bluuebunny/crossref_metadata_2025 huggingface dataset:
Effects of vertically aligned subsurface fractures on seismic reflections: A physical model study
Authors: Chang Chih‐Hsiung , Gardner Gerald H. F.
Published: October 2002

We investigate the effects of subsurface fractures on moveout velocity and on reflection amplitudes by constructing a fractured model with three layers. The physical model was constructed by embedding a Phenolitic disc within the intermediate layer, which acts as a zone of vertical fractures. Survey lines were run along seven azimuthal directions between the strike direction and the transverse direction to the fractures at an angle increment of 15°. For our set of experimental conditions, we observe that the horizontal moveout velocity decreases from the strike direction toward the transverse direction to the fractures, and that the rate of decrease in amplitude variation with offset (AVO) increases from the strike direction toward the transverse direction to the fracture.
Zero‐phasing seismic data without wells in offshore West Africa: Reducing uncertainty and variability of the wavelet
Authors: Foster Mark S. , Nunn Keith R. , Lewis Sarah A. , Reynolds David J.
Published: October 2002

Traditionally, many companies have zero‐phased seismic data using operators based on wavelets estimated from well matching. However, in new areas of exploration, other methods must be used. A data example from deep‐water West Africa is discussed in which the use of two independent methods of estimating the wavelet (physical modeling and statistical evaluation) allows for increased confidence in the resulting zero‐phasing. The two methods are complimentary in that they compensate for the inadequacies of each other's assumptions. The combination of the two to reduce uncertainty in wavelet estimation is the main objective. The acquisition and processing of the data are of great importance in ensuring wavelet stability in the section and allowing the wavelet estimation methods to be used reliably. Careful application of gapped deconvolutions in the processing sequence allows for wavelet compression and consistency over large areas of data that can then be zero‐phased using a single operator, even though the data covers diverse geology and water depths.
On: “Subsurface fault detection using seismic data for hazardous‐waste‐injection well permitting: An example from St. John the Baptist Parish, Louisiana” by E. V. Zinni (March‐April 1995 GEOPHYSICS, 60, p. 468–475)
Authors: Warner Don L.
Published: October 2002

Zinni (1995) has studied the stratigraphy and structural geology of injection reservoirs and aquifers in the vicinity of the DuPont Ponchartrain Works plant and has concluded that “The injection of liquid hazardous waste into the 2440-, 1430-m, and 1130-m injection reservoirs could jeopardize not only the water quality of the Covington aquifer, but possibly other shallow freshwater aquifers….”
Simple interpretation of time‐domain electromagnetic sounding using similarities between wave and diffusion propagation
Authors: Gershenson Mier
Published: October 2002

By using similarities between EM sounding in dielectric and conductive media, it is shown that one can transform between solutions in one type of propagation to the other. The method is based on the similarities of the Laplace transform between diffusive and nondiffusive cases. In the diffusive case, the equation involves the Laplace variable s in the first power, while for the nondiffusive cases, similar equations occur with [Formula: see text]. Three alternative implementations are developed, and their use is demonstrated. The first implementation is based on substituting [Formula: see text] for the Laplace transform variable s using forward and inverse numerical Laplace transforms. The second implementation is based on expanding the diffusive time response on an exponential time base and replacing it with its image function in the wave case, namely, a sinusoidal function. The third implementation is based on direct transformation in the time domain using exponential time interval sampling. The performance of the techniques on synthetic data is demonstrated. Besides the advantage of simple implementation of these techniques, other advantages and limitations of the method and each of the implementations are discussed. A case history is presented. The application of common techniques used in the processing of seismic and radar for processing and EM sounding in conductive media is discussed. The use of the Poynting vector as a means of determining distance and direction is demonstrated.
Transmission‐reflection tomography: Application to reverse VSP data
Authors: Mao Weijian , Stuart Graham W.
Published: October 2002

A multiphase tomographic algorithm is presented that allows 2-D and 3-D slowness (inverse of velocity) and variable reflector depth to be reconstructed simultaneously from both transmission and reflection traveltimes. We analyze the ambiguity in the determination of velocity and depth in transmission and reflection data and realize that depth perturbation is more sensitive to reflection traveltime anomalies than slowness perturbation, whereas the reverse is true of transmission traveltime anomalies. Because of the constraints on velocity and depth provided by the different wave types, this algorithm reduces the ambiguity substantially between velocity and depth prevalent in reflection tomography and also avoids the undetermined problem in transmission tomography. The linearized inversion was undertaken iteratively by decoupling velocity parameters from reflector depths. A rapid 2-D and 3-D ray‐tracing algorithm is used to compute transmission and reflection traveltimes and partial derivatives with respect to slowness and reflector depth. Both depth and velocity are parameterized in terms of cubic B‐spline functions. Synthetic examples indicate the improvement in tomographic results when both transmission and reflection times are included. The method has been applied to a reverse vertical seismic profile (VSP) data set recorded on the British coal measures along a crossed‐linear array. Traveltimes were picked automatically by the simultaneous determination of time delays and stacking weights using a waveform matching technique. The tomographic inversion of the observed reverse VSP images two fault‐zones of lower velocity than the surrounding media. The location of the faults was confirmed by near‐by reflection lines. The technique can be applied to offset VSPs or reverse VSPs and coincident VSP and surface reflection data.
True‐amplitude seismic migration: A comparison of three approaches
Authors: Gray Samuel H.
Published: October 2002

