bluuebunny/crossref_metadata_2025 huggingface dataset:
Efficient 3-D viscoelastic modeling with application to near‐surface land seismic data
Authors: Xu Tong , McMechan George A.
Published: October 2002

Three‐dimensional viscoelastic modeling is implemented by reparameterizing the viscoelastic wave equation for a standard linear solid. The formulation uses weighting factors corresponding to relaxation frequencies and composite memory variables. This novel 3-D formulation requires less computer memory than the traditional relaxation time formulation because one set of relaxation frequencies can be used for all mechanisms for all parts of a model, and only three sets of composite memory variables are needed rather than the seven used in the standard implementation, giving a net reduction of 40% in the total required memory. Computational time is also reduced approximately 25% because of reduced input/output (I/O). The algorithm is applied to 3-D modeling of the viscoelastic response of the near‐surface structure beneath a 3-D reflection survey in the Ouachita frontal thrust zone of southeast Oklahoma. Comparison of the 3-D field data with both viscoelastic and elastic response clearly demonstrates the importance of inclusion of viscoelasticity when accurate amplitude fitting is desired. Observed amplitude and traveltime variations can be explained by shallow velocity and Q distributions obtained independently by 3-D tomography.
3-D finite‐difference elastic wave modeling including surface topography
Authors: Hestholm Stig , Ruud Bent
Published: October 2002

Three‐dimensional finite‐difference (FD) modeling of seismic scattering from free surface topography has been pursued. We have developed exact 3-D free surface topography boundary conditions for the particle velocities. A velocity‐stress formulation of the full elastic wave equations together with the boundary conditions has been numerically modeled by an eighth‐order FD method on a staggered grid. We give a numerical stability criterion for combining the boundary conditions with curved‐grid wave equations, where a curved grid represents the physical medium with topography. Implementation of this stability criterion stops instabilities from arising in areas of steep and rough topographies. We have simulated scattering from teleseismic P-waves using a plane, vertically incident wavefront and real topography from a 40 × 40 km area centered at the NORESS array of seismic receiver stations in southeastern Norway. Synthetic snapshots and seismograms of the wavefield show clear conversion from P-waves to Rg (short period fundamental mode Rayleigh) waves in an area of rough topography approximately 10 km east of NORESS. This result is consistent with numerous observations.
Stationarity transformation of multiples to improve the performance of predictive deconvolution
Authors: Schoenberger Michael , Houston Louis M.
Published: October 2002

Predictive deconvolution is a very effective multiple attenuator for zero‐offset data and for nonzero offset data acquired in water depths less than 100 m. However, predictive deconvolution’s efficacy degrades rapidly with offset, a degradation that correlates highly with nonstationarity of the primary‐to‐multiple traveltime separation. For model data, predictive deconvolution’s performance degrades by a factor of two when the multiple period changes by only 5 ms (20% of the seismic wavelet’s dominant period) within the deconvolution gate. For two‐thirds of the model‐data offsets, the change in primary‐multiple separation on each trace exceeds 40% of the dominant period, and deconvolution is completely ineffective at removing multiples. We develop a stationarity transform, which is a moveout operation or a time‐variable time shift that can be applied separately to each trace. The stationarity transform stabilizes the traveltime separation between primary and first‐order multiple, based upon the assumptions of hyperbolic moveout, layer‐cake geology, and Dix multiple velocities. After applying the stationarity transform to a model data set consisting of primaries and first‐order multiples only, predictive deconvolution suppresses multiples at the theoretical suppression limit for all offsets. Furthermore, predictive deconvolution is equally effective for low‐frequency and high‐frequency wavelets. When the data set is made more realistic by including higher‐order multiples, predictive deconvolution’s ability to suppress multiple reflections degrades only slightly with offset. Stationarity transformation also improves predictive deconvolution’s multiple suppression on a real data set. Because the real data set is from a region where the water depth is shallower than 100 m, predictive deconvolution suppresses multiples effectively on the near‐ and middle‐offset traces, even without stationarity transformation. However, on the farthest offsets, stationarity transformation improves the efficacy of predictive deconvolution significantly.
Nonreflecting boundary condition in finite‐element formulation for an elastic wave equation
Authors: Sarma G. S. , Mallick K. , Gadhinglajkar V. R.
Published: October 2002

Numerical modeling of seismic wavefields using finite‐difference or finite‐element methods requires truncation of the model to finite computational domains. It is well known that the edges of such truncated models give boundary reflections on the synthetic seismograms. An essential step to successful numerical modeling is to eliminate these reflections. We present a simple scheme that eliminates such boundary reflections when computing synthetics. We also demonstrate the efficiency and robustness of our method on a variety of geological models.
Removal of diurnal tidal effects from an ultra‐high‐resolution 3-D marine seismic survey on the continental shelf offshore New Jersey
Authors: Luhurbudi Eddy C. , Pulliam Jay , Austin James A. , Saustrup Steffen , Stoffa Paul L.
Published: October 2002

