bluuebunny/crossref_metadata_2025 huggingface dataset:
Pore fluid effects on seismic velocity in anisotropic rocks
Authors: Mukerji Tapan , Mavko Gary
Published: October 2002

A simple new technique predicts the high‐ and low‐frequency saturated velocities in anisotropic rocks entirely in terms of measurable dry rock properties without the need for idealized crack geometries. Measurements of dry velocity versus pressure and porosity versus pressure contain all of the necessary information for predicting the frequency‐dependent effects of fluid saturation. Furthermore, these measurements automatically incorporate all pore interaction, so there is no limitation to low crack density. The velocities are found to depend on five key interrelated variables: frequency, the distribution of compliant crack‐like porosity, the intrinsic or noncrack anisotropy, fluid viscosity and compressibility, and effective pressure. The sensitivity of velocities to saturation is generally greater at high frequencies than low frequencies. The magnitude of the differences from dry to saturated and from low frequency to high frequency is determined by the compliant or crack‐like porosity. Predictions of saturated velocities based on dry data for sandstone and granite show that compressional velocities generally increase with saturation and with frequency. However, the degree of compressional wave anisotropy may either increase or decrease upon saturation depending on the crack distribution, the effective pressure, and the frequency at which the measurements are made. Shear‐wave velocities can either increase or decrease with saturation, and the degree of anisotropy depends on the microstructure, pressure, and frequency. Consequently great care must be taken when interpreting observed velocity anisotropy for measurements at low frequencies, typical of in situ observations, will generally be different from those at high frequencies, typical of the laboratory.
The equivalent data concept applied to the interpolation of potential field data
Authors: Mendonça Carlos Alberto , Silva João B. C.
Published: October 2002

The equivalent layer calculation becomes more efficient by first converting the observed potential data set to a much smaller equivalent data set, thus saving considerable CPU time. This makes the equivalent‐source method of data interpolation very competitive with other traditional gridding techniques that ignore the fact that potential anomalies are harmonic functions. The equivalent data set is obtained by using a least‐squares iterative algorithm at each iteration that solves an underdetermined system fitting all observations selected from previous iterations and the observation with the greatest residual in the preceding iteration. The residuals are obtained by computing a set of “predicted observations” using the estimated parameters at the current iteration and subtracting them from the observations. The use of Cholesky’s decomposition to implement the algorithm leads to an efficient solution update everytime a new datum is processed. In addition, when applied to interpolation problems using equivalent layers, the method is optimized by approximating dot products by the discrete form of an analytic integration that can be evaluated with much less computational effort. Finally, the technique is applied to gravity data in a 2 × 2 degrees area containing 3137 observations, from Equant‐2 marine gravity survey offshore northern Brazil. Only 294 equivalent data are selected and used to interpolate the anomalies, creating a regular grid by using the equivalent‐layer technique. For comparison, the interpolation using the minimum‐curvature method was also obtained, producing equivalent results. The number of equivalent observations is usually one order of magnitude smaller than the total number of observations. As a result, the saving in computer time and memory is at least two orders of magnitude as compared to interpolation by equivalent layer using all observations.
Kirchhoff migration using eikonal equation traveltimes
Authors: Gray Samuel H. , May William P.
Published: October 2002

The use of ray shooting followed by interpolation of traveltimes onto a regular grid is a popular and robust method for computing diffraction curves for Kirchhoff migration. An alternative to this method is to compute the traveltimes by directly solving the eikonal equation on a regular grid, without computing raypaths. Solving the eikonal equation on such a grid simplifies the problem of interpolating times onto the migration grid, but this method is not well defined at points where two different branches of the traveltime field meet. Also, computational and data storage issues that are relatively unimportant for performance in two dimensions limit the applicability of both schemes in three dimensions. A new implementation of a gridded eikonal equation solver has been designed to address these problems. A 2-D version of this algorithm is tested by using it to generate traveltimes to migrate the Marmousi synthetic data set using the exact velocity model. The results are compared with three other images: an F-X migration (a standard for comparison), a Kirchhoff migration using ray tracing, and a Kirchhoff migration using traveltimes generated by a commonly used eikonal equation solver. The F-X‐migrated image shows the imaging objective more clearly than any of the Kirchhoff migrations, and we advance a heuristic reason to explain this fact. Of the Kirchhoff migrations, the one using ray tracing produces the best image, and the other two are of comparable quality.
Potential‐field sounding using Euler’s homogeneity equation and Zidarov bubbling
Authors: Cordell Lindrith
Published: October 2002