Knowledge of elastic parameter (compressional and shear velocities and density) contrasts within the earth can yield knowledge of lithology changes. Elastic parameter contrasts manifest themselves on seismic records as angle‐dependent reflectivity. Interpretation of angle‐dependent reflectivity, or amplitude variation with offset (AVO), on unmigrated records is often hindered by the effects of common‐depth‐point smear, incorrectly specified geometrical spreading loss, source/receiver directivity, as well as other factors. It is possible to correct some of these problems by analyzing common‐reflection‐point gathers after prestack migration, provided that the migration is capable of undoing all the amplitude distortions of wave propagation between the sources and the receivers. A migration method capable of undoing such distortions and thus producing angle‐dependent reflection coefficients at analysis points in a lossless, isotropic, elastic earth is called a “true‐amplitude migration.” The principles of true‐amplitude migration are simple enough to allow several methods to be considered as “true‐amplitude.” I consider three such migration methods in this paper: one associated with Berkhout, Wapenaar, and co‐workers at Delft University; one associated with Bleistein, Cohen, and co‐workers at Colorado School of Mines and, more recently, Hubral and co‐workers at Karlsruhe University; and a third introduced by Tarantola and developed internationally by many workers. These methods differ significantly in their derivations, as well as their implementation and applicability. However, they share some fundamental similarities, including some fundamental limitations. I present and compare summaries of the three methods from a unified perspective. The objective of this comparison is to point out the similarities of these methods, as well as their relative strengths and weaknesses.
Decomposition of vibroseis data by the multiple filter technique
Authors: Li Xiao‐Ping
Published: October 2002

A harmonically distorted vibroseis signal is decomposed using the “multiple filter technique” in a similar manner as the wavelet transform. The 1-D vibroseis signal is transformed into a 2-D function of time and frequency. The procedure consists of applying a family of narrow Gaussian filters whose center frequencies are close to the instantaneous frequencies of the harmonically distorted vibroseis signal. As a result of this decomposition, an envelope trace is obtained for every center frequency. For a linear fundamental (pilot) sweep, the fundamental sweep and its harmonic distortions have different arrival times in the decomposed envelope trace. An accurate analysis of the harmonic distortion can be carried out using the amplitudes along the slopes of the instantaneous frequency defined for the linear fundamental sweep and its harmonic distortions. Plotting the contoured amplitudes of each envelope trace on a frequency‐versus‐time scale yields the amplitude distribution between the fundamental sweep and its harmonic distortions. They represent the frequency content of the uncorrelated vibroseis signal and can be used to examine the interaction and leakage of the signal and its harmonics. Similarly, the correlation noise, the so‐called “ghost sweep” in the correlated vibroseis data, can be decomposed with this technique. The method is applied to synthetic, harmonically distorted, vibroseis signals and to a real vibroseis vertical seismic profile (VSP) data set.
Fluid distribution effect on sonic attenuation in partially saturated limestones
Authors: Cadoret Thierry , Mavko Gary , Zinszner Bernard
Published: October 2002

Extensional and torsional wave‐attenuation measurements are obtained at a sonic frequency around 1 kHz on partially saturated limestones using large resonant bars, 1 m long. To study the influence of the fluid distribution, we use two different saturation methods: drying and depressurization. When water saturation (Sw) is higher than 70%, the extensional wave attenuation is found to depend on whether the resonant bar is jacketed. This can be interpreted as the Biot‐Gardner‐White effect. The experimental results obtained on jacketed samples show that, during a drying experiment, extensional wave attenuation is influenced strongly by the fluid content when Swis between approximately 60% and 100%. This sensitivity to fluid saturation vanishes when saturation is obtained through depressurization. Using a computer‐assisted tomographic (CT) scan, we found that, during depressurization, the fluid distribution is homogeneous at the millimetric scale at all saturations. In contrast, during drying, heterogeneous saturation was observed at high water‐saturation levels. Thus, we interpret the dependence of the extensional wave attenuation upon the saturation method as principally caused by a fluid distribution effect. Torsional attenuation shows no sensitivity to fluid saturation for Swbetween 5% and 100%.
Seismic wave attenuation in metamorphic rocks from VSP data recorded in Germany’s continental super‐deep borehole
Authors: Pujol José M. , Luschen Ewald , Hu Yiguang
Published: October 2002

