasa Rao (1984) describe methods based on Hilbert transforms. Radhakrishna Murthy et al. (1980) propose a method based on two components of the anomalous magnetic field. With the exception of the direct method of Prakasa Rao and Murthy (1976), the other methods mentioned involve reduction of field curves and then matching with master curves, solving linear equations, performing Hilbert transformations, and computation of derivatives, respectively. Hence they are not suitable for direct and rapid interpretation. This note contains a simple nomogram for the magnetic effect due to an arbitrarily magnetized horizontal cylinder.
COCORP: Northern California‐Nevada area and Southern Appalachian area: Part III.
Authors: Kaufman S.
Published: October 2002

The Consortium for Continental Reflection Profiling (COCORP) announces the availability of data packages and digital tapes for two areas: N. Cal‐Nevada area consisting of line 8 Nevada and line 7 California covering 282 line‐km; and Southern Appalachian area, part III, consisting of Florida lines 1, 2, and 4 and Georgia lines 10, 11, 12, 13, 14, and 15 covering 578.4 line‐km. The costs are the costs of reproduction and shipping, only. The COCORP activity is part of the U.S. Geodynamics Program sponsored by the National Academy of Sciences and funded by the National Science Foundation. The executive group of the consortium consists of representatives from Cornell University, Dartmouth College, Princeton University, Rice University, and the University of Wisconsin. Cornell University is the operating institution.
Archaeological site surveying program at the University of Nebraska
Authors: Weymouth John W.
Published: October 2002

A summary of geophysical applications peculiar to archaeology and magnetic surveying techniques applied by the University of Nebraska to archaeological sites is presented. In contrast to geophysical targets, the size and depth of the features of interest on archaeological sites are from several centimeters to a few meters. Typical features are historic foundations, wells, privies or prehistoric earthen features such as earth house floors, storage pits, or fire hearths. The most commonly used geophysical methods are resistivity, radar, and magnetometry. The program at the University of Nebraska has concentrated on magnetic surveying field methods based on the use of two magnetometers in the difference mode to correct for temporal variations. Data processing used both microcomputers and mainframe computers. Microcomputers are used in the field and near sites to log data and to do preliminary mapping. Mainframe computers are used for further processing and filtering and for producing a variety of graphical representations of the data for an archaeological audience. Case histories presented are from site surveys in North Dakota, Oklahoma, Colorado, and Nebraska.
Synthetic seismic sections for acoustic, elastic, anisotropic, and vertically inhomogeneous layered media
Authors: Hron F. , May B. T. , Covey J. D. , Daley P. F.
Published: October 2002

Synthetic seismic sections computed during forward modeling differ depending upon the type of media used to define the model. Four media types considered here are acoustic, elastic, elliptically anisotropic, and vertically inhomogeneous; significant differences are found among the seismic sections for these cases. Automatic ray generation, using kinematic and dynamic analog groups, permits retention and explicit identification of all significant arrivals, including primaries, multiples, converted waves, etc., for three‐dimensional, horizontally layered structures. Comparisons between arrivals common to the various models are shown by synthetic trace sections, amplitude‐distance plots, and velocity spectra. Results show significant energy in converted waves in the elastic models and marked differences between amplitude‐distance curves for elastic and acoustic cases. Anisotropic media produce noticeable differences in both amplitude‐ and time‐distance curves as a function of the degree of anisotropy. Modeling with vertically inhomogeneous media is practical and appealing because of how velocity and density functions are defined. Interestingly, a diving wave of high amplitude shown in our seismograms closely resembles the strong first arrival often present on field‐recorded seismograms.
Wave propagation from an explosive source
Authors: Jalinoos Farrokh , White J. E.
Published: October 2002

