bluuebunny/crossref_metadata_2025 huggingface dataset:
Modeling of marine seismic profiles in the t-x and τ-p domains
Authors: Dietrich Michel
Published: October 2002

In many cases, comparison of real data with synthetic seismograms provides additional constraints on the velocity‐depth profiles obtained with simple inversion techniques. Obtaining a satisfactory match between the real and computed data usually requires several trials with different models but can be performed rapidly if the theoretical seismograms are themselves easily interpretable, i.e., if the major contributions which make up the synthetic traces can be identified and separated. In horizontally stratified media, modeling is further simplified and is faster if the simulation techniques are implemented in the domain of the intercept time τ and the ray parameter p. The generalized reflection and transmission matrix method is well suited for these purposes and may be used to generate synthetic seismograms in both the t-x and τ-p planes. Computation of plane‐wave seismograms is straightforward and merely corresponds to an inverse Fourier transform of the overall reflectivity matrix for each ray parameter. The construction of point‐source seismograms can be carried out in several ways. In this paper, I combine the generalized reflection and transmission matrix method with a discrete wavenumber integration of the reflectivity function, extending previous work to include fluid‐solid interfaces. The introduction of scaling parameters also simplifies the reflectivity matrices. Simple numerical experiments demonstrate that the relations between the earth model and the corresponding seismic response are simpler in the τ-p domain than in the t-x domain. In particular, calculation of the PP, SP, and SS contributions to the complete seismic response shows that shear and converted waves may have a clearer expression in the τ-p plane than in the t-x plane and can in some cases provide discrimination between several earth models. Finally, the main features of a real marine seismic profile are well reproduced by synthetic sections in both the t-x and τ-p domains.
Inversion of bottom‐hole temperature data: The Pineview field, Utah‐Wyoming thrust belt
Authors: Deming Dave , Chapman David S.
Published: October 2002

The present day temperature field in a sedimentary basin is a constraint on the maturation of hydro‐carbons; this temperature field may be estimated by inverting corrected bottom‐hole temperature (BHT) data. Thirty‐two BHTs from the Pineview oil field are corrected for drilling disturbances by a Horner plot and inverted for the geothermal gradient in nine formations. Both least‐squares [Formula: see text] norm and uniform [Formula: see text] norm inversions are used; the [Formula: see text] norm is found to be more robust for the Pineview data. The inversion removes random error from the corrected BHT data by partitioning scatter between noise associated with the BHT measurement and correction processes and local variations in the geothermal gradient. Three‐hundred thermal‐conductivity and density measurements on drill cuttings are used, together with formation density logs, to estimate the in situ thermal conductivity of six of the nine formations. The thermal‐conductivity estimates are used in a finite‐element model to evaluate 2-D conductive heat refraction and, for a series of inversions of synthetic data, to assess the influence of systematic and random noise on the inversion results. A temperature‐anomaly map illustrates that a temperature field calculated by a forward application of the inversion results has less error than any single corrected BHT. Mean background heat flow at Pineview is found to be [Formula: see text] (±13 percent), but is locally higher [Formula: see text] due to heat refraction. The BHT inversion (1) is limited by systematic noise or model error, (2) achieves excellent resolution of a temperature field although resolution of individual formation gradients may be poor, and (3) generally cannot detect lateral variations in heat flow unless thermal‐conductivity structure is constrained.
Seismic reflection profiling for groundwater studies in Victoria, Australia
Authors: Geissler Paul E.
Published: October 2002

Experimental seismic reflection profiling was employed for groundwater studies in southeastern Australia. Equipment consisted of a simple engineering seismograph and tape recorder, and data reduction was carried out on a minicomputer using a graphics‐based processing system specifically written for the project. The investigation area is the site of a proposed induced groundwater recharge scheme in which surface water would be diverted to infiltrate aquifers outcropping several kilometers from a bore field which supplies up to half of the drinking water for the city of Geelong. The unconsolidated Tertiary aquifers of the region are known to be interrupted in places by steep normal and reverse faults. Since similar faulting had been inferred along the proposed recharge avenue, the objective of the seismic study was to verify, if possible, the assumption of aquifer continuity along the survey line. The reflection results reveal monoclinal folding in the upper unconsolidated sediments produced by recent movement on bedrock faults. The seismic study confirms that the aquifers are continuous between the proposed recharge and extraction areas despite structural complexity along the recharge avenue.
Quantitative interpretation of rotationally invariant parameters in magnetotellurics
Authors: Park S. K. , Livelybrooks D. W.
Published: October 2002