Vertical seismic profiling (VSP) data recorded in the German continental deep borehole (KTB) between 3 and 6 km have been used to study the attenuation of P-waves. A vibrator source was used to generate the data. In this depth range, the lithology is dominated by a metabasite unit (amphibolite and metagabbro) with various degrees of alteration, intercalated with paragneisses. The method used to determine attenuation is based on the fit of a straight line to the logarithm of amplitude ratios for variable depth and fixed frequency. Inspection of the corresponding attenuation curves showed sharp discontinuities, which correlate with changes in the seismic source (mostly related to changes in location), as recorded by a nearby monitor geophone. To avoid the uncertainties introduced by these changes, the analysis was restricted to a depth interval (3576–4538 m) for which the source was not moved. Even in this case, however, the monitor traces showed significant variations in their frequency content, although not much variation in their peak time‐domain amplitudes. To account for these variations, the attenuation coefficients obtained for the actual data were corrected for source variations by subtraction of the attenuation coefficients determined from the analysis of synthetic VSP data computed using source wavelets extracted from the monitor traces. After these corrections, the values of Q for frequencies between 7.8 and 46.9 Hz are between 14 and 32. These values are quite low, and may be related to the presence of fluids known to exist in the depth range under consideration, although scattering processes may also contribute to the high attenuation. The variation of Q with frequency may be the result of processing artifacts.
Prestack depth migration of an Alberta Foothills data set—The Husky experience
Authors: Wu W.-J. , Lines L. , Burton A. , Lu H.-X. , Zhu J. , Jamison W. , Bording R. P.
Published: October 2002

We produce depth images for an Alberta Foothills line by iteratively using a number of migration and velocity analysis techniques. In imaging steeply dipping layers of a foothills data set, it is apparent that thrust belt geology can violate the conventional assumptions of elevation datum corrections and common midpoint (CMP) stacking. To circumvent these problems, we use migration from topography in which we perform prestack depth migration on the data using correct source and receiver elevations. Migration from topography produces enhanced images of steep shallow reflectors when compared to conventional processing. In addition to migration from topography, we couple prestack depth migration with the continuous adjustment of velocity depth models. A number of criteria are used in doing this. These criteria require that our velocity estimates produce a focused image and that migrated depths in common image gathers be independent of source‐receiver offset. Velocity models are estimated by a series of iterative and interpretive steps involving prestack migration velocity analysis and structural interpretation. Overlays of velocity models on depth migrations should generally show consistency between velocity boundaries and reflection depths. Our preferred seismic depth section has been produced by using prestack reverse‐time depth migration coupled with careful geological interpretation.
Magnetic signature of magnetite‐enriched rocks hosting platinum‐group element mineralization within the Archean Boston Creek Flow, Ontario
Authors: Larson Michelle S. , Stone William E. , Morris William A. , Crocket James H.
Published: October 2002

Ground‐based magnetometer surveys detect high‐positive magnetic anomalies (up to 72 000 nT) which coincide with the location of subeconomic, magnetite‐associated platinum‐group element (PGE) mineralization within the Boston Creek Flow iron‐rich basalt, Archean Abitibi Greenstone Belt, Ontario. The magnetic anomalies confirm the presence of magnetite‐enriched zones (up to 20 modal%), and reveal that they are ovoid in shape, up to 10 m in size, and along strike from each other in the central gabbro‐diorite layer. Geological and geochemical surveys and mineralogical studies indicate that these zones host smaller zones of disseminated chalcopyrite + pyrite, some of which, in turn, host platinum‐group minerals (PGM) and are enriched in PGE and related metals (whole‐rock [Formula: see text], Ag = 1300 ppb, Cu = 0.3%, V = 0.1%, Ni = 0.05%, Ti = 2.5%, and Fe = 25%). The coincidence of the high‐positive magnetic anomalies with the location of PGE mineralization, points to ground‐based magnetometer surveys as a valuable exploration tool for magnetite‐associated PGE ore deposits. The distribution of the residual magnetic field anomalies indicate that such surveys are especially useful in: (1) identifying rock types and mapping their distribution in areas of limited outcrop exposure; (2) locating magnetite‐enriched gabbroic rock bodies, even in close proximity to serpentinized olivine cumulate rocks; and (3) delineating the detailed geometry of magnetite‐enriched rocks that may carry significant amounts of PGE and PGMs. Exploration strategies should be designed to use ground‐based geophysical surveys, in conjunction with geological and geochemical surveys, to locate and delineate the geometry of magnetite‐enriched zones within thick, differentiated mafic‐ultramafic volcanic flows and plutonic bodies.
Ultrasonic attenuation in Glenn Pool rocks, northeastern Oklahoma
Authors: Shatilo Andrew P. , Sondergeld Carl , Rai Chandra S.
Published: October 2002

Ultrasonic P-wave attenuation and phase velocity dispersion have been estimated for 29 samples of sandstones and 13 samples of shales from a Glenn Pool oil reservoir using a pulse transmission technique. The measurements were performed under effective pressures from atmospheric to 15 MPa. There is a strong correlation between attenuation coefficient and phase velocity dispersion. Even though the observed attenuation may deviate from a “constant Q” model, it generally agrees with a minimum‐phase prediction. Attenuation in the water‐saturated sandstones increases with porosity and permeability. We found no correlation between the attenuation and clay content within the sandstone subset. Attenuation in the shales is much less than that in the sandstones. This difference may be used in reservoir characterization.
To: “A unified approach to 3-D seismic reflection imaging, Part II: Theory” (M. Tygel, J. Schleicher, and P. Hubral, GEOPHYSICS, 61, 759–775)
Authors: Jaramillo Herman , Schleicher Jörg , Tygel Martin
Published: October 2002