Potential‐field (gravity) data are transformed into a physical‐property (density) distribution in a lower half‐space, constrained solely by assumed upper bounds on physical‐property contrast and data error. A two‐step process is involved. The data are first transformed to an equivalent set of line (2-D case) or point (3-D case) sources, using Euler’s homogeneity equation evaluated iteratively on the largest residual data value. Then, mass is converted to a volume‐density product, constrained to an upper density bound, by “bubbling,” which exploits circular or radial expansion to redistribute density without changing the associated gravity field. The method can be developed for gravity or magnetic data in two or three dimensions. The results can provide a beginning for interpretation of potential‐field data where few independent constraints exist, or more likely, can be used to develop models and confirm or extend interpretation of other geophysical data sets.
On: “An integrated surface and borehole seismic case study: Fort St. John Graben area, Alberta, Canada,” by R. C. Hinds, R. Kuzminski, N. L. Anderson, and B. R. Richards (November 1993 GEOPHYSICS, 58, p. 1662–1675).
Authors: Roksandic Miodrag M.
Published: October 2002

Hinds et al.’s paper is an interesting case history describing the acquisition and interpretive processing of VSP data and presenting an integrated interpretation of well log, surface seismic, and vertical seismic profile data. However, a question of principle arises. What is an integrated interpretation?
Nonhyperbolic reflection moveout in anisotropic media
Authors: Tsvankin Ilya , Thomsen Leon
Published: October 2002

The standard hyperbolic approximation for reflection moveouts in layered media is accurate only for relatively short spreads, even if the layers are isotropic. Velocity anisotropy may significantly enhance deviations from hyperbolic moveout. Nonhyperbolic analysis in anisotropic media is also important because conventional hyperbolic moveout processing on short spreads is insufficient to recover the true vertical velocity (hence the depth). We present analytic and numerical analysis of the combined influence of vertical transverse isotropy and layering on long‐spread reflection moveouts. Qualitative description of nonhyperbolic moveout on “intermediate” spreads (offset‐to‐depth ratio x/z  < 1.7–2) is given in terms of the exact fourth‐order Taylor series expansion for P, SV, and P‐SV traveltime curves, valid for multilayered transversely isotropic media with arbitrary strength of anisotropy. We use this expansion to provide an analytic explanation for deviations from hyperbolic moveout, such as the strongly nonhyperbolic SV‐moveout observed numerically in the case where δ < ε. With this expansion, we also show that the weak anisotropy approximation becomes inadequate (to describe nonhyperbolic moveout) for surprisingly small values of the anisotropies δ and ε. However, the fourth‐order Taylor series rapidly loses numerical accuracy with increasing offset. We suggest a new, more general analytical approximation, and test it against several transversely isotropic models. For P‐waves, this moveout equation remains numerically accurate even for substantial anisotropy and large offsets. This approximation provides a fast and effective way to estimate the behavior of long‐spread moveouts for layered anisotropic models.
Wave‐equation extrapolation‐based multiple attenuation: 2-D filtering in the f-k domain
Authors: Zhou Binzhong , Greenhalgh Stewart A.
Published: October 2002

A new nonlinear filter for wave‐equation extrapolation‐based multiple suppression is designed in the f-k domain. The realization of the new filter in the f-k domain is an extension of the conventional f-k dip filter. However, the new demultiple filter is superior to the conventional f-k dip filter in the sense that the multiple reject zones are determined automatically (based on the information of the input original data and the multiple model traces obtained by the wave‐extrapolation method) rather than by prior information on multiple moveout (dip) range. Therefore, it can easily cope with situations such as aliasing and the mixture of energy from multiples and primaries in the same quadrant. The new filter is smooth on the boundary of the reject area. Numerical examples demonstrate that the new filter is equivalent to the conventional f-k dip filter in multiple suppression for simple situations. However, when the multiples and primaries are mixed in the same quadrant and have only slight difference in dip, the new filter offers significant advantages over the conventional technique.
A dispersive‐wave processing technique for estimating formation shear velocity from dipole and Stoneley waveforms
Authors: Tang X. M. , Reiter E. C. , Burns D. R.
Published: October 2002

A model‐guided dispersive‐wave processing technique has been developed to estimate formation shear‐wave velocity from borehole acoustic logging waveforms. These waveform data can be the Stoneley waves in monopole logging or the flexural waves in dipole logging. In this technique, the waveform recorded on a given receiver is compared to the waveform from a second receiver that is numerically propagated to the given receiver’s position using a trial formation shear‐wave velocity. The numerical propagation step uses the proper dispersion relation for the wave mode (dipole or Stoneley). The phase difference between the two waveforms is minimized by varying the shear velocity. The velocity value that minimizes the phase difference is chosen as the final shear velocity at which the waveforms attain the optimum phase match. In this procedure the dispersion effect is automatically accounted for by using the model theory and is demonstrated by a comparison with the results of the semblance method. Using this technique with a multiple‐shot scheme to process array acoustic logging data, formation shear velocity can be estimated to the resolution of one receiver spacing [typically 0.5 ft (0.1524 m)]. This result has been demonstrated by a field example in which the improved resolution in the shear velocity log is convincingly supported by the same character in the density log measured at one receiver spacing intervals. Shear velocity logs obtained using field Stoneley and dipole sonic data are also compared to demonstrate the ability of the technique to obtain high‐resolution formation shear velocity logs from the dispersive logging waveforms. The new technique may find very useful applications in the determination of formation shear‐wave properties using acoustic waveform logging.
Extraction of P‐ and S‐waves from the vertical component of the particle velocity at the sea floor
Authors: Amundsen Lasse , Reitan Arne
Published: October 2002