The model proposed describes the radiation of the primary seismic pulse from an explosive source. The model incorporates a viscous Voigt liquid in description of the nonelastic rock deformation that the explosion causes. The problem is solved in the frequency domain, followed by Fourier synthesis to obtain waveforms. Comparisons of the theoretical results with field data in three sedimentary environments of shale, sandstone, and marl indicate good quantitative agreements in shape and duration of transient pulses. Values of angular normal stress obtained at the deformed boundary suggest a dynamic tensile strength of rocks that decreased with duration of the tensile stress transient. The radius of the deformed zone (B) scales with the charge size Q approximately as [Formula: see text] where n is [Formula: see text] or larger.
Multichannel estimate of the seismic wavelet
Authors: Thomas José Eduardo
Published: October 2002

One of the fundamental problems in exploration seismology is to obtain a seismic record which has both high resolution and high ratio of signal to noise. If the seismic trace has a fair signal‐to‐noise (S/N) ratio, then subsequent data processing can be applied to improve the resolution. Basically, this data‐processing technique is the deconvolution of the source wavelet from the field seismic traces.
Transient electromagnetic sounding for groundwater
Authors: Fitterman David V. , Stewart Mark T.
Published: October 2002

The feasibility of using the transient electromagnetic sounding (TS or TDEM) method for groundwater exploration can be studied by means of numerical models. As examples of its applicability to groundwater exploration, we study four groundwater exploration problems: (1) mapping of alluvial fill and gravel zones over bedrock; (2) mapping of sand and gravel lenses in till; (3) detection of salt or brackish water interfaces in freshwater aquifers; and (4) determination of hydrostratigraphy. These groundwater problems require determination of the depth to bedrock; location of resistive, high‐porosity zones associated with fresh water; determination of formation resistivity to assess water quality; and determination of lithology and geometry, respectively. The TS method is best suited for locating conductive targets, and has very good vertical resolution. Unlike other sounding techniques where the receiver‐transmitter array must be expanded to sound more deeply, the depth of investigation for the TS method is a function of the length of time the transient is recorded. Present equipment limitations require that exploration targets with resistivities of 50 Ω ⋅ m or more be at least 50 m deep to determine their resistivity. The maximum depth of exploration is controlled by the geoelectrical section and background electromagnetic (EM) noise. For a particular exploration problem, numerical studies are recommended to determine if the target is detectable.
Three‐dimensional Born inversion with an arbitrary reference
Authors: Cohen Jack K. , Hagin Frank G. , Bleistein Norman
Published: October 2002

Recent work of G. Beylkin helped set the stage for very general seismic inversions. We have combined these broad concepts for inversion with classical high‐frequency asymptotics and perturbation methods to bring them closer to practically implementable algorithms. Applications include inversion schemes for both stacked and unstacked seismic data. Basic assumptions are that the data have relative true amplitude, and that a reasonably accurate background velocity c(x, y, z) is available. The perturbation from this background is then sought. Since high‐frequency approximations are used throughout, the resulting algorithms essentially locate discontinuities in velocity. An expression for a full 3-D velocity inversion can be derived for a general data surface. In this degree of generality the formula does not represent a computationally feasible algorithm, primarily because a key Jacobian determinant is not expressed in practical terms. In several important cases, however, this shortcoming can be overcome and expressions can be obtained that lead to feasible computing schemes. Zero‐offsets, common‐sources, and common‐receivers are examples of such cases. Implementation of the final algorithms involves, first, processing the data by applying the FFT, making an amplitude adjustment and filtering, and applying an inverse FFT. Then, for each output point, a summation is performed over that portion of the processed data influencing the output point. This last summation involves an amplitude and traveltime along connecting rays. The resulting algorithms are computationally competitive with analogous migration schemes.
Observations of the air‐coupled wave as a function of depth
Authors: Knapp Ralph W.
Published: October 2002

The air‐coupled wave is the result of sound energy (typically from the seismic source) coupling with the Earth’s surface. This energy is not abated by shallow burial or insulating of the geophones because it is imparted into the ground rather than being imparted into the geophone on impact as it would be in a microphone (Mooney and Kaasa, 1962).
The electromagnetic response of thin sheets buried in a uniformly conducting half‐space
Authors: Robertson R. Clark
Published: October 2002