It came to our attention that in the paper of Tygel et al. (1996), formula (A-5) is incorrect. First, it is different from the cited equation (17) of Tygel et al. (1995). Second, the derivation of formula (17) in Appendix A of Tygel et al. (1995) is invalid for the purposes of Tygel et al., (1996) because in the 1995 paper, a rotation is treated, whereas in Tygel et al. (1996), a projection matrix is needed. Further investigation of the subject was needed to resolve these inconsistencies.
Marine magnetotellurics for petroleum exploration, Part II: Numerical analysis of subsalt resolution
Authors: Hoversten G. Michael , Morrison H. Frank , Constable Steven C.
Published: October 2002

In areas where seismic imaging of the base of salt structures is difficult, seaborne electromagnetic techniques offer complementary as well as independent structural information. Numerical models of 2-D and 3-D salt structures demonstrate the capability of the marine magnetotelluric (MT) technique to map the base of the salt structures with an average depth accuracy of better than 10%. The mapping of the base of the salt with marine MT is virtually unaffected by internal variation within the salt. Three‐dimensional anticlinal structures with a horizontal aspect ratio greater than two can be interpreted adequately via two‐dimensional inversions. Marine MT can distinguish between salt structures which possess deep vertical roots and those which do not. One measure of the relative accuracy of MT and seismic methods can be made by considering the vertical and lateral position errors in the locations of interfaces caused by neglecting velocity anisotropy in migration. For the shallow part of the section where two‐way travel times are on the order of 1 s, the vertical and lateral position errors in the locations of salt‐sediment interfaces from 2-D MT inversion is more than twice the expected migration error in reflectors in transversely isotropic sediments, such as those in the Gulf of Mexico. Deeper in the section where two‐way times are on the order of 4 s, lateral position errors in migration become comparable to those of the MT inverse, whereas seismic vertical position errors remain more than a factor of two smaller than MT errors. This analysis shows that structural mapping accuracy would be improved using MT and seismic together.
On the limited aperture migration in two dimensions
Authors: Sun Jianguo
Published: October 2002

Migration of incomplete data aperture is an important problem in exploration seismology because both the location and the size of the migration aperture affect the quality of migration. In 2-D cases, a stationary phase (high‐frequency) analysis concludes that a finitely large migration aperture results in a migrated image with three components. One comes from the tangent point between the traveltime curves of reflected and point‐diffracted rays and gives migration signal. The others are from the two endpoints of the migration aperture and result in migration noise. To guarantee the true‐amplitude reconstruction as well as to remove the migration noise, the migration aperture should be positioned so its central part contains the tangent point mentioned above, and the true‐amplitude weight function should be modified so it tapers the input data near the boundary of the migration aperture. Also, the central part of the migration aperture should be not smaller than the interval confined by the points where the difference between the traveltimes of reflected and point‐diffracted rays equals the half‐duration of the recorded seismic pulse. If the central part of the migration aperture is equal to the interval described here, the whole migration aperture should be confined by the points where the difference between the traveltimes of reflected and point‐diffracted rays equals the duration of the recorded seismic pulse. A migration aperture larger than this size does not improve the migration quality. Furthermore, for the migration apertures suggested here, the form of the taper function is not essential for migration. These results apply to both time and depth (poststack and prestack) migration.
Modal expansion of one‐way operators in laterally varying media
Authors: Grimbergen Joris L. T. , Dessing Frank J. , Wapenaar Kees
Published: October 2002

One of the main benefits of prestack depth migration in seismic processing is its ability to handle complicated medium configurations. When considerable lateral variations in the acoustic parameters are present in the subsurface, prestack depth migration is necessary for optimal lateral resolution. However, most migration algorithms still deal with lateral variations in an approximate manner because these variations are in many cases moderate compared to the profound variations in the depth direction. From other areas of science (e.g., optics, oceanography, and seismology), it is known that lateral variations can be dealt with by a decomposition of the wavefield into wave modes. In this paper, we explore the possibility of applying this concept to the construction of one‐way wavefield operators for depth migration. We expand the Helmholtz operator on an orthogonal basis of wave modes and obtain one‐way wavefield operators that are unconditionally stable and significantly increase the lateral resolution of the result.
Electrical conductivity of steam‐flooded, clay‐bearing geologic materials
Authors: Butler David B. , Knight Rosemary J.
Published: October 2002