An ultra‐high‐resolution 3-D, single‐channel seismic survey was performed off the coast of New Jersey in 1993 to study the late Quaternary history of sedimentation on the northwest Atlantic continental margin (see Davies et al., 1992) as a part of the Office of Naval Research STRATAFORM initiative (Nittrouer and Kravitz, 1995). Three different sets of profiles were acquired (Figure 1), but only the set with highest spatial density is discussed here. A single ten‐element receiver recorded 300 ms of data for every shot during the survey, which covers a total area of 0.6 km (north‐south) × 7.75 km (east‐west) (see Table 1). The deep‐towed Huntec™ source (deployed at ∼30 m depth) produced frequencies of 500 to 3500 Hz; a band‐pass filter with corner frequencies at 1000 and 3500 Hz was applied during preprocessing.
Shallow VSP work in the U.S. Appalachian coal basin
Authors: Gochioco Lawrence M.
Published: October 2002

Most geophysical applications in North American coal exploration have centered around the conventional surface seismic reflection method to provide continuous subsurface coverage for evaluating both good and anomalous coal reserve areas (Ruskey, 1981; Dobecki and Bartel, 1982; Greaves, 1984; Lawton, 1985; Lyatsky and Lawton, 1988; Gochioco and Cotten, 1989; Lawton and Lyatsky, 1989; Gochioco and Kelly, 1990; Gochioco, 1991; Henson and Sexton, 1991). The surface seismic reflection method, however, has inherent resolution limitations because the seismic wavelet must propagate substantial distances through the weathered layer, resulting in rapid attenuation of the desired higher frequencies. Since the depths and thicknesses of coal seams are usually known before‐hand, it is imperative that the seismic reflection associated with the target coal seam is absolutely identified in the seismic section to avoid misinterpretations. However, it is common that checkshot data and sonic and density logs are not available to generate synthetic seismograms to assist in the interpretation of coal seismic data. To overcome some of these limitations, the vertical seismic profiling (VSP) technique was tested in a coal exploration program to provide additional information for correlation with surface seismic reflection [or common‐depth‐point (CDP)] data and a synthetic seismogram generated from density and sonic logs.
Mapping plate boundaries using TEM method along the Longitudinal Valley, Taiwan
Authors: Chen Chow‐Son
Published: October 2002

The transient electromagnetic (TEM) method was used to map plate boundaries in the Longitudinal Valley (LV), Taiwan. The SIROTEM in‐loop configuration with square transmitting loops 90 to 200 m on a side were used for this survey. More than 350 soundings were conducted in the valley. The field data were inverted by a smooth model inversion, and the soundings resolved more than 300 m beneath the LV. A set of geoelectric maps containing horizontal slices at different depths and vertical profiles from north to south along the LV have been constructed based on these inversion results. Based on the TEM sounding results, one predominant electrical discontinuity can be recognized in the LV that agrees well with the known suture trace on the surface between the Philippine Sea and the Eurasian plates. Moreover, the fact that the sedimentation trend thickened southward in the LV supports the geologic viewpoint that the LV is undergoing severe compression‐closure action; the northern part of the valley seems to have been closed already, whereas the southern part has not.
The effects of pore‐fluid salinity on ultrasonic wave propagation in sandstones
Authors: Jones Simon M. , McCann Clive , Astin Timothy R. , Sothcott Jeremy
Published: October 2002

Petrophysical interpretation of increasingly refined seismic data from subsurface formations requires a more fundamental understanding of seismic wave propagation in sedimentary rocks. We consider the variation of ultrasonic wave velocity and attenuation in sandstones with pore‐fluid salinity and show that wave propagation is modified in proportion to the clay content of the rock and the salinity of the pore fluid. Using an ultrasonic pulse reflection technique (590–890 kHz), we have measured the P-wave and S-wave velocities and attenuations of 15 saturated sandstones with variable effective pressure (5–60 MPa) and pore‐fluid salinity (0.0–3.4 M). In clean sandstones, there was close agreement between experimental and Biot model values of [Formula: see text], but they diverged progressively in rocks containing more than 5% clay. However, this effect is small: [Formula: see text] changed by only 0.6% per molar change in salinity for a rock with a clay content of 29%. The variation of [Formula: see text] with brine molarity exhibited Biot behavior in some samples but not in others; there was no obvious relationship with clay content. P-wave attenuation was independent of pore‐fluid salinity, while S-wave attenuation was weakly dependent. The velocity data suggest the frame bulk and shear moduli of sandstones are altered by changes in the pore‐fluid salinity. One possible mechanism is the formation damage caused by clay swelling and migration of fines in low‐molarity electrolytes. The absence of variation between the attenuation in water‐saturated and brine‐saturated samples indicates the attenuation mechanism is relatively unaffected by changes in the frame moduli.
What is noise?
Authors: Scales John A. , Snieder Roel
Published: October 2002