The interpretation of magnetotelluric data is hampered by the effect of three‐dimensional (3-D) conductivity variations within the earth. In particular, the effects of deep structures are masked by heterogeneities near the surface. In order to understand the effects of 3-D anomalies on magnetotelluric investigations, the electromagnetic response of 3-D models of the earth must be investigated. One technique used to model a 3-D earth is the thin‐sheet approximation. This technique confines all lateral changes in conductivity to a horizontal layer in a laterally homogeneous earth; however, the thin‐sheet technique can be applied only to anomalies that are electrically thin at the frequency of investigation. The thin‐sheet technique can be extended to include a greater variety of models by stacking heterogeneous thin layers. As a first step, the thin‐sheet technique is extended to model a buried, heterogeneous thin layer. Extension of the method to account for buried thin sheets is theoretically and computationally more involved than for a surface thin sheet, but the buried thin sheet still has computational advantages over other 3-D models.
A simple method of interpreting dipole resistivity soundings
Authors: Niwas Sri , Israil M.
Published: October 2002

A computational method has been developed based on a linear relationship between apparent resistivity and the kernel function through a matrix operator. Forward modeling of dipole apparent resistivity values over a one‐dimensional layered earth model as well as the inversion of electrical sounding data can be easily accomplished using this matrix operator. For a few two‐layer, three‐layer, and four‐layer earth models, the apparent resistivity values can be calculated quickly and accurately. It is shown that the technique is adaptable to automatic interpretation in both the resistivity and the kernel domains.
Phase‐field imaging: The electromagnetic equivalent of seismic migration
Authors: Lee Seunghee , McMechan George A. , Aiken Carlos L. V.
Published: October 2002

An alternative approach to the interpretation of electromagnetic (EM) data is to downward continue the observations to construct a two‐dimensional resistivity image of the medium that produced them. The downward continuation can be done in a straightforward manner by drawing a parallel between the EM and acoustic wave equations. With appropriate approximations and identification of specific terms that are equivalent and with transformation from an initial‐value problem to a boundary‐value problem, EM data can be imaged using any of the methods originally developed for migration of seismic data. The method we chose here is Claerbout’s one‐way, finite‐difference, wave‐equation migration. The algorithm is implemented in the frequency domain. Independent images of relative reflectivity are obtained by processing E and H pseudosections separately; the best estimate of the actual reflector position is the region of coincidence of the two images. The same approach can be used in reverse for modeling the EM responses of two‐dimensional resistivity distributions. The main assumptions are direct analogies of the assumptions involved in state‐of‐the‐art seismic processing: details of EM reflectivity contained in the data wave fields are separable from the estimated background conductivity through which the wave field is downward continued, and there are no multiple reflections. Thus, the main restriction is that the resistivity variation be sufficiently small. The concept of imaging resistivity, as a function of position, is shown to be feasible and a direct analogy of seismic migration.
On: “Evaluation of the BGM-3 sea gravity meter system onboard R/V Conrad by Robin E. Bell and A. B. Watts (GEOPHYSICS, 51, 1480–1493, July 1986.)
Authors: LaCoste Lucien
Published: October 2002

I would like to comment on Bell and Watt’s interesting article. First, the following statement is incorrect, “Of the new generation of axially symmetric sea gravity systems, only the Bodenseewerk KSS-30 and the Bell Aerospace BGM-3 systems are presently available.” Actually, LaCoste and Romberg Gravity Meters, Inc., owns U.S. Patent No. 3,717,036 which describes the axially symmetric sea gravity meter being built and sold by LaCoste and Romberg. The actual gravity meter is described in my article “LaCoste and Romberg straight‐line gravity meter” (LaCoste, 1983) Also, field tests of the first of these straight‐line gravity meters are described in Valliant (1983). In addition, a comparative sea test between the straight‐line sea gravity meter and the Bodensee KSS-30 has been made (Macnab et al., 1985). Since late 1985, we have had our straight‐line meters available for immediate sale, and they were available on order as early as 1983. Our straight‐line (axially symmetric) gravity meters are definitely available and proven.
Hybrid modeling of elastic‐wave propagation in two‐dimensional laterally inhomogeneous media
Authors: Kummer B. , Behle A. , Dorau F.
Published: October 2002