The effect of clay content on the electrical response of steamflooded geologic material is studied using a combination of laboratory experiments and numerical simulations. The presence of clay can increase the conductivity of a steam zone by providing a surface conduction path that is enhanced strongly by temperature increases. Clay also increases the residual water saturation in a steam zone, further increasing conductivity. These effects can result in steam zones that are more conductive than initial conditions. However, the presence of clay alone is not sufficient to make all portions of a steam zone conductive relative to initial conditions. Equally important to the electrical behavior is the fluid response of the reservoir to the injection of steam. In particular, the speed of the steam front, relative to the speed of the liquid water in the steam zone, plays a key role. Relatively fast‐moving steam fronts cause distilled water banks to form around the front. This leads to steam zones with electrically resistive forward sections, even in clay‐rich material. The rear sections of these steam zones can be either resistive or conductive, depending in part on the clay content and the salinity. Relatively slow‐moving steam fronts do not cause distilled water banks to form and allow the formation of steam zones that are completely conductive relative to initial conditions. These experimental results demonstrate the potential complexities in steam‐flood electrical data. The numerical method used in this study can be used to help interpret those complexities.
Mapping shallow faults at the Evrona playa site using high‐resolution reflection method
Authors: Shtivelman Vladimir , Frieslander Uri , Zilberman Ezra , Amit Rivka
Published: October 2002

A shallow high‐resolution seismic reflection survey was carried out at the Evrona playa site in the southern Arava valley, Israel. The aim of the survey was to detect and map faults in the shallow subsurface (upper 100–150 m) and establish the relationship of the morphological features revealed by aerial photographs and surface geological mapping with the faults detected in the subsurface. The survey included three seismic lines shot using the P-wave technique and one SH-wave line, which overlapped one of the P-wave lines. The seismic energy source on all the lines was a sledge hammer. The acquired reflection data were of good quality and did not require special processing efforts. The seismic sections along the lines show a sequence of reflected events within the 8–150 m range. At several locations, continuity of the events is interrupted by a system of faults. These faults form flower structures apparently related to strike‐slip motions typical of the region. Comparison of the faults mapped on the seismic sections with those expressed by surface morphological features generally show good correspondence. The results of the seismic survey provide important information for the study of paleoseismicity and seismic hazards in the investigated area.
Magnetotelluric tensor decomposition: Part I, Theory for a basic procedure
Authors: Lilley F. E. M. (Ted)
Published: October 2002

The problem of expressing a general 3-D magnetotelluric (MT) impedance tensor in the form of a 2-D tensor that has been distorted in some way is addressed first in terms of a general theorem. This theorem shows that when the real and quadrature parts of a tensor are analyzed separately as distinct matrices, all that is necessary to make a matrix with 2-D characteristics from one with 3-D characteristics is to allow the electric and magnetic observing axes to rotate independently. The process is then examined in terms of the operations of twist and pure shear (“split”) on such matrices. Both of two basic sequences of split after twist, and twist after split, produce a typical 3-D matrix from one initially 1-D, with the parameters of split contributing 2-D characteristics to the final matrix. Taken in reverse, these sequences offer two basic paths for the decomposition of a 3-D matrix, and are seen to be linked to the initial theorem. The various operations on matrices are expressed diagrammatically using the Mohr circle construction, of which it is demonstrated two types are possible. Mohr circles of an observed MT tensor display all the information held by the tensor, and the two types of circle construction respectively make clear whether particular data are well suited to modeling by either split after twist, or twist after split. Generally, tensor decompositions may be displayed by charting their progress in Mohr space. The Mohr construction also displays the invariants of a tensor and shows that tensor decomposition can be viewed as a process of determining an appropriate set of invariants. An expectation that the origin of axes should be outside every circle categorizes as irregular any tensors which, in either the real or quadrature part, do not satisfy a [Formula: see text] criterion. The theory of the present paper applies equally to procedures for distorting 1-D and 2-D model calculations for the purpose of matching observed 3-D data.
Using seismic crosswell surveys to determine the aperture of partially water‐saturated fractures
Authors: Kaelin Bruno , Johnson Lane R.
Published: October 2002

An air injection experiment in a shallow fractured limestone at Conoco’s borehole test facility near Newkirk, Oklahoma, has shown large effects on the amplitude but small effects on the traveltime of the transmitted seismic waves. We have analyzed data from a seismic monitor survey in the kilohertz range performed during the experiment and have modeled the fracture zone as a single fracture. The large amplitude decrease during the experiment is mainly attributable to the impedance contrast between the small velocities of gas‐water mixtures inside the fracture and the formation. The intrinsic attenuation of the fracture fluid seems to be a second‐order effect for small apertures. During the experiment the seismic wavelengths inside the fracture become comparable to the aperture dimension, which allows an estimation of fracture apertures. We also have analyzed a crosswell survey acquired shortly after the experiment and computed aperture and gas concentration profiles. Our aperture estimates range from <1 mm to a few millimeters, which is comparable to previous tracer tests. The results of this study are generally consistent with prior hydrologic work and single‐well surveys. This study demonstrates that crosswell surveys could be an effective tool for obtaining in situ estimates of fracture aperture and gas concentration.
Fast 2-D ray+Born migration/inversion in complex media
Authors: Thierry Philippe , Operto Stéphane , Lambaré Gilles
Published: October 2002