The concept of “noise” plays a crucial role in the statistical analysis of data. As an example of a noisy record consider Figure 1 that shows the ground motion of the seismological station NE51 in St. Petersburg after an earthquake in Egypt. (In earthquake seismology, periods may be orders of magnitude larger than in exploration seismology, but the principles are the same.) This time series shows no distinct arrivals or other apparent signatures of an organized nature. Given the proximity of the recording station to a major population center and to the coast, such a noisy record does not seem to be very surprising.
Errors in the total Bouguer reduction
Authors: Talwani Manik
Published: October 2002

This short note discusses various errors in the Bouguer reduction that have been discussed recently in the literature. It also discusses two other errors arising out of the “indirect effect” and the uncertainty in the value of the universal constant of gravitation, G, that previously have not been discussed extensively in the literature.
Transmission and detection of guided seismic waves in attenuating media
Authors: Parra Jorge O. , Zook Brian J. , Xu Pei‐Cheng , Brown Raymon L.
Published: October 2002

We can use guided seismic waves to map properties of reservoirs between wells, with the low‐velocity layers acting as waveguides. When guided waves are detected, they are an indication of the continuity of the bed examined. Guided waveforms are characterized by time‐frequency representations to study important physical properties of the beds acting as waveguides. We used full waveform seismic modeling in viscoelastic media to examine the required velocity contrasts and distances over which guided‐wave signals can be used. In one set of models, sandstones are the central waveguide lithology; in another set, shales. We applied these models, referred to here collectively as shaly sandstone waveguides, to a range of geological circumstances where either the sands or the shales represent the low‐velocity layers within a reservoir. To study the distances over which guided waves can be detected, we compared the amplitudes of the signals computed for the models, using a realistic source strength, to the signal levels determined from published borehole noise studies. In shaly sandstone waveguides, we find it is feasible to use particle velocity measurements to record guided waves above seismic noise levels in the frequency range of 60 to 800 Hz at well separations exceeding a distance of 800 m. However, pressure detectors such as hydrophones may only be useful up to distances of 400 m between wells. In addition to the issues of shaly sandstone waveguides and practical distances between wells, we present an application of guided waves using crosswell seismic data from the Gypsy test site in Oklahoma (a site originally established by British Petroleum). In this field example within a sandstone reservoir, we demonstrate the sensitivity of leaky mode amplitudes to source‐receiver location. Another telltale characteristic of continuity in the type of reservoir studied at the Gypsy test site, where there is a low shear velocity contrast between the host medium and the waveguide, is the head wave followed by the leaky mode.
Imaging a shallow aquifer in temperate glacial sediments using seismic reflection profiling with DMO processing
Authors: Bradford John H. , Sawyer Dale S. , Zelt Colin A. , Oldow John S.
Published: October 2002

We acquired a seismic reflection profile to image a shallow (<100 m) aquifer system on a small island in Puget Sound, north of Seattle, Washington. The aquifer system is comprised of temperate glacial sedimentary strata, with the primary aquifer lying approximately 45 m below the surface. We chose the site because there are water‐well boring descriptions available and a sea cliff parallels the profile location, providing stratigraphic control. A 20-lb (9-kg) weight drop was used as an energy source to acquire a 30-fold common‐midpoint (CMP) reflection profile along a 400-m line. Analysis of the recorded wavefield was not straightforward because of complex stratigraphy and the presence of a laterally variable thin bed (∼5–15 m) of high‐impedance lodgement till within a few meters of the surface. We used finite‐difference modeling to determine that conventional CMP processing would provide a reasonable approximation for imaging strata in the primary target zone, roughly 20 m below the high velocity till. For CMP processing, we analyzed the velocity structure using iterative dip moveout (DMO) velocity analysis. Use of this method results in a velocity field that dramatically improves the poststack depth‐migrated section.
A noninvasive shallow seismic source comparison on the Oak Ridge Reservation, Tennessee
Authors: Doll William E. , Miller Richard D. , Xia Jianghai
Published: October 2002

Nine seismic sources were compared in preparation for production seismic reflection profiling to about 500 m depth at a hazardous waste site on the Oak Ridge Reservation, Tennessee. Test data provided a 125-shotpoint common midpoint profile and a walkaway vertical seismic profile for each source. Sources tested included five swept sources and four impulsive sources. Eight of the sources were “noninvasive,” in that they would not penetrate the ground surface. When spectral whitening methods were applied to the data, the IVI Minivib provided the best image of the subsurface on the basis of continuity and clarity of reflections. Without prewhitening, the performance of the IVI Minivib and the Bison elastic wave generator were similar.
Muting the noise cone in near‐surface reflection data: An example from southeastern Kansas
Authors: Baker Gregory S. , Steeples Don W. , Drake Matt
Published: October 2002