At the boundary between two solid media in welded contact, all three components of particle velocity and vertical traction are continuous through the boundary. Across the boundary between a fluid and a solid, however, only the vertical component of particle velocity is continuous while the horizontal components can be discontinuous. Furthermore, the pressure in the fluid is the negative of the vertical component of traction in the solid, while the horizontal components of traction vanish at the interface. Taking advantage of this latter fact, we show that total P‐ and S‐waves can be computed from the vertical component of the particle velocity recorded by single component geophones planted on the sea floor. In the case when the sea floor is transversely isotropic with a vertical axis of symmetry, the computation requires the five independent elastic stiffness components and the density. However, when the sea floor material is fully isotropic, the only material parameter needed is the local shear wave velocity. The analysis of the extraction problem is done in the slowness domain. We show, however, that the S‐wave section can be obtained by a filtering operation in the space‐frequency domain. The P‐wave section is then the difference between the vertical component of the particle velocity and the S‐wave component. A synthetic data example demonstrates the performance of the algorithm.
Spectral properties of the earth’s contribution to seismic resolution
Authors: Okaya David A.
Published: October 2002

Layered reflectivity sequences have spectral signatures (impulse responses) in accordance with time‐frequency transformations. These signatures are filtered by a source under the convolutional definition of a seismogram. Spectral signatures of wedge models indicate that thin layers have preferred source bandwidths needed to produce either a tuned reflection or separate interface reflections. Sources that do not include these preferred frequencies do not produce optimally imaged reflections. Criteria for the classic tuning thickness and behavior of source‐dependent amplitude versus time‐thickness crossplots are better understood in relation to the reflectivity impulse response. Reflectivity spectra indicate that higher‐order tuning thicknesses exist. Earth reflectivity also prevents the return of certain source frequencies; this behavior may possibly be an interpretive tool.
A block iterative algorithm for 3-D electromagnetic modeling using integral equations with symmetrized substructures
Authors: Xiong Zonghou , Tripp Alan C.
Published: October 2002

The integral equation method is in many cases a cost effective way of modeling the electromagnetic response of 3-D conductivity structures. Yet the requirements on computer storage and on computation time in forming and inverting the scattering matrix limit its applications for large structures.
A wraparound elimination technique for the pseudospectral wave synthesis using an antiperiodic extension of the wavefield
Authors: Furumura Takashi , Takenaka Hiroshi
Published: October 2002

The pseudospectral method (e.g., Kosloff and Baysal, 1982) is an attractive alternative to numerical modeling schemes such as finite difference or finite element because it requires several orders of magnitude less computer memory and computation time. In the pseudospectral method, the field variables are expanded in terms of Fourier interpolation polynomials which impose periodic boundary conditions on the equation of motion. Numerical differentiation is then implemented via the discrete Fourier transform. The periodicity condition causes the periodically extended wavefield on either side of the computational domain to propagate in from the sides, interfering with the actual solution. This phenomenon is called wraparound. In many current applications (e.g., Cerjan et al., 1985), an absorbing boundary condition has been used to damp the wraparound phases through a gradual reduction of the wavefield amplitude in the vicinity of the grid boundary. Such a method works effectively when the appropriate absorption coefficients are used. However, improper selection of absorption parameters can result in reflected waves of relatively large amplitude. Thus a major disadvantage of such methods is the difficulty of selecting appropriate damping parameters to suppress both the wraparound and the boundary reflected phases.
Tunnel signature prediction for a cross‐borehole seismic survey
Authors: Rechtien Richard D. , Greenfield Roy J. , Ballard Robert F.
Published: October 2002

Seismic location of tunnels or voids with a cross‐borehole survey is examined with field data and theory. The field data were taken at a site with a 2.2-m high by 2.7-m wide, roughly rectangular cross‐section tunnel, using a newly developed 1 to 5 kHz system employing a P‐wave sparker source. The synthetic records were obtained using a 2.5-D boundary‐valued solution for an explosive point source near a cylindrical void, and the solution was evaluated with the method of steepest descent. The synthetic waveforms compared well to the field data; both showed a maximum reduction of amplitude in the tunnel shadow of 8 dB and a maximum first arrival delay of 0.1 ms. Additional theoretical modeling was used to examine the variations of the received signals with tunnel size and frequency and showed amplitude reduction increased with frequency and tunnel size. Calculations showed that S‐waves scattered from the tunnel are more than 20 dB smaller than the primary P‐wave on hydrophones and more than 12 dB smaller on particle velocity sensors and so could be difficult to see in field data. The close comparison of synthetic waveforms to the field data indicate that the cylindrical model can be used to model data for roughly square cross‐section tunnels or voids, as well as for circular cross‐section tunnels, and thus is useful for data interpretation and survey planning.
Preferential continuation for potential‐field anomaly enhancement
Authors: Pawlowski Robert S.
Published: October 2002