In this paper, we evaluate the capacity of a fast 2-D ray+Born migration/inversion algorithm to recover the true amplitude of the model parameters in 2-D complex media. The method is based on a quasi‐Newtonian linearized inversion of the scattered wavefield. Asymptotic Green’s functions are computed in a smooth reference model with a dynamic ray tracing based on the wavefront construction method. The model is described by velocity perturbations associated with diffractor points. Both the first traveltime and the strongest arrivals can be inverted. The algorithm is implemented with several numerical approximations such as interpolations and aperture limitation around common midpoints to speed the algorithm. Both theoritical and numerical aspects of the algorithm are assessed with three synthetic and real data examples including the 2-D Marmousi example. Comparison between logs extracted from the exact Marmousi perturbation model and the computed images shows that the amplitude of the velocity perturbations are recovered accurately in the regions of the model where the ray field is single valued. In the presence of caustics, neither the first traveltime nor the most energetic arrival inversion allow for a full recovery of the amplitudes although the latter improves the results. We conclude that all the arrivals associated with multipathing through transmission caustics must be taken into account if the true amplitude of the perturbations is to be found. Only 22 minutes of CPU time is required to migrate the full 2-D Marmousi data set on a Sun SPARC 20 workstation. The amplitude loss induced by the numerical approximations on the first traveltime and the most energetic migrated images are evaluated quantitatively and do not exceed 8% of the energy of the image computed without numerical approximation. Computational evaluation shows that extension to a 3-D ray+Born migration/inversion algorithm is realistic.
Weak elastic‐wave scattering from massive sulfide orebodies
Authors: Eaton David W.
Published: October 2002

Massive sulfide ore deposits, traditionally the target of electromagnetic or potential‐field geophysical investigations, can potentially be recognized and mapped using seismic methods based on their scattering response. To characterize the seismic expression of massive sulfide orebodies, I review formulas that describe elastic‐wave scattering from isolated inclusions in the far‐field and weak‐scattering limits (the Born approximation) and conduct a series of numerical tests. The minerals pyrite, sphalerite, and galena are used as the basis for these numerical modeling studies because they are relatively abundant and collectively span the full range of observed velocities and densities for ore rocks. The assumption of weak scattering, on which the Born approximation rests, is verified empirically in a representative example, by examining in‐situ wavefield measurements from a vertical seismic profiling experiment in northern Québec, Canada. For simplicity, orebodies are modeled as ellipsoidal inclusions in a homogeneous medium. The mathematical formalism leads to decoupling of factors for “composition” and “shape.” At seismic frequencies (∼50 Hz) and for ore deposits of sufficient size to represent economically viable targets (more than 109 kg), the shape factor effectively controls the scattering response. In this regime, negligible backscattering from spherical inclusions is predicted by the theory. In the case of flattened ellipsoids, which represent a more realistic orebody morphology, the shape‐factor effect leads to significant backscattering that is focused in the direction of specular reflection. For noisy 2-D data, numerical modeling indicates that these characteristics can cause scattering from an isolated dipping orebody to resemble reflections from a planar interface. For 3-D seismic surveys, however, isolated scattering bodies will produce a diagnostic pattern of concentric circular diffractions in unmigrated time‐slice sections.
3-D seismic survey design for linearv(z) media
Authors: Liner Chris L. , Underwood William D.
Published: October 2002

The standard formula for bin size is based, ultimately, on constant velocity assumptions. We extend the calculation of bin size and related parameters to media characterized by a linear v(z) velocity function. We present design equations accurate for all dips, including those beyond 90°, and these expressions reduce to known forms in the constant velocity limit. The variable velocity bin size is larger than would be calculated by standard methods, whereas migration distance and travel times are smaller. Since bin size has a first‐order effect on acquisition and processing cost, this allows design of cost‐efficient 3-D seismic surveys.
Estimation of near‐surface shear‐wave velocity by inversion of Rayleigh waves
Authors: Xia Jianghai , Miller Richard D. , Park Choon B.
Published: October 2002

The shear‐wave (S-wave) velocity of near‐surface materials (soil, rocks, pavement) and its effect on seismic‐wave propagation are of fundamental interest in many groundwater, engineering, and environmental studies. Rayleigh‐wave phase velocity of a layered‐earth model is a function of frequency and four groups of earth properties: P-wave velocity, S-wave velocity, density, and thickness of layers. Analysis of the Jacobian matrix provides a measure of dispersion‐curve sensitivity to earth properties. S-wave velocities are the dominant influence on a dispersion curve in a high‐frequency range (>5 Hz) followed by layer thickness. An iterative solution technique to the weighted equation proved very effective in the high‐frequency range when using the Levenberg‐Marquardt and singular‐value decomposition techniques. Convergence of the weighted solution is guaranteed through selection of the damping factor using the Levenberg‐Marquardt method. Synthetic examples demonstrated calculation efficiency and stability of inverse procedures. We verify our method using borehole S-wave velocity measurements.
Geophones on a board
Authors: Steeples Don W. , Baker Gregory S. , Schmeissner Chris , Macy Brian K.
Published: October 2002