A 300-m near‐surface seismic reflection profile was collected in southeastern Kansas to locate a fault(s) associated with a recognized stratigraphic offset on either side of a region of unexposed bedrock. A substantial increase in the S/N ratio of the final stacked section was achieved by muting all data arriving in time after the airwave. Methods of applying traditional seismic data processing techniques to near‐surface data (200 ms of data or less) often differ notably from hydrocarbon exploration‐scale processing (3–4 s of data or more). The example of noise cone muting used is contrary to normal exploration‐scale seismic data processing philosophy, which is to include all data containing signal. The noise cone mute applied to the data removed more than one‐third of the total data volume, some of which contains signal. In this case, however, the severe muting resulted in a higher S/N ratio in the final stacked section, even though some signal could be identified within the muted data. This example supports the suggestion that nontraditional techniques sometimes need to be considered when processing near‐surface seismic data.
Integrating high‐resolution refraction data into near‐surface seismic reflection data processing and interpretation
Authors: Miller Kate C. , Harder Steven H. , Adams Donald C. , O’Donnell Terry
Published: October 2002

Shallow seismic reflection surveys commonly suffer from poor data quality in the upper 100 to 150 ms of the stacked seismic record because of shot‐associated noise, surface waves, and direct arrivals that obscure the reflected energy. Nevertheless, insight into lateral changes in shallow structure and stratigraphy can still be obtained from these data by using first‐arrival picks in a refraction analysis to derive a near‐surface velocity model. We have used turning‐ray tomography to model near‐surface velocities from seismic reflection profiles recorded in the Hueco Bolson of West Texas and southern New Mexico. The results of this analysis are interval‐velocity models for the upper 150 to 300 m of the seismic profiles which delineate geologic features that were not interpretable from the stacked records alone. In addition, the interval‐velocity models lead to improved time‐to‐depth conversion; when converted to stacking velocities, they may provide a better estimate of stacking velocities at early traveltimes than other methods.
Recent developments in shallow‐depth electrical and electrostatic prospecting using mobile arrays
Authors: Panissod Cédric , Dabas Michel , Hesse Albert , Jolivet Alain , Tabbagh Jeanne , Tabbagh Alain
Published: October 2002

Application of mobile electrical and electrostatic quadripoles during the past ten years has allowed a considerable increase in the size of the surveyed areas, together with keeping a high spatial resolution and a reduction of the total cost of a survey. Two new developments of towed arrays are illustrated here: (1) a pole‐pole array pulled by the operator provides a lightweight solution for mapping large surfaces at a unique given depth of investigation, as shown by the prospection of the Roman‐British city of Wroxeter; and (2) a multipole, multidepth system allows a 3-D investigation of the ground resistivity, as illustrated by the experiments undertaken on the test site of Garchy and on the archaeological site of Montbaron (Indre, France).
A borehole‐to‐surface electromagnetic survey
Authors: Tseng H. -W. , Becker Alex , Wilt M. J. , Deszcz‐Pan M.
Published: October 2002

The results of a limited field trial confirm the usefulness of borehole‐to‐surface electromagnetic (EM) measurements for monitoring fluid extraction. A vertical EM profiling experiment was done at the University of California Richmond Field Station, where we simulated a brine spill plume by creating a saline water injection zone at the depth of 30 m. The data acquisition mode was analogous to the reverse vertical seismic profiling (VSP) configuration used for seismic measurements in that the EM transmitter traversed the PVC-cased borehole used for fluid injection and extraction while the receivers were deployed on the surface. The EM measurements were made at 9.6 kHz with an accuracy of 1% in signal amplitude and 1° in signal phase. Observations were taken at 5-m intervals along two intersecting profiles that were centered on the injection well and extended for 60 m on either side of it. The presence of the injected salt water, at the expected 30 m depth, was indicated clearly by differences between the pre‐extraction and postextraction data. A limited amount of numerical modeling showed that the experimental data were consistent with the presence of two superposed saline plumes. The uppermost of these, located at 26 m depth, was 2 m thick and had an area of 30 m2. The lower plume, located at 30 m, is the major cause of the observed anomaly, as it has an areal extent of 120 m2 and a thickness of 3 m. Surprisingly, the measurements were very sensitive to the presence of the cultural surficial conductivity anomalies. These spurious effects were reduced by spatial filtering of the data prior to interpretation.
Elastic reverse time migration of marine walkaway vertical seismic profiling data
Authors: Hokstad Ketil , Mittet Rune , Landrø Martin
Published: October 2002

Walkaway vertical seismic profiling (VSP) acquisition with three‐component geophones allows for direct measurement of compressional as well as shear energy. This makes full elastic reverse time migration an attractive alternative for imaging data. We present results from elastic reverse time migration of a marine walkaway VSP acquired offshore Norway. The reverse time migration scheme is based on a high‐order finite‐difference solution to the two‐way elastic wave equation. Depth images of the subsurface are constructed by correlation of forward‐ and back‐propagated elastic wavefields. In the walkaway VSP configuration, the number of shots is much larger than the number of geophone levels. Using processing methods operating in the shot/receiver domain, it is advantageous to use the reciprocal relationship between the walkaway VSP and the reverse VSP configurations. We do this by imaging each component of each geophone level as a reverse VSP common shot gather. The final images are constructed by stacking partial images from each level. The depth images obtained from the vertical components reveal the major characteristics of the geological structure below geophone depth. A graben in the base Cretaceous unconformity and a faulted coal layer can be identified. The horizontal components are more difficult to image. Compared to the vertical components, the horizontal component images are more corrupted by migration artifacts. This is because the horizontal component images are more sensitive to aperture effects and to the shear‐wave velocity macromodel. When converted to two‐way time, the migration results tie well with the surface seismic section. Comparison of fully elastic and acoustic reverse time migration shows that the vertical component is dominantly PP-reflected events, whereas the horizontal components get important contributions from PS-converted energy. The horizontal components also provide higher resolution because of the shorter wavelength of the shear waves.
Focusing aspects of the parabolic Radon transform
Authors: Maeland Einar
Published: October 2002