A new class of filter transfer function derived from Wiener filter and Green’s equivalent layer principles is presented for upward and downward‐continuation enhancement of potential‐field data. The newly developed transfer function is called the preferential continuation operator. In contrast to the conventional continuation operator, the preferential continuation operator possesses a continuation response that acts preferentially upon a specific band of the observed potential field’s Fourier amplitude spectrum. The transfer function response approaches the response of an all‐pass filter away from this band. This response characteristic is useful for at least two common potential‐field signal enhancement applications. First, it is possible with preferential upward continuation to attenuate shallow‐source, short‐wavelength, potential‐field signals while minimally attenuating deep‐source, long wavelength signals (as often happens after application of conventional upward continuation) Second, it is possible with preferential downward continuation to enhance deep‐source, long wavelength signals without overamplifying shallow‐source, short‐wavelength signals (as often happens after application of conventional downward continuation) Preferential continuation, used qualitatively for anomaly enhancement, ably overcomes these two limitations of conventional continuation enhancement.
On: “Linear and parabolic τ-p transforms revisited” by B. Zhou and S.A. Greenhalgh (July 1994 GEOPHYSICS, p. 1133–1149).
Authors: Mars Jerome , Rector James W.
Published: October 2002

In this interesting paper, Zhou and Greenhalgh proposed new derivations for linear and parabolic τ-p transforms in the continuous domain. For linear τ-p transform, two versions to construct τ-p transforms pairs are presented.
Crosswell methods: Where are we, where are we going?
Authors: Rector James W.
Published: October 2002

This special issue on crosswell methods was constructed in response to the large number of crosswell papers submitted during 1993 and 1994. The editorial staff felt that rather than distributing these papers throughout the year the society would be better served by having an archival volume composed completely of crosswell‐related papers. This was not a publicly solicited issue, and we undoubtedly did not receive some excellent papers that may have been submitted with a public solicitation. Nevertheless, we feel that this volume is an excellent snapshot of crosswell technology as it stood in 1993–1994.
Time‐lapse crosswell seismic tomography to characterize flow structure in the reservoir during the thermal stimulation
Authors: Lee Doo Sung , Stevenson Veronica M. , Johnston Phil F. , Mullen C. E.
Published: October 2002

Time‐lapse crosswell seismic tomography data, recorded with an interval of six months, indicate a strong directional thermal response in a fractured eolian sandstone reservoir at a five‐spot thermal stimulation site in the South Casper Creek oil field, Wyoming. The seismic thermal response depicted on the tomogram and in conjunction with the geological data from cores and a wireline log, reveals the multichannel flow mechanism in the reservoir formation. The three factors that control steam or heat propagation are the fractures, the directional permeability existing in the rock matrix, and the fault. Crosswell tomograms imply that the primary fluid flow is through fractures oriented north‐south, whereas the secondary fluid flow is through the matrix in the direction of maximum horizontal permeability. The thermal response expressed on the tomogram infers that a fault oriented N80°E offsets flow units and acts as a flow barrier or baffle. The flow structure implied by the crosswell seismic tomography is strikingly different from the initial conjecture, as deduced from engineering perception based on geological reasoning. However, the tomographic implications were supported by both a tracer test and fluid temperature measurements at the four producing wells around the injector.
Theoretical and practical considerations for crosswell electromagnetic tomography assuming a cylindrical geometry
Authors: Alumbaugh David L. , Morrison H. Frank
Published: October 2002

An iterative Born imaging scheme is employed to analyze the resolution properties of crosswell electromagnetic tomography. The imaging scheme assumes a cylindrical symmetry about a vertical magnetic dipole source and employs approximate forward modeling at each iteration to update the internal electric fields. Estimation of the anomalous conductivity is accomplished through least‐squares inversion. Much of the mathematical formulation of this diffusion process appears similar to the analysis of wavefield solutions, but the attenuation implicit in the complex propagation constant invalidates many of the accepted wavefield criteria for resolution. Images of illustrative models show that vertical resolution improves with increasing frequency and with increased spatial sampling density. In addition, greater conductivity contrasts between the target and the background can result in better resolution. The horizontal resolution depends on the maximum aperture that is employed and with increasing frequency, larger apertures are needed to obtain optimal results. However, the maximum aperture that can be employed, and thus the horizontal resolution, is limited by the rate of attenuation and the noise present in the measurements. Weighting the long‐offset data equally with the zero‐offset data can improve the resolution if the noise is not a function of the dynamic range of the measurement system. At lower frequencies, the resolution can be improved by measuring both the horizontal and vertical components of the magnetic fields. In addition, multiple frequencies can be employed to improve the resolution for limited aperture measurements. The general applicability of the cylindrically symmetric geometry is examined by comparing the 2-D sensitivity functions to those produced by a 2.5-D model, and by imaging a 3-D body with the 2-D iterative Born scheme. For borehole separations greater than five skin depths it is demonstrated that the measurements, and thus the images, are not affected by the geometry of the conductive zone outside of the interwell plane. Thus the 2-D imaging scheme can be employed in these situations. For borehole separations less than five skin depths, artifacts are produced in the images which will lead to faulty interpretations.
Predicting stress‐induced velocity anisotropy in rocks
Authors: Mavko Gary , Mukerji Tapan , Godfrey Nicola
Published: October 2002