We examined the feasibility of using seismic reflections to image the upper 10 m of the earth’s surface quickly and effectively by rigidly attaching geophones to a wooden board at 5-cm intervals. The shallow seismic reflection information obtained was equivalent to control‐test data gathered using classic, single‐geophone plants with identical 5-cm intervals. Tests were conducted using both a .22-caliber rifle source and a 30.06-rifle source. In both cases, the results were unexpected: in response to our use of small, high‐resolution seismic sources at offsets of a few meters, we found little intergeophone interference that could be attributed to the presence of the board. Furthermore, we noted very little difference in a 60-ms intra‐alluvial reflection obtained using standard geophone plants versus that obtained using board‐mounted geophones. For both sources, amplitude spectra were nearly identical for data gathered with and without the board. With the 30.06 source, filtering at high‐frequency passbands revealed a wave mode of unknown origin that appears to be related to the presence of the board; however, this mode did not interfere with the usefulness of the shallow‐reflection data. The results of these experiments suggest that deploying large numbers of closely spaced geophones simultaneously—perhaps even automatically—is possible. Should this method of planting geophones prove practical after further testing, the cost‐effectiveness of very shallow seismic reflection imaging may be enhanced. The technique also may be useful at greater reflector depths in situations employing bunched geophones. However, this approach may not be applicable in all circumstances because larger energy sources may induce interference between the geophones and produce undesirable modes of motion within the medium holding the geophones.
P- and S-wave characterization of near‐surface reflectivity from glacial tills using vertical seismic profiles
Authors: Carr Bradley J. , Hajnal Zoltan
Published: October 2002

Fundamental reflectivity properties are established within the glacial deposits of central Saskatchewan, Canada. Multicomponent vertical seismic profile (VSP) data collected in three shallow boreholes are used to obtain detailed acoustic property information within the first 80 m of the near‐surface strata. The integration of both P- and S-wave VSP data, in conjunction with other borehole geophysics, provided a unique opportunity to obtain in‐situ seismic reflection response properties in layered clay and sand tills. P- and S-wave interval velocity profiles, in conjunction with P- and S-wave VSP reflectivities are analyzed to provide insight into seismic wavefield behavior within ∼80 m of the surface. In general, shear wave energy identifies more reflective intervals than the P-wave energy because of better vertical resolution for S-wave energy (0.75 m) compared to P-wave energy (2.3 m) based on quarter wavelength criterion. For these saturated, unconsolidated glacial deposits, more details about the lithologic constituents and in‐situ porosity are detectable from the S-wave reflectivity, but P-wave reflections provide a good technique for mapping the bulk changes. The principal cause of seismic reflectivity is the presence and/or amount of sand, and the degree of fluid‐filled porosity within the investigated formations.
Resolution limits of migrated images
Authors: Chen Jing , Schuster Gerard T.
Published: October 2002

Far‐field formulas are derived for the point scatterer responses, the horizontal resolution limits, and the dynamic ranges of 2-D and 3-D migrated images. Numerical tests verify the validity of these formulas for practical CDP geometries. Our results show that in the far field, where the depth is much greater than the width of the recording aperture, the horizontal resolution limit for migrated images is proportional to the depth of the scatterer and inversely proportional to the wavenumber and aperture size. Given the same recording aperture size, the 2-D prestack migration image has the same horizontal resolution limit as the corresponding 2-D poststack image. For the same aperture size, the 3-D poststack migration image has twice the resolution as the 3-D prestack migration with sources and receivers distributed in fixed areas. Also, prestack migration images have a better dynamic range than poststack migration images, and dynamic range improves with an increase in width of the recording aperture. The resolution limits are based on a Rayleigh‐like zero crossing criterion.
Relationship ofP-wave seismic attributes, azimuthal anisotropy, and commercial gas pay in 3-DP-wave multiazimuth data, Rulison Field, Piceance Basin, Colorado
Authors: Lynn Heloise B. , Campagna David , Simon K. Michele , Beckham Wallace E.
Published: October 2002