Use of rotationally invariant parameters derived from the magnetotelluric impedance tensor avoids problems with identification of electrical strike. However, quantitative analysis of an invariant must be used with caution. Layered models from inversion of invariant sounding curves accurately estimate the structure, as does one‐dimensional inversion of an invariant parameter, if the site is away from conductive three‐dimensional (3‐D) heterogeneities. Inversions at sites both above and away from a resistive heterogeneity and above a conductive heterogeneity result in errors. The errors are most serious at sites above a finite conductor. A section created by interpolation of layered models derived from invariants should always be modeled with multidimensional programs to verify the section’s accuracy. The above conclusions hold regardless of the type of invariant parameter used. We found no advantage to using the determinant over the arithmetic mean of the impedance tensor, or vice versa.
On: “In quest of the flank” by K. Larner, C. J. Beasley, and W. Lyn (GEOPHYSICS, 54, 701–717, June 1989)
Authors: Domenico S. N.
Published: October 2002

The subject paper explores the effectiveness of various reflection migration techniques in the imaging of salt‐dome flanks. Unfortunately, the authors do not consider extraction of the salt‐face reflection uniquely and, from this reflection and knowledge of velocity in sediments adjoining the salt dome, the accurate delineation of the salt dome. This procedure is described and demonstrated in the landmark paper “Structural inversion of salt dome flanks” by May and Covey (1983), which is not referenced by Larner et al.
Imaging of near‐borehole structure using full‐waveform sonic data
Authors: Hornby Brian E.
Published: October 2002

The full waveforms recorded by an array of receivers in a modern borehole sonic tool contain secondary arrivals that are reflected from near‐borehole structural features. These arrivals are used to form an image of the near‐borehole structural features in a manner similar to seismic migration. Possible uses of this technique include horizontal well logging; structural dip and contour determination; fault, salt dome, pinnacle reef, and fracture zone imaging; and EOR steam‐flood monitoring. Since both the source and the receivers pass through structures that cross the borehole, the downdip structure and the updip structure can be imaged separately. The technique involves a backprojection of the recorded data into a matrix of accumulation bins representing distances radially out from the borehole and along the borehole axis. Separate matrices are formed for the updip and for the downdip raypaths. The basic technique is illustrated with synthetic data, generated to approximate the case of a sonic tool logging through a dipping bed boundary. Results are shown for a borehole experiment performed in Alaska. The data were acquired with a research sonic prototype tool and specially recorded with a long acquisition time—20 ms per trace instead of the normal 5 ms. This longer acquisition time enabled the acquisition of scattered P and S arrivals to be recorded after most of the direct signal had died out. Images are shown of near‐borehole structural features to a distance of 18 m from the borehole. The images are presented against an independently derived formation lithology analysis and a high‐resolution synthetic seismic display computed from the measured density and slowness logs.
Wavelengths of earth structures that can be resolved from seismic reflection data
Authors: Jannane M. , Beydoun W. , Crase E. , Cao D. , Koren Z. , Landa E. , Mendes M. , Pica A. , Noble M. , Roeth G. , Singh S. , Snieder R. , Tarantola A. , Trezeguet D. , Xie M.
Published: October 2002

The aim of inverting seismic waveforms is to obtain the “best” earth model. The best model is defined as the one producing seismograms that best match (usually under a least‐squares criterion) those recorded. Our approach is nonlinear in the sense that we synthesize seismograms without using any linearization of the elastic wave equation. Since we use rather complete data sets without any spatial aliasing, we do not have the problem of secondary minima (Tarantola, 1986). Nevertheless, our gradient methods fail to converge if the starting earth model is far from the true earth (Mora, 1987; Kolb et al., 1986; Pica et al., 1989).
Finite‐element prestack reverse‐time migration for elastic waves
Authors: Teng Yu‐chiung , Dai Ting‐fang
Published: October 2002