A simple transformation, using measured isotropic [Formula: see text] and [Formula: see text] versus hydrostatic pressure, is presented for predicting stress‐induced seismic velocity anisotropy in rocks. The compliant, crack‐like portions of the pore space are characterized by generalized compressional and shear compliances that are estimated from the isotropic [Formula: see text] and [Formula: see text]. The physical assumption that the compliant porosity is crack‐like means that the pressure dependence of the generalized compliances is governed primarily by normal tractions resolved across cracks and defects. This allows the measured pressure dependence to be mapped from the hydrostatic stress state to any applied nonhydrostatic stress. Predicted P‐ and S‐wave velocities agree reasonably well with uniaxial stress data for Barre Granite and Massillon Sandstone. While it is mechanically similar to methods based on idealized ellipsoidal cracks, the approach is relatively independent of any assumed crack geometry and is not limited to small crack densities.
Plumes: Response of time migration to lateral velocity variation
Authors: Bevc Dimitri , Black James L. , Palacharla Gopal
Published: October 2002

We analyze how time migration mispositions events in the presence of lateral velocity variation by examining the impulse response of depth modeling followed by time migration. By examining this impulse response, we lay the groundwork for the development of a remedial migration operator that links time and depth migration. A simple theory by Black and Brzostowski predicted that the response of zero‐offset time migration to a point diffractor in a v(x, z) medium would be a distinctive, cusp‐shaped curve called a plume. We have constructed these plumes by migrating synthetic data using several time‐migration methods. We have also computed the shape of the plumes by two geometrical construction methods. These two geometrical methods compare well and explain the observed migration results. The plume response is strongly influenced by migration velocity. We have studied this dependency by migrating synthetic data with different velocities. The observed velocity dependence is confirmed by geometrical construction. A simple first‐order theory qualitatively explains the behavior of zero‐offset time migration, but a more complete understanding of migration velocity dependence in a v(x, z) medium requires a higher order finite‐offset theory.
Information on elastic parameters obtained from the amplitudes of reflected waves
Authors: Dȩbski Wojciech , Tarantola Albert
Published: October 2002

Seismic amplitude variation with offset data contain information on the elastic parameters of geological layers. As the general solution of the inverse problem consists of a probability over the space of all possible earth models, we look at the probabilities obtained using amplitude variation with offset (AVO) data for different choices of elastic parameters. A proper analysis of the information in the data requires a nontrivial definition of the probability defining the state of total ignorance on different elastic parameters (seismic velocities, Lamé’s parameters, etc.). We conclude that mass density, seismic impedance, and Poisson’s ratio constitute the best resolved parameter set when inverting seismic amplitude variation with offset data.
Simple time‐variant, band‐pass filtering by operator scaling
Authors: Park Choonbyong , Black Ross A.
Published: October 2002

A convolutional method of time‐variant, band‐pass filtering presented shows that a change of filter cutoff frequencies with time is achieved by frequency scaling the amplitude spectrum of a reference operator. According to the scaling property of the Fourier transform, this frequency scaling is actually accomplished by a simple time‐domain scaling of the reference operator in which the filter operator at a sample point on a seismogram is obtained by compressing the reference operator after multiplication by a constant value. Therefore, the length of filter operator changes as the cutoff frequencies and the pass band change with time; the higher the cutoff frequencies and the broader the passband, the shorter the operator length. The algorithm does not involve any complex‐valued arithmetic that may significantly reduce the computational efficiency if a small computer is used. Because the time‐variant convolution formula is exact, the change of cutoff frequencies is not limited to slowly varying or monotonic variations used in other algorithms. The way of changing cutoff frequencies restricts the passband of the filter to a constant value in terms of octaves. However, this restriction can be relaxed significantly in practical usage by a cascaded implementation if the Nyquist frequency is well above the passband of the filter. Computational efficiency of the method is quite comparable to that of the time‐invariant, band‐pass filtering. Tests of the method on both real and synthetic data sets confirm the effectiveness of the filter.
3-D inversion of magnetic data
Authors: Li Yaoguo , Oldenburg Douglas W.
Published: October 2002