From a geometrical point of view, the parabolic Radon transform of a common shotpoint gather is a focusing technique where the “focal length” is determined by the velocity field. When the traveltime curves at small offset are approximated by hyperbolas, the reciprocal of the curvature of an “image” is related to the square of the curvature at zero offset of the corresponding traveltime curve. Each event on a common‐shotpoint gather will be separated by the parabolic Radon transform, and the position of the foci associated with peg‐leg multiples can be predicted. Examples on synthetic common‐shotpoint gathers illustrate the merits of the analysis.
Polarization, phase velocity, and NMO velocity of qP-waves in arbitrary weakly anisotropic media
Authors: Pšenčk Ivan , Gajewski Dirk
Published: October 2002

We present approximate formulas for the qP-wave phase velocity, polarization vector, and normal moveout velocity in an arbitrary weakly anisotropic medium obtained with first‐order perturbation theory. All these quantities are expressed in terms of weak anisotropy (WA) parameters, which represent a natural generalization of parameters introduced by Thomsen. The formulas presented and the WA parameters have properties of Thomsen’s formulas and parameters: (1) the approximate equations are considerably simpler than exact equations for qP-waves, (2) the WA parameters are nondimensional quantities, and (3) in isotropic media, the WA parameters are zero and the corresponding equations reduce to equations for isotropic media. In contrast to Thomsen’s parameters, the WA parameters are related linearly to the density normalized elastic parameters. For the transversely isotropic media with vertical axis of symmetry, the equations presented and the WA parameters reduce to the equations and linearized parameters of Thomsen. The accuracy of the formulas presented is tested on two examples of anisotropic media with relatively strong anisotropy: on a transversely isotropic medium with the horizontal axis of symmetry and on a medium with triclinic anisotropy. Although anisotropy is rather strong, the approximate formulas presented yield satisfactory results.
Asymptotic theory for imaging the attenuation factorQ
Authors: Ribodetti Alessandra , Virieux Jean
Published: October 2002

To describe accurately the propagation of elastic waves for characterizing and monitoring hydrocarbon reservoirs, as well as to obtain improved earth models, it is important to take into account seismic attenuation. We describe a method to estimate anelastic medium properties by a complete SH-waveform inversion. We use an optimization approach based on the iterative minimization of the mismatch between the seismic data and the computed response. To obtain a fast analytical imaging procedure, we include an asymptotic theory for attenuation in a linearized inverse scattering formulation. The forward modeling is solved by the Born approximation for a smooth and attenuative background medium. An asymptotic ray‐tracing method is used to calculate traveltime, amplitude, and attenuation between source, receiver, and scattering points. The resulting method is computationally efficient and allows for a variety of data‐ acquisition geometries, including those with redundant or incomplete source‐receiver coverage. Synthetic examples with realistic surface‐to‐surface geometry show an acceptable convergence in a few iterations when anomaly perturbations are less than 10% of the reference values and when associated diffracting structures are smaller than one‐tenth of the predominant seismic wavelength. Through there remains the fundamental trade‐off between density and shear modulus, the iterative asymptotic inversion is able to recover the elastic parameters (density and shear modulus) and the attenuation factor.
Side‐looking underground radar (SLUR): Physical modeling and case history
Authors: Daniels Jeffrey J. , Brower James
Published: October 2002

A modification of conventional surface ground‐penetrating radar (GPR) was conceived, tested, and successfully applied in the field at Brookhaven National Laboratory (BNL) to investigate waste pits. The modified GPR method consists of making measurements along a traverse line in a sloping trench with the radar’s antenna oriented at an angle of up to 45° from the horizontal. The direction of propagation of the electromagnetic field for this configuration is not vertical, and the amount of energy scattered from objects that are oriented vertically relative to the energy scattered from horizontal layers is increased. This fundamental feature of side‐looking underground radar (SLUR) measurements is illustrated by physical modeling. Measurements made along parallel trenches that are offset at different distances from a vertically oriented object provides GPR cross‐sections with a primary plane of investigation that intersects the vertical feature at different depths. SLUR was used at BNL in conjunction with conventional surface GPR measurements (displayed as 3-D blocks and plan‐view time slices) to enhance the vertical definition and improve the depth estimates of the waste pits.
Effects of attenuation and scattering on AVO measurements
Authors: Adriansyah  , McMechan George A.
Published: October 2002