Reverse‐time migration of zero‐offset data for acoustic waves has been successfully implemented by Whitmore (1983), Baysal et al. (1983), McMechan (1983), and Loewenthal and Mufti (1983). In reverse‐time migration, data recorded on the surface are used as the boundary condition and are extrapolated backward in time (Whitmore, 1983; Levin, 1984). Reverse‐time migration is mathematically a well‐posed problem. This is in contrast to conventional depth‐extrapolation‐migration schemes, in which the surface data are initial‐value conditions for solving the wave equation. Reverse‐time migration may offer improvements over conventional depth migration due to its freedom from dip‐angle limitations.
Encoding techniques for multiple source point seismic data acquisition
Authors: Womack J. E. , Cruz J. R. , Rigdon H. K. , Hoover G. M.
Published: October 2002

Recent advances in vibrator electronics have made the use of encoded sweeps for multiple source point data acquisition possible in an operational setting. Alternatives to existing operational multiple source point data acquisition techniques, using complementary series and E‐codes, are developed in this paper. Most existing techniques are, at each source point, a series of linear sweeps of predetermined polarity that enables the cancellation of the contributions from the other source points in processing. The complementary series techniques developed here also choose polarities such that the contributions from other source points can be cancelled. Pairs of E‐codes have been found that produce no crosscorrelation, which makes it possible to use E‐codes to produce a dual source point technique that is fundamentally different from the more conventional techniques. Field tests are carried out using E‐codes in dual source point schemes. Records from the respective source points are readily separated from the composite data collected and compared with records produced by a linear sweep from a single source point. Harmonic distortion appears to be the major limiting factor; however, record quality indicates that E‐codes can be used in operational multiple source point data acquisition.
Harnessing the ghost
Authors: Domenico S. N.
Published: October 2002

A previous field experiment demonstrated that the interface between an air‐water mixture of low fractional air volume (say, 0.005) and air‐free water is an effective reflector of acoustic waves, suggesting that acoustic waves in water might be beamed by placing an energy source at the focus of a paraboloidal interface between an air‐water mixture and air‐free water. When this interface is concave downward, wave energy traveling upward and outward from the source at the focus is reflected downward and the surface reflection (ghost) is eliminated. Accordingly, a paraboloid reflector consisting of perforated circular air pipes was constructed and tested with a small water gun at its focus. The structure, suspended from its apex, had a height of 4 ft (1.2 m), a base diameter of 8 ft (2.4 m), and a focus 1 ft (0.3 m) below the apex. The wave field, measured with an air‐bubble stream emanating from the perforated pipes, displays a beam with a nearly constant half‐width of 22 ft (6.7 m) created by the paraboloid reflector. Signal amplitudes directly below the paraboloid on an extension of its axis are as much as 9 dB above, and off‐axis amplitudes are as much as 17 dB below, signal amplitudes for no air‐bubble stream. The source signal’s amplitude spectrum, extending to about 1.5 kHz, is skewed toward higher frequencies by the paraboloid reflector, resulting in a dominant peak frequency of about 1210 Hz. The ghost is not evident. Theoretical wave fields of beamed monofrequency source signals demonstrate that the paraboloid reflector behaves as a high‐cut filter, the band‐pass narrowing as axial distance to the paraboloid decreases and off‐axis distance increases. Axial rates of decrease of the beamed experimental signal with increasing depth, at depths of 20 ft (6.1 m) and greater below the source, compare favorably to those of beamed theoretical continuous sinusoidal signals which are nearly equal at all frequencies within the experimental signal’s frequency band. Additional research is required to determine the complete effect of the paraboloid reflector on water‐gun signal characteristics. The small prototype reflector used in this experiment is not suitable for typical seismic exploration efforts because it produces excessively high‐frequency content. A useful paraboloid reflector may have to be several times the size of this prototype.
Fracture apertures from electrical borehole scans
Authors: Luthi S. M. , Souhaité P.
Published: October 2002