We present a method for inverting surface magnetic data to recover 3-D susceptibility models. To allow the maximum flexibility for the model to represent geologically realistic structures, we discretize the 3-D model region into a set of rectangular cells, each having a constant susceptibility. The number of cells is generally far greater than the number of the data available, and thus we solve an underdetermined problem. Solutions are obtained by minimizing a global objective function composed of the model objective function and data misfit. The algorithm can incorporate a priori information into the model objective function by using one or more appropriate weighting functions. The model for inversion can be either susceptibility or its logarithm. If susceptibility is chosen, a positivity constraint is imposed to reduce the nonuniqueness and to maintain physical realizability. Our algorithm assumes that there is no remanent magnetization and that the magnetic data are produced by induced magnetization only. All minimizations are carried out with a subspace approach where only a small number of search vectors is used at each iteration. This obviates the need to solve a large system of equations directly, and hence earth models with many cells can be solved on a deskside workstation. The algorithm is tested on synthetic examples and on a field data set.
Fast inversion of formation permeability from Stoneley wave logs using a simplified Biot‐Rosenbaum model
Authors: Tang Xiaoming , Cheng C. H.
Published: October 2002

This paper describes a fast algorithm for estimating formation permeability from Stoneley wave logs. The procedure uses a simplified Biot‐Rosenbaum model formulation. The input to the inversion is the Stoneley‐wave spectral amplitudes at each receiver position, the bore‐hole fluid properties (velocity and density), the borehole caliper log, the formation density and porosity (from log data), and the compressional and shear velocities for the interval of interest. The model uses the borehole caliper and elastic properties to compute the Stoneley wave excitation (that is, predicted amplitude without permeability effects) as a function of frequency, and the porosity and permeability to compute the fluid flow amplitude reduction. This method also uses a reference depth of known permeability and compares amplitude variations at other depths relative to the reference depth. The permeability value obtained from the inversion represents the best fit over all receivers and all relevant frequencies. A processing example is shown to demonstrate the ability of this technique to extract formation permeability from Stoneley wave logs.
Finite‐difference depth migration of exploration‐scale 3-D seismic data
Authors: Mufti Irshad R. , Pita Jorge A. , Huntley Ross W.
Published: October 2002

Most migration methods are based on a variety of one‐way approximations of the wave equation, one noticeable exception being the finite‐difference, reverse‐time, depth migration algorithm. Since this method requires enormous computer resources as compared to all other migration algorithms, its applications have been restricted primarily to 2-D synthetic data. Consequently, its potential for migrating poststack real data and imaging complex 3-D structures by constructive interference of wavefronts has not been exploited. Finite‐difference depth migration is subject to the same conditions for avoiding grid dispersion and numerical instability as are forward modeling techniques. For field data, this can necessitate interpolation both in space and time. One can, however, exploit the fact that in forward modeling one tries to generate accurate reflection signals; whereas in migration, the primary objective is to accomplish imaging from the prerecorded signals, which may be attainable under less stringent conditions. Indeed our investigations indicate that accurate imaging can be clone without making rigid provisions for grid dispersion in the lateral direction, which reduces or eliminates the use of interpolated traces. In the case of 3-D data, the elimination of an interpolation step reduces the computational task by a factor of 50 or more, with similar reductions in memory requirements. Further efficiency can be achieved by using a nonuniform grid in the vertical direction that adapts to the expansion and contraction of the downward propagating wavelet in response to variations in velocity and frequency content of the input data. These steps reduce the time required to do high‐resolution migration of large 3-D data volumes to several hours or less, depending on the machine and the size of the input data. Two applications on large, exploration‐scale, 3-D field data carried out on a massively‐parallel machine are presented. We compare our results with the results obtained by the Hale‐McClellan algorithm.
Suppression of sea‐floor‐scattered energy using a dip‐moveout approach—Application to the mid‐ocean ridge environment
Authors: Kent Graham M. , Kim Isaac I. , Harding Alistair J. , Detrick Robert S. , Orcutt John A.
Published: October 2002