We have constructed a hybrid scheme for elastic‐wave propagation in two‐dimensional laterally inhomogeneous media. The algorithm is based on a combination of finite‐difference techniques and the boundary integral equation method. It involves a dedicated application of each of the two methods to specific domains of the model structure; finite‐difference techniques are applied to calculate a set of boundary values (wave field and stress field) in the vicinity of the heterogeneous domain. The continuation of the near‐field response is then calculated by means of the boundary integral equation method. In a numerical example, the hybrid method has been applied to calculate a plane‐wave response for an elastic lens embedded in a homogeneous environment. The example shows that the hybrid scheme enables more efficient modeling, with the same accuracy, than with pure finite‐difference calculations.
Incorporation of attenuation into time‐domain computations of seismic wave fields
Authors: Emmerich Helga , Korn Michael
Published: October 2002

The only numerically tractable way yet found to incorporate attenuation into numerical time‐domain computations of seismic wave fields is to approximate the viscoelastic modulus by a low‐order rational function of frequency. The coefficients of this function can be determined by the Padé approximation. Our test computations show, however, that this approximation generally is of poor quality. Therefore, we suggest a new approach which is based on the rheological model of the generalized Maxwell body, which has a modulus of the desired rational form. We choose the relaxation frequencies logarithmically equidistant in the frequency band of interest, and determine the weight factors by simple numerical curve fitting to an arbitrary Q law. This approach is superior to the method above both in accuracy and in computational efficiency. For most practical applications, approximations of orders 2 or 3 are sufficient. The computing time and memory requirements for a finite‐difference calculation are then approximately twice those of a purely elastic calculation. As a first application of the method, we compute SH channel waves in discontinuous coal seams with Q = 50 within the coal. The results show that the high‐ frequency Airy phase is strongly attenuated. This indicates that care has to be taken in comparing the results of purely elastic model calculations of the propagation of seam waves with experimental data.
Transient electromagnetic inversion based on an approximate solution to the forward problem
Authors: Goldman Mark M.
Published: October 2002

A rapid algorithm for forward one‐dimensional modeling is based on the graphical construction of a multi‐layered apparent resistivity curve using an appropriate combination of two‐layered curves. A collection of two‐layered curves is calculated only once for fixed geoelectrical parameters and saved for future use; an arbitrary two‐layered curve within the wide range of the geoelectrical parameters is then obtained by simple interpolation. This method reduces computation time over other fast algorithms by at least one order of magnitude; in addition, it does not produce any significant computation errors in the late stage as do most other methods. A maximum relative error of about 10 to 15 percent may occur at a few points (usually two to three) in the vicinity of the intersection of the two‐layered curves. In most cases, however, this error does not affect the inversion since the relative contributions of these points to an objective function are small. The application of such a rapid forward algorithm allows one to attack the equivalence problem. For this purpose, several starting search points are randomly distributed within a feasible range in the parameter space. The inversion is then begun with the initial guesses for the parameters; several if not all of the minima of the objective function are found within the specified parameter range. To reduce ambiguity of the interpretation, all reasonable solutions are then correlated with available a priori geologic and/or geophysical information. Application of the above technique to real data shows the ability of the algorithm to detect equivalence and, thus, render the interpretation more objective. Both forward and inverse programs have been installed on a portable desktop computer (an IBM-PC compatible). The programs are easy to use and allow interpretation to be carried out in the field.
Approximate traveltimes in laterally inhomogeneous media
Authors: Wenzel F.
Published: October 2002