Three-dimensional finite-element modeling was performed to investigate the response to fractures of the Formation MicroScanner (Mark of Schlumberger), which records high-resolution electrical scans of the borehole wall. It is found that the equation [Formula: see text] describes, over two orders of magnitude of resistivity contrasts between borehole mud and the formation, the relationship between fracture width W (in mm), formation sensitivity [Formula: see text], mud resistivity [Formula: see text], and the additional current flow A caused by the presence of the fracture. A is the additional current which can be injected into the formation divided by the voltage, integrated along a line perpendicular across the fracture trace. Coefficient c and exponent b are obtained numerically from forward modeling. Tool standoffs of up to 2.5 mm and fracture dips in the range from 0° to 40° were found to have an insignificant effect on the above relation. A three‐step approach to detect, trace,and quantify fractures is used. Potential fractures in Formation MicroScanner images are detected as locations where conductivity exceeds the local matrix conductivity by a statistically significant amount. Integration over a circular area is performed around these locations to gather all excessive currents; this integral is then geometrically reduced to approximate the line integral A. Line sharpening and neighborhood connectivity tests are done to trace the fractures, and apertures are computed for all fracture locations. Results from a well into basement in Moodus (Connecticut) show that the method successfully traces fractures seen on Formation MicroScanner images. The resulting fracture apertures range from 10 μm to 1 mm. For the wider fractures there is acceptable agreement with apertures obtained from Stoneley wave reflection measurements. This unique and novel technique for characterizing fractures in wellbores has a very low detection threshold of around 10 μm and resolves fractures as little as 1 cm apart. Furthermore, it provides azimuthal orientation of the fractures.
Shortest path calculation of seismic rays
Authors: Moser T. J.
Published: October 2002

Like the traveling salesman who wants to find the shortest route from one city to another in order to minimize his time wasted on traveling, one can find seismic raypaths by calculating the shortest traveltime paths through a network that represents the earth. The network consists of points that are connected with neighboring points by connections as “long” as the traveltime of a seismic wave along it. The shortest traveltime path from one point to another is an approximation to the seismic ray between them, by Fermat’s principle. The shortest path method is an efficient and flexible way to calculate the raypaths and traveltimes of first arrivals to all points in the earth simultaneously. There are no restrictions of classical ray theory: diffracted raypaths and paths to shadow zones are found correctly. There are also no restrictions to the complexity or the dimensionality of the velocity model. Furthermore, there are no problems with convergence of trial raypaths toward a specified receiver nor with raypaths with only a local minimal traveltime. Later arrivals on the seismogram, caused by reflections on interfaces or by multiples, can be calculated by posing constraints to the shortest paths. The computation time for shortest paths from one point to all other points of the networks is almost linearly dependent on the number of points. The accuracy of the results is quadratically dependent upon the number of points per coordinate direction and the number of connections per point.
Orthorhombic anisotropy: A physical seismic modeling study
Authors: Cheadle Scott P. , Brown R. James , Lawton Don C.
Published: October 2002

An industrial laminate, Phenolic CE, is shown to possess seismic anisotropy. This material is composed of laminated sheets of canvas fabric, with an approximately orthogonal weave of fibers, bonded with phenolic resin. It is currently being used in scaled physical modeling studies of anisotropic media at The University of Calgary. Ultrasonic transmission experiments using this material show a directional variation of compressional‐ and shear‐wave velocities and distinct shear‐wave birefringence, or splitting. Analysis of group‐velocity measurements taken for specific directions of propagation through the material demonstrates that the observed anisotropy is characteristic of orthorhombic symmetry, i.e., that the material has three mutually orthogonal axes of two‐fold symmetry. For P waves, the observed anisotropy in symmetry planes varies from 6.3 to 22.4 percent, while for S waves it is observed to vary from 3.5 to 9.6 percent. From the Kelvin‐Christoffel equations, which yield phase velocities given a set of stiffness values, expressions are elaborated that yield the stiffnesses of a material given a specified set of group‐velocity observations, at least three of which must be for off‐symmetry directions.
Estimating grain‐scale fluid effects on velocity dispersion in rocks
Authors: Mavko Gary , Jizba Diane
Published: October 2002