The trends and variance in amplitude variation with offset (AVO) observations caused by near‐surface structure, attenuation, and scattering are numerically synthesized by pseudospectral viscoelastic 2-D modeling. Near‐surface structure produces amplitude focusing and defocusing that significantly distort AVO observations in offset windows at a scale comparable to that of the lateral variations in the structure. Attenuation and scattering decrease absolute amplitudes at all offsets. Scattering and wave interference increase the variance associated with AVO measurements. Depending on the relative influence of intrinsic attenuation, apparent attenuation associated with scattering, and geometrical focusing, a normalized AVO response can increase or decrease with offset (relative to that for the associated elastic, nonscattering, 1-D solution), and so mimic the behavior predicted as a function of contrasts in density, velocity, porosity or Poisson’s ratio. If only relative (normalized) amplitudes are available, it is difficult to distinguish between effects of parameters whose main contributions are to absolute amplitude; for example, a trend of decreasing amplitude (relative to that for an elastic flat‐layered model) produced by intrinsic attenuation may be counteracted by focusing/scattering or anisotropic effects over wide aperture ranges. Diagnostic information on AVO effects of scattering and attenuation is lost when the noise level is sufficiently high. Interpretations of AVO observations based on homogeneous layered elastic models must therefore be used with caution as they are, in general, nonunique. Lateral variations in AVO parameters are the key to detecting hydrocarbons, so lateral changes in AVO produced by lateral changes in the overburden properties have potential for being misinterpreted, especially if the recording aperture is small.
Stable depth extrapolation of seismic wavefields by a Neumann series
Authors: Kostecki Andrzej , Półchłopek Anna
Published: October 2002

Several migration methods fail to work when applied to complex geological structures with strong lateral heterogeneity. The generalized migration in the frequency‐wavenumber (f-k) domain based on a convolution with a slowness- (inverse of velocity) dependent operator is capable of downward continuation of wavefield in media with strong vertical and lateral variations of velocity. Unfortunately, this method, as presented in the literature, is potentially unstable. We propose a new, stable extrapolator based on the solution of the integral Fredholm equation, which describes a one‐way wave equation in the form of a Neumann series. The resulting algorithm of depth migration is implemented in both the frequency‐wavenumber (f-k) and frequency‐space (f-x) domains and takes into account arbitrary lateral gradients of velocity, using a low‐frequency filter (in x-f domain) that is the sum of the power series. The computation time of depth migration by a Neumann series is slightly longer than for split‐step Fourier migration. The examples presented suggest that the depth migration by Neumann’s series method can be used to map complex structures with strong lateral gradients of velocity.
Kirchhoff diffraction mapping in media with large velocity contrasts
Authors: Zhao Ping , Uren Norm F. , Wenzel Friedemann , Hatherly P. J. , McDonald John A.
Published: October 2002

Finite‐difference methods for calculating traveltimes are superior to ray‐tracing methods in inhomogeneous media. However, when these techniques are applied to Kirchhoff migration, a severe problem occurs in the presence of large velocity contrasts. If finite‐difference traveltime methods are used to calculate first arrivals, an incomplete image is created because substantial subsurface information is often carried by direct body waves. We propose a solution to this problem by developing a new method of calculating later arrival times and applying both first and later arrival times to a Kirchhoff diffraction mapping algorithm. A comparison shows that the implementation of both first arrivals and later arrivals in Kirchhoff migration can substantially improve the images in media with large velocity contrasts.
Ergodicity of stationary white Gaussian processes
Authors: Ghosh Santi K.
Published: October 2002

Stationary time series is an important concept in seismic signal processing. According to Robinson (1967), the method of predictive deconvolution is the minimum‐delay interpretation of the decomposition theorem of Wold (1938) for stationary time series. Stationary noise models have found use in geophysics as well (Robinson and Treitel, 1980).
True‐amplitude transformation to zero offset of data from curved reflectors
Authors: Bleistein Norman , Cohen Jack , Jaramillo Herman
Published: October 2002