A particularly convenient method for the calculation of approximate traveltimes in a two‐dimensional (2-D( medium has become popular in recent years. In this method, the slowness of a velocity field varying in both coordinates x and z is considered as being the sum of a slowness [Formula: see text], depending upon depth only, and a perturbation Δu of arbitrary shape but small compared with [Formula: see text]. The ray from the origin to any point can be easily traced for the laterally homogeneous part of the slowness, and the associated traveltime is quickly evaluated. The traveltime perturbation due to the lateral heterogeneities is approximated by the integral over the slowness perturbations along this raypath. The purpose of this note is to derive this approximation rigorously. Advantages of the method are the availability of an analytic expression for the time perturbation and the fact that no complicated ray tracing by solving differential equations is necessary. Consequently, the method allows several applications, e.g., in seismic modeling, migration, and tomography.
Borehole gravity drift correction: A new approach
Authors: Pennybaker Kent A.
Published: October 2002

Gravity meter drift is the gradual change in the gravity reading over time; this change is unrelated to actual gravity changes. Drift is caused by creep in the gravity meter mechanism and by external influences which produce a change in the physical properties of the gravity element. Previous methods of drift correction for the LaCoste and Romberg borehole gravity meter are either linear random noise filters or nonlinear techniques relying upon the judgement of an interpreter for filtering. The method presented in this paper responds to the nonlinearity of the drift signal while retaining the ability to filter out the noise. The drift rate function is defined by repeat readings, which are integrated to yield a drift correction. The drift correction data’s Fourier transform has a sharp amplitude break between the drift signal and the noise. A low‐pass filter removes the higher frequency noise, resulting in a smoothed drift correction. This drift correction method, which attenuates random errors while retaining the characteristic drift signal, works well with a variety of drift patterns and leads to consistently better quality data.
Joseph geology and seismic deconvolution
Authors: Todoeschuck John P. , Jensen Oliver G.
Published: October 2002

Common practice in seismic deconvolution is to assume that the reflection sequence is uncorrelated, that is, that the sequence has a white power spectrum and a delta function autocorrelation. A white spectrum implies that the acoustic impedance function has a power spectrum proportional to [Formula: see text], which is characteristic of a nonstationary Brownian process (f is frequency). However, the maximum power spectrum permissible for the acoustic impedance function is 1/f; we call a spectrum of this kind a Joseph spectrum. A Joseph spectrum corresponds to a reflection sequence with a power spectrum proportional to f and a negative autocorrelation at small lags. Joseph spectrum behavior for reflection sequences has been seen before and we show it again in a well off Newfoundland and in two wells from Quebec. If the power spectrum is proportional to f, then the first term of the discretized autocorrelation function is −0.405 of the zero‐lag term and higher terms are negligible. We construct a Joseph filter analogous to the prediction error filter (PEF) using this extra term. The method requires one additional term in the normal equations, equations which are solved iteratively. When used to deconvolve artificial seismograms from the wells, the Joseph filter recovered the reflection sequences with as little as one‐tenth the error of the PEF.
Rapid computation of multioffset vertical seismic profile synthetic seismograms for layered media
Authors: Mallick Subhashis , Frazer L. Neil
Published: October 2002

By rearranging the formulas for the responses of buried sources and receivers in the Kennett reflectivity algorithm, we have obtained a new algorithm that is very efficient for computing multioffset VSP synthetic seismograms. The rearrangement of the response formulas is quite general inasmuch as it applies to both isotropic and anisotropic Kennett codes. Our new algorithm and the original single‐receiver algorithm can both be made to run much faster on vector computers by taking the layer loop out of the p-loop, but leaving it inside the frequency loop. The resulting vector codes can still compute the response of media with frequency‐ dependent velocities.
Absorbing boundary condition for the elastic wave equation
Authors: Randall C. J.
Published: October 2002