The magnitude of the grain‐scale local flow effect on velocity dispersion in saturated rocks is quantified, by estimating the high‐frequency unrelaxed shear and bulk frame moduli, which are then combined with the Biot formulation to predict total dispersion. The method is relatively independent of assumptions about idealized pore geometries and unknown parameters such as pore aspect ratios. The local flow effect depends on the heterogeneity of pore stiffness, in particular the presence of compliant cracks and grain contacts; the pressure dependence of the dry rock properties is shown to contain the essential information about the distribution of pore stiffnesses needed to estimate the high‐frequency saturated behavior. To first order, the unrelaxed wet frame compressibility at any given pressure is shown to be approximately the dry frame compressibility at very high pressure; second order corrections add the additional compressibility gained by replacing an amount of mineral equal to the compliant pore volume with fluid. The method predicts that the difference between relaxed and unrelaxed shear compliance is simply proportional to that in bulk. The results for total dispersion (local flow plus Biot) explain quite well the measured P- and S-wave dispersion for a variety of saturated rocks.
Inversion of airborne electromagnetic survey data for sea‐ice keel shape
Authors: Liu Guimin , Kovacs Austin , Becker Alex
Published: October 2002

It is possible to interpret conventional airborne electromagnetic (EM) data acquired over ice‐covered Arctic seas to obtain values of the sea ice thickness and, where needed, the actual sea ice keel geometry. To do so, we require high‐frequency (inductive limit) data that allows us to assume that the ice is virtually transparent to the EM fields while the sea water forms a perfect conductor. Practically, a 100 kHz operating frequency is needed, but data acquired at a lower frequency can be scaled to obtain the required inductive limit anomaly. The data inversion is done by linking Occam’s inversion method to a rapid numerical, two‐dimensional, forward solution for the ice keel problem. A most useful feature of the adopted inversion scheme is the minimization of the roughness or the mean square slope of the keel boundary. In some cases, where the keel might be bounded by steeply dipping walls, this constraint may result in a less accurate solution than might be obtained with a conventional technique. In most cases the advantage in stability that it provides outweighs the possible loss of accuracy that it may occasion. Tests on synthetic data show a possible worst case ice thickness error of about 15 percent. The results of inversion tests for two sets of survey data acquired near Prudhoe Bay, Alaska, also indicate an accuracy of this order of magnitude. While some portion of the inversion error must be ascribed to the roughness constraint and is therefore inherent to the inversion technique used, the remainder must be ascribed to the instrumentation and is probably remediable.
Regional‐residual gravity anomaly separation using the minimum‐curvature technique
Authors: Mickus K. L. , Aiken C. L. V. , Kennedy W. D.
Published: October 2002

One of the most difficult problems in gravity interpretation is the separation of regional and residual gravity anomalies from the Bouguer gravity anomaly. This study discusses the application of the minimum‐curvature method to determine the regional and residual gravity anomalies.
Geoelectric sounding for the determination of aquifer characteristics in parts of the Umuahia area of Nigeria
Authors: Mbonu P. D. C. , Ebeniro J. O. , Ofoegbu C. O. , Ekine A. S.
Published: October 2002

Seventeen Schlumberger vertical electrical soundings (VES) were carried out in parts of the Umuahia area of Nigeria, using a maximum current electrode separation of 1 km. The data were interpreted using a conventional partial curve‐matching method to obtain initial model parameters, which were used in a computer program to obtain final parameters. Three soundings were made at existing boreholes for comparison. Aquifer parameters of hydraulic conductivity and transmissivity were obtained by analyzing pumping test data from existing boreholes. The results of the interpretation revealed three distinct geoelectric layers overlying a conductive geoelectric basement. Based on the model obtained, aquifer hydraulic conductivity and transmissivity were calculated. The hydraulic conductivity calculated agreed closely with that determined from pumping test data. The results of the present study also indicate that the entire area is divided into two zones, each of which is homogeneous in hydraulic properties and water quality, but distinct from the other zone. A local groundwater divide between the Imo and Kwa‐Ibo drainage systems was also defined.
3-D tomographic imaging of near‐surface seismic velocity and attenuation
Authors: Brzostowski Matthew A. , McMechan George A.
Published: October 2002