Transformation to zero offset (TZO), alternatively known as migration to zero offset (MZO), or the combination of normal moveout and dip moveout (NMO/DMO), is a process that transforms data collected at finite offset between source and receiver to a pseudozero offset trace. The kinematic validity of NMO/DMO processing has been well established. The TZO integral operators proposed here differ from their NMO/DMO counterparts by a simple amplitude factor. (The form of the operator depends on how the input and output variables are chosen from among the combinations of midpoint or wavenumber with time or frequency.) With this modification in place, the dynamical validity for planar reflectors of the proposed TZO operators of this paper have been established in earlier studies. This means that the traveltime and geometrical spreading terms of the finite offset data are transformed to their counterparts for zero offset data, while the finite offset reflection coefficient is preserved. The main purpose of this study is to show that dynamical validity of the TZO operator extends to the case of curved reflectors in the 2.5-D limit. Thus, at the cost of a simple additional multiplicative factor in any standard NMO/DMO operator to produce the corresponding TZO operator, the amplitude factor attributed to curvature effects in finite offset data is transformed by this TZO processing to the corresponding curvature factor for zero offset data. This problem has also been addressed in a more general context by Tygel and associates. However, in the generality, some of the specifics and interpretations of the simpler problem are lost. Thus, we see some value in presenting this analysis where one can carry out all calculations explicitly and see specific quantities that are more familiar and accessible to users of DMO. Furthermore, in this paper, we show how processing of the input data with a second TZO operator allows for the extraction of the cosine of the preserved specular angle, a necessary piece of information for amplitude versus angle (AVA) analysis. We then discuss the possibility of using the output of our processing formalism at multiple offsets to create a table of angularly dependent reflection coefficients and attendant incidence angles as a function of offset. This is the basis of a proposed amplitude versus offset/amplitude versus angle (AVO/AVA) analysis of the pseudozero offset traces. Finally, we describe the modifications of Hale DMO and Gardner/Forel DMO to obtain true amplitude output equivalent to ours and also how to extract the cosine of the specular angle for these forms of DMO. This last does not depend on true amplitude processing, but only on processing two DMO operators with slightly different kernels and then taking the quotient of their peak amplitudes.
Fourier prestack migration by equivalent wavenumber
Authors: Margrave Gary F. , Bancroft John C. , Geiger Hugh D.
Published: October 2002

Fourier prestack migration is reformulated through a change of variables, from offset wavenumber to a new equivalent wavenumber, which makes the migration phase shift independent of horizontal wavenumber. After the change of variables, the inverse Fourier transform over horizontal wavenumber can be performed to create unmigrated, but fully horizontally positioned, gathers at each output location. A complete prestack migration then results by imaging each gather independently with a poststack migration algorithm. This equivalent wavenumber migration (EWM) is the Fourier analog of the space‐time domain method of equivalent offset migration (EOM). The latter is a Kirchhoff time‐migration technique which forms common scatterpoint (CSP) gathers for each migrated trace and then images those gathers with a Kirchhoff summation. These CSP gathers are formed by trace mappings at constant time, and migration velocity analysis is easily done after the gathers are formed. Both EWM and EOM are motivated by the algebraic combination of a double square root equation into a single square root. This result defines equivalent wavenumber or offset. EWM is shown to be an exact reformulation of prestack f-k migration. The EWM theory provides explicit Fourier integrals for the formation of CSP gathers from the prestack data volume and the imaging of those gathers to form the final prestack migrated result. The CSP gathers are given by a Fourier mapping, at constant frequency, of the unmigrated spectrum followed by an inverse Fourier transform. The mapping requires angle‐dependent weighting factors for full amplitude preservation. The imaging expression (for each CSP gather) is formally identical to poststack migration with the result retained only at zero equivalent offset. Through a numerical simulation, the impulse responses of EOM and EWM are shown to be kinematically identical. Amplitude scale factors, which are exact in the constant velocity EWM theory, are implemented approximately in variable velocity EOM.
Elastic finite‐difference method for irregular grids
Authors: Opršal Ivo , Zahradník Jiří
Published: October 2002

Finite‐difference (FD) modeling of complicated structures requires simple algorithms. This paper presents a new elastic FD method for spatially irregular grids that is simple and, at the same time, saves considerable memory and computing time. Features like faults, low‐velocity layers, cavities, and/or nonplanar surfaces are treated on a fine grid, while the remaining parts of the model are, with equal accuracy, represented on a coarse grid. No interpolation is needed between the fine and coarse parts due to the rectangular grid cells. Relatively abrupt transitions between the small and large grid steps produce no numerical artifacts in the present method. Planar or nonplanar free surfaces, including underground cavities, are treated in a way similar to internal grid points but with consideration of the zero‐valued elastic parameters and density outside the free surface (vacuum formalism). A theoretical proof that vacuum formalism fullfills the free‐surface conditions is given. Numerical validation is performed through comparison with independent methods, comparing FD with explicitly prescribed boundary conditions and finite elements. Memory and computing time needed in the studied models was only about 10 to 40% of that employing regular square grids of equal accuracy. A practical example of a synthetic seismic section, showing clear signatures of a coal seam and cavity, is presented. The method can be extended to three dimensions.
Simultaneous reconstruction of 1-D susceptibility and conductivity from electromagnetic data
Authors: Zhang Zhiyi , Oldenburg Douglas W.
Published: October 2002

In this paper, we develop an inversion algorithm to simultaneously recover 1-D distributions of electric conductivity and magnetic susceptibility from a single data set. The earth is modeled as a series of homogeneous layers of known thickness with constant but unknown conductivities and susceptibilities. The medium of interest is illuminated by a horizontal circular loop source located above the surface of the earth. The secondary signals from the earth are received by a circular loop receiver located some distance from the source. The model objective function in the inversion, which we refer to as the cost function, is a weighted sum of model objective functions of conductivity and susceptibility. We minimize this cost function subject to the data constraints and show how the choice of weights for the model objective functions of conductivity and susceptibility affects the results of the inversion through 1-D synthetic examples. We also invert 3-D synthetic and field data. From these examples we conclude that simultaneous inversion of electromagnetic (EM) data can provide useful information about the conductivity and susceptibility distributions.
An analytical expression for the gravity field of a polyhedral body with linearly varying density
Authors: Hansen R. O.
Published: October 2002