This case history is one of three field projects funded by the US Department of Energy as part of its ongoing research effort aimed to expand current levels of drilling and production efficiency in naturally‐fractured tight‐gas reservoirs. The original stated goal for the 3-D P-wave seismic survey was to evaluate and map fracture azimuth and relative fracture density throughout a naturally‐fractured gas reservoir interval. At Rulison field, this interval is the Cretaceous Mesaverde, approximately 2500 ft (760 m) of lenticular sands, silts, and shales. Three‐dimensional full‐azimuth P-wave data were acquired for the evaluation of azimuthal anisotropy and the relationship of the anisotropy to commercial pay in the target interval. The methodology is based on the evaluation of two restricted‐azimuth orthogonal (source‐receiver azimuth) 3-D P-wave volumes aligned with the natural principal axes of the azimuthal anisotropy, as estimated from velocity analysis of multiazimuth prestack gathers. The Dix interval velocity, as well as the interval amplitude variation with offset (AVO) gradient, was calculated for both azimuths for the gas‐saturated Mesaverde interval. The two seismic attributes best correlated with commercial gas pay (at a 21-well control set) were (1) values greater than 4% azimuthal variation in the interval velocity ratio (source‐receiver azimuth N60E/N30W) of the target interval (the gas‐saturated Mesaverde), and (2) the sum of the interval AVO gradients (N60E + N30W). The sum of the interval AVO gradients is an attribute sensitive to the presence of gas, but not diagnostic of an azimuthal variation in the amplitude. The two‐azimuth interval velocity anisotropy mapped over the survey area suggests spatial variations in the orientation of the maximum horizontal stress field and the open (to flow) fracture system.
First‐break timing: Arrival onset times by direct correlation
Authors: Molyneux Joseph B. , Schmitt Douglas R.
Published: October 2002

In attenuating media, pulse characteristics evolve with propagation distance and saturation or pressure‐dependent changes in rock properties. This nonstationarity of the waveform complicates determination of meaningful traveltimes. As a result, depending on the time‐picking criteria used, substantially different values of interval velocity can be obtained. This problem is particularly severe in high‐frequency laboratory time‐of‐flight measurements on porous rock. A potentially less ambiguous measure of wave speed is the signal velocity that is calculated using the pulse onset time. Here, a semiautomated method is developed to determine this onset time in high‐fidelity, pressure‐dependent core measurements. The greatest value of Pearson’s correlation coefficient between segments of observed waveforms near the pulse onset and at an appropriate reference serves as the time determination criterion. Tests of the method on artificial data suggest the signal velocity may be determined to better than 0.3% for −60 dB noise or 1.2% for −37 dB noise. A real data set is tested, comprised of a series of ultrasonic (1 MHz) velocity measurements in microcracked rock to confining pressures of 300 MPa (∼45,000 psi). At the lowest confining pressure, where attenuation is greatest, signal onset and more conventionally derived traveltimes differ by more than 4%. This large discrepancy illustrates that care should be exercised when determining velocity in such attenuating materials. Conversely, the consistency of waveform attributes, such as the difference between the onset time and the first peak time or the apparent quality factor, is useful when estimating intrinsic material velocities in low‐porosity, microcracked carbonate and metamorphic rocks at high confining pressures.
Extended local Born Fourier migration method
Authors: Huang Lian‐Jie , Fehler Michael C. , Wu Ru‐Shan
Published: October 2002

A migration approach based on a local application of the Born approximation within each extrapolation interval contains a singularity that can make direct application unstable. Previous authors have suggested adding an imaginary part to the vertical wavenumber to eliminate the singularity. However, their method requires that the reference slowness must be the maximum slowness of a given layer; consequently, the slowness perturbations are larger than those when the average slowness is selected as a reference slowness. Therefore, its applicability is limited. We develop an extended local Born Fourier migration method that circumvents the singularity problem of the local Born solution and makes it possible to choose the average slowness as a reference slowness. It is computationally efficient because of the use of a fast Fourier transform algorithm. It can handle wider angles (or steeper interfaces) and scattering effects of heterogeneities more accurately than the split‐step Fourier (SSF) method, which accounts for only the phase change as a result of the slowness perturbations but not amplitude change. To handle large lateral slowness variations, we introduce different reference slownesses in different regions of a medium to ensure the condition of small perturbation. The migration result obtained using the extended local Born Fourier method with multiple reference slownesses demonstrates that the method can produce high‐quality images of complex structures with large lateral slowness variations.
Multipole acoustic waveforms in fluid‐filled boreholes in biaxially stressed formations: A finite‐difference method
Authors: Liu Qing‐Huo , Sinha Bikash K.
Published: October 2002

A finite‐difference method is developed to simulate elastic wave propagation in a borehole surrounded by a biaxially stressed solid formation. The linear elastic formation is altered by such tectonic stresses that cause significant changes in the characteristics of wave propagation in a borehole. The 2.5-dimensional problem addressed in this work concerns the three‐dimensional wave propagation in a medium inhomogeneous in two spatial coordinates transverse to the borehole axis. A second‐order finite‐difference method is developed to solve the partial differential equations arising from a published acoustoelastic model for borehole acoustic wave propagation in prestressed formations. The algorithm is validated and applied to model both the borehole flexural and axisymmetric Stoneley waves. The computed waveforms are processed by a variation of Prony’s algorithm that yields dispersion curves for flexural waves polarized both parallel and perpendicular to the stress direction. The flexural dispersion crossover in a uniaxially stressed formation is quantitatively confirmed. The Stoneley dispersion in the presence of such stresses exhibits approximately a uniform shift toward lower slownesses over the entire bandwidth of interest. This implies that azimuthal averaging of formation stiffnesses approximately yields the same effective Stoneley stiffness at different radial positions.