As a result of the similarity between velocity and attenuation imaging, we have implemented both using the same 3-D tomography software, with simple variable changes. The resulting sets of linear equations are solved by the Simultaneous Iterative Reconstruction Technique (SIRT). The algorithm is applied to 3-D estimation of near‐surface velocity and attenuation distributions from 3-D surface‐survey field data from the Ouachita frontal thrust zone in southeastern Oklahoma; the images obtained correlate well with the known surface geology. Resolution analysis by computation of point spread functions indicates highest resolution in the direction parallel to the densest distribution of survey points (the receiver lines).
A comparison of satellite and shipboard gravity measurements in the Gulf of Mexico
Authors: Small Christopher , Sandwell David T.
Published: October 2002

Satellite altimeters have mapped the marine geoid over virtually all of the world’s oceans. These geoid height measurements may be used to compute free air gravity anomalies in areas where shipboard measurements are scarce. Two‐dimensional (2-D) transformations of geoid height to gravity are limited by currently available satellite track spacing and usually sacrifice short wavelength resolution. Full resolution may be retained along widely spaced satellite tracks if a one dimensional (1-D) transformation is used. Although the 1-D transform retains full resolution, it assumes that the gravity field is lineated perpendicular to the profile and is therefore limited by the orientation of the profile relative to the field. We investigate the resolution and accuracy of the 1-D transform method in the Northern Gulf of Mexico by comparing satellite gravity profiles with high quality shipboard data provided by Edcon Inc. The long wavelength components of the gravity field are constrained by a low degree reference field while the short wavelength components are computed from altimeter profiles. We find that rms misfit decreases with increasing spherical harmonic degree of the reference field up to 180 degrees (λ > 220 km) with negligible improvement for higher degrees. The average rms misfit for the 17 profiles used in this study was 6.5 mGal with a 180 degree reference field. Spectral coherence estimates indicate that the satellite data resolve features with wavelengths as short as 25 km.
Relating P‐wave attenuation to permeability
Authors: Akbar Nabil , Dvorkin Jack , Nur Amos
Published: October 2002

To relate P‐wave attenuation to permeability, we examine a three‐dimensional (3-D) theoretical model of a cylindrical pore filled with viscous fluid and embedded in an infinite isotropic elastic medium. We calculate both attenuation and permeability as functions of the direction of wave propagation. Attenuation estimates are based on the squirt flow mechanism; permeability is calculated using the Kozeny‐Carman relation. We find that in the case when a plane P‐wave propagates perpendicular to the pore orientation [Formula: see text], attenuation is always higher than when a wave propagates parallel to this orientation [Formula: see text]. The ratio of these two attenuation values [Formula: see text] increases with an increasing pore radius and decreasing frequency and saturation. By changing permeability, varying the radius of the pore, we find that the permeability‐attenuation relation is characterized by a peak that shifts toward lower permeabilities as frequency decreases. Therefore, the attenuation of a low‐frequency wave decreases with increasing permeability. We observe a similar trend on relations between attenuation and permeability experimentally obtained on sandstone samples.
Can we image complex structures with first‐arrival traveltime?
Authors: Geoltrain Sébastien , Brac Jean
Published: October 2002

We experienced difficulties when attempting to perform seismic imaging in complex velocity fields using prestack Kirchhoff depth migration in conjunction with traveltimes computed by finite‐differencing the eikonal equation. The problem arose not because of intrinsic limitations of Kirchhoff migration, but rather from the failure of finite‐differencing to compute traveltimes representative of the energetic part of the wavefield. Further analysis showed that the first arrival is most often associated with a marginally energetic event wherever subsequent arrivals exist. The consequence is that energetic seismic events are imaged with a kinematically incorrect operator and turn out mispositioned at depth. We therefore recommend that first‐arrival traveltime fields, such as those computed by finite‐differencing the eikonal equation, be used in Kirchhoff migration only with great care when the velocity field hosts multiple transmitted arrivals; such a situation is typically met where geological structure creates strong and localized velocity heterogeneities, which partition the incident and reflected wavefields into multiple arrivals; in such an instance, imaging cannot be strictly considered a kinematic process, as it must be performed with explicit reference to the relative amplitudes of multiple arrivals.
Accurate and efficient seismic modeling in random media
Authors: Kneib Guido , Kerner Claudia
Published: October 2002