Multichannel seismic (MCS) images are often contaminated with in‐ and out‐of‐plane scattering from the sea floor. This problem is especially acute in the mid‐ocean ridge environment where sea‐floor roughness is pronounced. Energy shed from the unsedimented basaltic sea floor can obscure primary reflections such as Moho, and scattering off of elongated sea‐floor features like abyssal hills and fault scarps can produce linear events in the seismic data that could be misinterpreted as subsurface reflections. Moreover, stacking at normal subsurface velocities may enhance these water‐borne events, whose stacking velocity depends on azimuth and generally increases with time, making them indistinguishable from subsurface arrivals. To suppress scattered energy in deep water settings, we propose a processing scheme that invokes the application of dip moveout (DMO) to deliberately increase the differential moveout between sea‐floor‐scattered and subsurface events, thereby facilitating the removal of unwanted energy in the stacked section. After application of DMO, all sea‐floor scatterers stack at the water velocity, while subsurface reflections like Moho still stack at their original velocity. The application of DMO in this manner is contrary to the intended use that reduces the differential moveout between dipping events and allows a single stacking velocity to be used. Unlike previous approaches to suppress scattered energy, dip filtering is applied in the common‐midpoint (CMP) domain after DMO. Moveover, our DMO‐based approach suppresses out‐of‐plane scattering, and therefore is not limited to removal of in‐plane scattering as is the case with shot and receiver dip filtering techniques. The success of our DMO‐based suppression scheme is limited to deep water (a few kilometers of water depth for conventional offsets), where the traveltime moveout of energy scattered from the sea floor has a hyperbolic moveout with a stacking velocity that depends on the cosine of the scatterer steering angle in a manner analogous to how the moveout of a dipping reflector depends on the dip angle. The application of DMO‐based suppression to synthetics and MCS data collected along the southern East Pacific Rise demonstrates the effectiveness of our approach. Cleaner images of primary reflectors such as Moho are produced, even though present shot coverage along the East Pacific Rise is unduly sparse, resulting in a limited effective spatial bandwidth.
Fowler DMO and time migration for transversely isotropic media
Authors: Anderson John , Alkhalifah Tariq , Tsvankin Ilya
Published: October 2002

The main advantage of Fowler’s dip‐moveout (DMO) method is the ability to perform velocity analysis along with the DMO removal. This feature of Fowler DMO becomes even more attractive in anisotropic media, where imaging methods are hampered by the difficulty in reconstructing the velocity field from surface data. We have devised a Fowler‐type DMO algorithm for transversely isotropic media using the analytic expression for normal‐moveout velocity. The parameter‐estimation procedure is based on the results of Alkhalifah and Tsvankin showing that in transversely isotropic media with a vertical axis of symmetry (VTI) the P‐wave normal‐moveout (NMO) velocity as a function of ray parameter can be described fully by just two coefficients: the zero‐dip NMO velocity [Formula: see text] and the anisotropic parameter η (η reduces to the difference between Thomsen parameters ε and δ in the limit of weak anisotropy). In this extension of Fowler DMO, resampling in the frequency‐wavenumber domain makes it possible to obtain the values of [Formula: see text] and η by inspecting zero‐offset (stacked) panels for different pairs of the two parameters. Since most of the computing time is spent on generating constant‐velocity stacks, the added computational effort caused by the presence of anisotropy is relatively minor. Synthetic and field‐data examples demonstrate that the isotropic Fowler DMO technique fails to generate an accurate zero‐offset section and to obtain the zero‐dip NMO velocity for nonelliptical VTI models. In contrast, this anisotropic algorithm allows one to find the values of the parameters [Formula: see text] and η (sufficient to perform time migration as well) and to correct for the influence of transverse isotropy in the DMO processing. When combined with poststack F-K Stolt migration, this method represents a complete inversion‐processing sequence capable of recovering the effective parameters of transversely isotropic media and producing migrated images for the best‐fit homogeneous anisotropic model.
On: “Exploration of a Lignite‐Bearing Basin in Northern Ireland Using Ground and Magnetic VLF-EM Methods,” R. J. McCaffrey, John McElroy, and Graham Leslie (March‐April 1995 GEOPHYSICS, p. 408–412)
Authors: Steenland N.
Published: October 2002

This paper presents an analysis of ground magnetic and VLF-EM data over a basin of several hundred acres which is an appendage to the larger Lough Neagh autogeosynclinal basin in northeastern Ireland. There is little to do with lignite and the VLM-EM of the title. There is quite a bit to do with the magnetic sector which is, however, not analyzed by time‐proven methods of depth determination but rather by running a synthetic, one dimensional first derivative over the traverses given the name MAGGRO.
Prestack plane‐wave Kirchhoff migration in laterally varying media
Authors: Akbar Faruq E. , Sen Mrinal K. , Stoffa Paul L.
Published: October 2002

Conventional Kirchhoff migration methods are applied to seismograms in the offset‐time (x − t) domain. We describe the theory, numerical details, and examples of a prestack depth migration method in the plane‐wave domain that is valid in laterally inhomogeneous media. The theory is based on a Kirchhoff‐Helmholtz formulation of the wavefield and uses plane‐wave‐transformed shot gathers for migration. We use geometric ray theory for the source wavefield continuation operator and a plane‐wave expansion of the receiver wavefield in the integrand of the Kirchhoff‐Helmholtz integral. The source and receiver plane‐wave traveltimes are computed at each grid point in the subsurface using a finite‐difference approximation of the eikonal equation with appropriate initial and boundary conditions. We developed an efficient technique to compute imaging time by a combination of these two times. The technique allows us to design algorithms for migrating shot gather or constant ray‐parameter sections efficiently. We evaluate the efficiency and accuracy of the algorithm with three sets of synthetic data examples with varying degrees of complexity. We also compare the performance of the parallel algorithms using Parallel Virtual Machine (PVM). Migration of a marine data set results in excellent images of a mud volcano and the top of an accretionary prism of an active continental margin on the Nicoya Peninsula of Costa Rica.
Closed form solutions for the geometrical spreading in inhomogeneous media
Authors: Najmi Amir‐Homayoon
Published: October 2002