Extant absorbing boundary conditions for the elastic wave equation are generally effective only for waves nearly normally incident upon the boundary. High reflectivity is exhibited for waves traveling obliquely to the boundary. In this paper, a new and efficient absorbing boundary condition for two‐dimensional and three‐dimensional finite‐difference calculations of elastic wave propagation is presented. Compressional and shear components of the incident vector displacement fields are separated by calculating intermediary scalar potentials, allowing the use of Lindman’s boundary condition for scalar fields, which is highly absorbing for waves incident at any angle. The elastic medium is assumed to be homogeneous in the region immediately adjacent to the boundary. The reflectivity matrix of the resulting absorbing boundary for elastic waves is calculated, including the effects of finite‐difference truncation error. For effectively all angles of incidence, reflectivities are much smaller than those of the commonly employed paraxial absorbing boundaries, and the boundary condition is stable for any physical Poisson’s ratio. The nearly complete absorption predicted by the reflectivity matrix calculations, even at near grazing incidence, is demonstrated in a finite‐difference application.
Acoustic prestack migration of cross‐hole data
Authors: Hu Liang‐Zie , McMechan George A. , Harris Jerry M.
Published: October 2002

Subsurface imaging with common‐source cross‐hole data can be achieved using prestack reverse‐time migration. The algorithm consists of extrapolation of the recorded wave field, application of the excitation‐time imaging condition, and postprocessing of the resulting image with a low‐pass wavenumber filter. The wavenumber filter removes the artifact associated with the direct arrival; this artifact is not separable from the scattered data before migration because, in the cross‐hole geometry, they significantly overlap in time, space, and wavenumber. Migration of synthetic data produces the best possible results, but images produced by migration of scale‐model data are not greatly inferior. Apparently, acceptable images can be obtained from a surprisingly few sources, if these sources are located sufficiently far apart to give independent information and the recording aperture is sufficiently wide.
P-wave attenuation measurements from laboratory resonance and sonic waveform data
Authors: Goldberg D. , Zinszner B.
Published: October 2002

We computed compressional‐wave velocity [Formula: see text] and attenuation [Formula: see text] from sonic log waveforms recorded in a cored, 30 m thick, dolostone reservoir; using cores from the same reservoir, laboratory measurements of [Formula: see text] and [Formula: see text] were also obtained. We used a resonant bar technique to measure extensional and shear‐wave velocities and attenuations in the laboratory, so that the same frequency range as used in sonic logging (5–25 kHz) was studied. Having the same frequency range avoids frequency‐dependent differences between the laboratory and in‐situ measurements. Compressional‐wave attenuations at 0 MPa confining pressure, calculated on 30 samples, gave average [Formula: see text] values of 17. Experimental and geometrical errors were estimated to be about 5 percent. Measurements at elevated effective pressures up to 30 MPa on selected dolostone samples in a homogeneous interval showed mean [Formula: see text] and [Formula: see text] to be approximately equal and consistently greater than 125. At effective stress of 20 MPa and at room temperature, the mean [Formula: see text] over the dolostone interval was 87, a minimum estimate for the approximate in‐situ conditions. We computed compressional‐wave attenuation from sonic log waveforms in the 12.5–25 kHz frequency band using the slope of the spectral ratio of waveforms recorded 0.914 m and 1.524 m from the source. Average [Formula: see text] over the interval was 13.5, and the mean error between this value and the 95 percent confidence interval of the slope was 15.9 percent. The laboratory measurements of [Formula: see text] under elevated pressure conditions were more than five times greater than the mean in‐situ values. This comparison shows that additional extrinsic losses in the log‐derived measurement of [Formula: see text], such as scattering from fine layers and vugs or mode conversion to shear energy dissipating radially from the borehole, dominate the apparent attenuation.
Seismic expression of structural style in Norphlet formation, offshore Alabama
Authors: Bearden Bennett L. , Mink Robert M.
Published: October 2002