The optimum method for seismic modeling in random media must (1) be highly accurate to be sensitive to subtle effects of wave propagation, (2) allow coarse sampling to model media that are large compared to the scale lengths and wave propagation distances which are long compared to the wavelengths. This is necessary to obtain statistically meaningful overall attributes of wavefields. High order staggered grid finite‐difference algorithms and the pseudospectral method combine high accuracy in time and space with coarse sampling. Investigations for random media reveal that both methods lead to nearly identical wavefields. The small differences can be attributed mainly to differences in the numerical dispersion. This result is important because it shows that errors of the numerical differentiation which are caused by poor polynomial interpolation near discontinuities do not accumulate but cancel in a random medium where discontinuities are numerous. The differentiator can be longer than the medium scale length. High order staggered grid finite‐difference schemes are more efficient than pseudospectral methods in two‐dimensional (2-D) elastic random media.
Scale effects on velocity dispersion: From ray to effective medium theories in stratified media
Authors: Marion Dominique , Mukerji Tapan , Mavko Gary
Published: October 2002

Wave propagation in stratified media may be explained by ray theory, effective medium theory, or scattering theory depending on the scales of wavelength and layer spacing. To effectively integrate and use seismic data at different frequencies and widely varying scales, it is essential to understand the domain of applicability of long and short wavelength behavior and the transition between them. A joint experimental and theoretical study was conducted to investigate velocity behavior at the transition from ray theory to effective medium theory in stratified media. Velocity measurements were performed at 50 and 500 kHz on periodic media composed of steel and plastic discs. The ratio of wavelength to layer spacing, λ/d, spanned more than two orders of magnitude between 0.1 and 50, and the volume fraction of steel ranged from 9 to 89 percent by volume. Our results confirm that velocities in stratified media depend on composition and are controlled by the ratio of wavelength to layer spacing. Velocities in the short wavelength limit are generally faster than velocities in the long wavelength limit. We find that transition from ray to effective medium approximations occurs over a narrow range of λ/d at a value of approximately 10. The amount of velocity change increases with impedance contrast, but the value of λ/d at the transition is generally independent of the composition of the stratified medium. Our numerically simulated waveforms are in close agreement with the experimentally observed delayed first arrival in the long wavelength limit and with the reduced amplitudes at the transition from short to long wavelength regime.
Comparison of AVO indicators: A modeling study
Authors: Castagna John P. , Smith Steven W.
Published: October 2002

A worldwide collection of 25 sets of velocity and density measurements from adjacent shales, brine sands, and gas sands was acquired with full‐waveform sonic, dipole sonic, and conventional well logging devices and/or in the laboratory. These data provide theoretical shale over brine‐sand and shale over gas‐sand P‐wave and S‐wave normal‐incedence reflection coefficents [Formula: see text] and [Formula: see text]), AVO intercepts (A), AVO gradients (B), the AVO indicators [Formula: see text] (reflection coefficient difference), and A * B (AVO product). The reflection coefficient difference is found to be a more universal indicator than the AVO product in clastic stratigraphic intervals. For shale over brine‐sand reflections, the average [Formula: see text] tends to be near zero and relatively invariant with depth. Irrespective of gas‐sand impedance, [Formula: see text] is always negative for shale over reservoir quality gas‐sand reflections and more negative than for the corresponding brine‐sand reflections. In comparison, the AVO product may be positive, near zero, or negative for gas‐sands depending on the impedance contrast with the overlying shale. These measurements also verify that [Formula: see text] is well approximated by a simple linear combination of A and B.
Migration of shallow seismic reflection data
Authors: Black Ross A. , Steeples Don W. , Miller Richard D.
Published: October 2002

We present an analysis of migration effects on seismic reflection images of very shallow targets such as those that are common objectives of engineering, groundwater, and environmental investigations. We use an example of seismic reflection data from depths of 5 to 15 m that show negligible effect from migration, despite the apparent steep dip on the seismic section. Our analysis of the question of when to migrate shallow reflection data indicates it is critical to take into account the highly variable near‐surface velocities and the vertical exaggeration on the seismic section. A simple set of calculations is developed as well as a flow chart based on the “migrator’s equation” that can predict whether migration of an arbitrary shallow seismic section is advisable. Because shallow reflection data are often processed on personal computers, unnecessary migration of a large data set can be prohibitively time‐consuming and wasteful.
Predicting lithology and transport properties from acoustic velocities based on petrophysical classification of siliciclastics
Authors: Vernik L.
Published: October 2002