True‐amplitude migration is a subject of great interest to exploration geophysicists. The procedure should provide a means of computing angle‐dependent reflection coefficients of reflectors within the Earth and is therefore essential in any AVO analysis. The migration weighting functions in the Kirchhoff integral include geometrical spreading factors whose determination in terms of traveltime functions and their end point derivatives are the main subject of this paper. Such “closed form” solutions for the geometrical spreading of an acoustic P‐wave in an isotropic and inhomogeneous medium are presented, and their symmetry properties are used to simplify the Kirchhoff integral migration weight functions. Emphasis is put on derivation of the equations based on simple physical and mathematical requirements. The result of applying the derived forms to a synthetic example comprised of a velocity field that varies linearly with depth and dipping reflectors is also included. It is suggested that the migration weight functions could be simplified substantially for smooth velocity backgrounds.
Waveform‐based AVO inversion and AVO prediction‐error
Authors: Simmons James L. , Backus Milo M.
Published: October 2002

A practical approach to linear prestack seismic inversion in the context of a locally 1-D earth is employed to use amplitude variation with offset (AVO) information for the direct detection in hydrocarbons. The inversion is based on the three‐term linearized approximation to the Zoeppritz equations. The normal‐incidence compressional‐wave reflection coefficient [Formula: see text] models the background reflectivity in the absence of hydrocarbons and incorporates the mudrock curve and Gardner’s equation. Prediction‐error parameters, [Formula: see text] and [Formula: see text], represent perturbations in the normal‐incidence shear‐wave reflection coefficient and the density contribution to the normal incidence reflectivity, respectively, from that predicted by the mudrock curve and Gardner’s equation. This prediction‐error approach can detect hydrocarbons in the absence of an overall increase in AVO, and in the absence of bright spots, as expected in theory. Linear inversion is applied to a portion of a young, Tertiary, shallow‐marine data set that contains known hydrocarbon accumulations. Prestack data are in the form of angle stack, or constant offset‐to‐depth ratio, gathers. Prestack synthetic seismograms are obtained by primaries‐only ray tracing using the linearized approximation to the Zoeppritz equations to model the reflection amplitudes. Where the a priori assumptions hold, the data are reproduced with a single parameter [Formula: see text]. Hydrocarbons are detected as low impedance relative to the surrounding shales and the downdip brine‐filled reservoir on [Formula: see text], also as positive perturbations (opposite polarity relative to [Formula: see text]) on [Formula: see text] and [Formula: see text]. The maximum perturbation in [Formula: see text] from the normal‐incidence shear‐wave reflection coefficient predicted by the a priori assumptions is 0.08. Hydrocarbon detection is achieved, although the overall seismic response of a gas‐filled thin layer shows a decrease in amplitude with offset (angle). The angle‐stack data (70 prestack ensembles, 0.504–1.936 s time range) are reproduced with a data residual that is 7 dB down. Reflectivity‐based prestack seismograms properly model a gas/water contact as a strong increase in AVO and a gas‐filled thin layer as a decrease in AVO.
The impact of migration on AVO
Authors: Mosher Charles C. , Keho Timothy H. , Weglein Arthur B. , Foster Douglas J.
Published: October 2002

Amplitude variation with offset (AVO) analysis is often limited to areas where multidimensional propagation effects such as reflector dip and diffractions from faults can be ignored. Migration‐inversion provides a framework for extending the use of seismic amplitudes to areas where structural or stratigraphic effects are important. In this procedure, sources and receivers are downward continued into the earth using uncollapsed prestack migration. Instead of stacking the data as in normal migration, the prestack migrated data are used in AVO analysis or other inversion techniques to infer local earth properties. The prestack migration can take many forms. In particular, prestack time migration of common‐angle sections provides a convenient tool for improving the lateral resolution and spatial positioning of AVO anomalies. In this approach, a plane‐wave decomposition is first applied in the offset direction, separating the wavefield into different propagating angles. The data are then gathered into common‐angle sections and migrated one angle at a time. The common‐angle migrations have a simple form and are shown to adequately preserve amplitude as a function of angle. Normal AVO analysis is then applied to the prestack migrated data. Examples using seismic lines from the Gulf of Mexico show how migration improves AVO analysis. In the first set of examples, migration is shown to improve imaging of subtle spatial variations in bright spots. Subsequent AVO analysis reveals dim spots associated with dry‐hole locations that were not resolvable using traditional processing techniques, including both conventional AVO and poststack migration. A second set of examples shows improvements in AVO response after migration is used to reduce interference from coherent noise and diffractions. A final example shows the impact of migration on the spatial location of dipping AVO anomalies. In all cases, migration improves both the signal‐to‐noise ratio and spatial resolution of AVO anomalies.