Over the past 24 years, the gravity fields of homogeneous polyhedra have been studied extensively (Paul, 1974; Barnett, 1976; Okabe, 1979; Golizdra, 1981; Strakhov et al., 1986a, 1986b; Gotze and Lahmeyer, 1988; Pohanka, 1988; Ivan, 1990; Pohanka, 1990; Holstein and Ketteridge, 1996). This intensive scrutiny is well deserved because polyhedra provide a framework in which complex body shapes can be modeled parsimoniously and because the analytic expressions for the gravity fields of uniform polyhedra involve only elementary transcendental functions available as part of the run‐time library for most computational programming languages.
Acoustic behavior at the fluid/solid transition of kaolinite suspensions
Authors: Green Douglas H. , Esquivel‐Sirvent Raul
Published: October 2002

Anomalously high ultrasonic attenuation is observed in kaolinite/water suspensions near 40% solid‐volume concentrations. Within the range of frequencies used (3–7 MHz), the concentration of this loss maximum is nearly independent of wave frequency. Velocity extrema are observed near this same concentration. This behavior is attributed to viscous losses in the oscillating fluid between adjacent particles. At low concentrations (<40%), this mechanism becomes stronger with decreasing interparticle separation and therefore with increasing concentration as well. As particles begin to touch at high concentrations, their oscillatory motion is inhibited and the wave damping decreases. Thus, the loss maximum can be used as a signature of the onset of rigidity in suspensions and colloids. The 40% concentration is consistent with water contents of published Atterberg liquid limits for kaolinite/water mixtures. Full elastic rigidity is not likely to be realized until the two‐phase material achieves a dense particle packing, such as close packing (62% concentration) for well‐sorted particles.
Some practical aspects of prestack waveform inversion using a genetic algorithm: An example from the east Texas Woodbine gas sand
Authors: Mallick Subhashis
Published: October 2002

In this paper, a prestack inversion method using a genetic algorithm (GA) is presented, and issues relating to the implementation of prestack GA inversion in practice are discussed. GA is a Monte‐Carlo type inversion, using a natural analogy to the biological evolution process. When GA is cast into a Bayesian framework, a priori information of the model parameters and the physics of the forward problem are used to compute synthetic data. These synthetic data can then be matched with observations to obtain approximate estimates of the marginal a posteriori probability density (PPD) functions in the model space. Plots of these PPD functions allow an interpreter to choose models which best describe the specific geologic setting and lead to an accurate prediction of seismic lithology. Poststack inversion and prestack GA inversion were applied to a Woodbine gas sand data set from East Texas. A comparison of prestack inversion with poststack inversion demonstrates that prestack inversion shows detailed stratigraphic features of the subsurface which are not visible on the poststack inversion.
2-D and 3-D interpretation of electrical tomography measurements, Part 1: The forward problem
Authors: Lesur Vincent , Cuer Michel , Straub André
Published: October 2002

We have developed a computer code to model the electrical potential field for borehole‐to‐borehole measurements. This scheme supports a large class of model geometries including 2-D and 3-D structures embedded in a homogeneous half‐space. It enables the computation of the electrical potential at any point due to a direct current injection at any source point within the model. A new boundary integral formulation is used that generates a sparse linear system. The sparsity is exploited in order to optimize the memory size and the computation time needed to solve the forward problem. This formulation is new because two unknown quantities—the electrical potential and a current‐related quantity—are solved for each interface. The numerical accuracy of this code has been extensively tested. Simulations of a simple model geometry are used to gain insight on when 3-D phenomena differ from those of 2-D models.
2-D and 3-D interpretation of electrical tomography measurements, Part 2: The inverse problem
Authors: Lesur Vincent , Cuer Michel , Straub André
Published: October 2002

The interpretation of borehole‐to‐borehole electrical measurements requires solving an inverse problem for a given class of model geometries. The usual approach to an inverse problem includes a model dependent task (i.e., forward modeling) and a generic task (i.e., an optimization scheme). We have developed an optimization algorithm using a nonlinear inversion technique. This algorithm allows recovery of a possible resistivity distribution in an investigated zone between two boreholes or in the vicinity of them. This resistivity distribution is defined as a set of 2-D or 3-D volumes of constant resistivity. The inversion procedure minimizes a least‐squares term plus a damping term. This latter term seeks to minimize the roughness of the solution. An improved form of this smoothness term may enhance the spatial resolution of the resistivity image, assuming that the resistivity contrast is known a priori. This reconstruction algorithm has been tested for both 2-D and 3-D geometries. These inversion tests were conclusive enough such that a successful interpretation on a 16 × 16 grid has been carried out for a field data set obtained from a mineral exploration test site.