During the past several years, the Jurassic Norphlet formation in offshore Alabama has been the focus of active exploration and development operations. Since the 1979 discovery of deep gas [greater than 6096 m (20 000 ft)] in Norphlet sandstones which contain estimated reserves of several trillion cubic feet, six Norphlet fields have been established in Alabama state waters and an additional six fields have been established in Federal Outer Continental Shelf (OCS) waters in offshore Alabama. We describe, using seismic data, the structural style associated with the Norphlet formation in offshore Alabama. More than 563 line‐kilometers (350 line‐miles) of multifold common‐depth‐point (CDP) seismic reflection data in Mobile Bay and offshore Alabama have been analyzed, interpreted, and mapped. The Lower Mobile Bay‐Mary Ann natural gas field provides an excellent seismic case study for the structural style in the deep Norphlet play. The field may be used as a geophysical exploration model for other Jurassic structures in offshore Alabama and the central and eastern Gulf of Mexico. Interpretation of the seismic data and maps indicates that Norphlet structures in offshore Alabama are predominantly east‐west trending, low‐relief, broad, elongate anticlines. The Lower Mobile Bay fault trend associated with the anticlines consists of pull‐apart, listric, normal faults characteristic of salt‐detachment structures. Many of these faults exhibit small‐scale growth. Salt thickness ostensibly increases from Mobile Bay to offshore Alabama and is exemplified by the development of a sequence of various structures typically associated with basinward increase of salt. Offshore Alabama structures may be classified as early horizontal phase or pillow‐stage features. Strata above the Haynesville seismic marker appear to be relatively flat, indicating early salt movement in the area. Small downbends associated with salt withdrawal exhibit thickening in the Haynesville‐Smack‐over section and are further complicated by normal faulting. The preponderance of the data suggests that the structures containing the large gas accumulations in the Norphlet formation in offshore Alabama are the result of salt tectonism.
Concept of effective density: Key to gravity depth determinations for sedimentary basins
Authors: Litinsky Vadim A.
Published: October 2002

The gravity anomaly observed over a layered sedimentary basin is close to that calculated over a basin with the same configuration and depth but filled by homogeneous sediments with density equal to the effective (weighted average) density of the real layered basin. Therefore, it is possible to calculate the effective density contrast of a basin from the residual gravity anomaly over it, if the depth of the basin is known at least at one point. Assuming a mathematical function for density‐depth dependence, an expression for the gravity‐depth dependence using the infinite slab (Bouguer) formula can be developed. This expression makes it possible to calculate the depth of a basin or an isopach map from gravity data. An exponential function and a new hyperbolic density‐depth function and their gravity‐depth functions are analyzed and implemented for determining the depths of basins from gravity data for the San Jacinto graben, California, and the Tucson basin, southern Arizona. The hyperbolic functions are more reliable and realistic than exponential ones. The effective density contrast of sediments filling the Tucson basin and density‐depth dependence were calculated using the infinite‐slab formula from residual gravity data over the deepest borehole, which entered pre‐Eocene bedrock at a depth of 3.66 km. The hyperbolic density‐depth dependence for the Tucson basin is also assumed to be effective for all other basins in the Basin and Range Province, southern Arizona and southwestern New Mexico. The density‐depth function is easily converted into a gravity‐depth function, using the infinite‐slab formula. The residual gravity map of each basin in this Province can then be transformed into a map of basin depth contours, using the hyperbolic gravity‐depth function. Comparison of depths of basins calculated from gravity data with available borehole information (19 wells) showed that the proposed simple and fast method has an error in the range of about 13 percent of the actual depth.
Mapping a bedrock surface under dry alluvium with shallow seismic reflections
Authors: Miller Richard D. , Steeples Don W. , Brannan Michael
Published: October 2002

Shallow seismic‐reflection techniques were used to image the bedrock‐alluvial interface, near a chemical evaporation pond in the Texas Panhandle, allowing optimum placement of water‐quality monitor wells. The seismic data showed bedrock valleys as shallow as 4 m and accurate to within 1 m horizontally and vertically. The normal‐moveout velocity within the near‐surface alluvium varies from 225 m/s to 400 m/s. All monitor‐well borings near the evaporation pond penetrated unsaturated alluvial material. On most of the data, the wavelet reflected from the bedrock‐alluvium interface has a dominant frequency of around 170 Hz. Low‐cut filtering at 24 dB/octave below 220 Hz prior to analog‐to‐digital conversion enhanced the amplitude of the desired bedrock reflection relative to the amplitude of the unwanted ground roll. The final bedrock contour map derived from drilling and seismic‐reflection data possesses improved resolution and shows a bedrock valley not interpretable from drill data alone.