Based on the recently developed petrophysical classification of siliciclastics, which takes into account the amount of the volumetric clay content C and textural position of clay, it is shown that acoustic velocities can be fairly accurate tools in predicting lithology, porosity, and ultimately, transport properties of these rocks. Four major petrophysical groups of carbonate‐ and organic‐poor siliciclastics are distinguished: (1) clean arenites (C < 2 percent), (2) arenites and arkoses (C = 2–15 percent), (3) wackes (C = 15–35 percent), and (4) shales (C > 35 percent). The compressional velocity versus porosity relation for consolidated rocks in each of these groups is found to be linear with very high correlation coefficients. This allows for remarkably accurate porosity estimates or lithology prediction in consolidated siliciclastics from acoustic velocities compared to the widely used time average (Wyllie) equation or its improved modification (Raymer equations), both of which neglect textural factors, or recently proposed relations based on the critical porosity concept. The transforms proposed display fundamental trends subject to only a second‐order regional effects, such as details of mineralogy, grain size distribution, and authigenic clay development. These trends primarily reflect the processes of chemical diagenesis, including pressure solution, cementation, and mineral phase transformation. The processes of lithification of unconsolidated sediments by physical compaction and initial cementation are characterized by a steeper slope of the velocity‐porosity transform because of a more pronounced velocity increase compared to the porosity reduction at this stage. The use of the [Formula: see text] ratio versus velocity relation for lithology prediction is limited compared to the [Formula: see text] versus porosity plots; however, if both porosity and lithology are unknown, the velocity ratio can still be used for discriminating between predominantly grain‐supported reservoir rocks (clean arenite, arenite and arkose) and clay matrix‐supported (wacke, shale) rocks. Finally, a strong correlation between porosity and permeability of clean arenites is weakened somewhat in arenites. Nonetheless, even in the latter case, an order of magnitude accuracy in permeability assessment based on porosity can be achieved.
Residual statics estimation using the genetic algorithm
Authors: Wilson William G. , Laidlaw William G. , Vasudevan Kris
Published: October 2002

An optimization problem as complex as residual statics estimation in seismic image processing requires novel techniques. One interesting technique, the genetic algorithm, is based loosely on the optimization process forming the basis of biological evolution. The objective of this paper is to examine this algorithm’s applicability to residual statics estimation and present three new ingredients that help the algorithm successfully resolve residual statics. These three ingredients include (1) breaking the population into subpopulations with restricted breeding between the subpopulations, (2) localizing the search, to varying degrees, about the uncorrected input stack, and (3) modifying the optimization function to take account of CDP‐dependent structural features. Introducing subpopulations has the effect of enhancing the search when the volume of phase space being searched is large and limited information is given about where the algorithm should concentrate its efforts. Subpopulations work well initially, but as the performance increases, the search efficiency decreases. Thus, search efficiency is dependent on both the subpopulation size and the present performance of the subpopulation. The greediness of genetic algorithms in their rapid acceptance of a local minimum can be recompensed through a more cautious and user‐controlled exploration of the phase space. Specifically, genetic algorithms can be "fed" the uncorrected input stack as a way of biasing the search in the region of phase space that contains the rough event images observable in most uncorrected seismic stacks. We compare three types of starting populations: (1) a randomized population, (2) a biased start with a randomized population save one individual representing the input stack, and (3) a biased start restricted to a slowly expanding (generation‐dependent) volume of phase space. Efficient searches also require an optimization function that places the perfectly corrected seismic image at the function’s global maximum. Constructing such a function is nontrivial, and we implement a seismic data set that allows us to examine the genetic algorithm’s sensitivity to inappropriate optimization functions.
Minimum entropy deconvolution with frequency‐domain constraints
Authors: Sacchi Mauricio D. , Velis Danilo R. , Comínguez Alberto H.
Published: October 2002

A method for reconstructing the reflectivity spectrum using the minimum entropy criterion is presented. The algorithm (FMED) described is compared with the classical minimum entropy deconvolution (MED) as well as with the linear programming (LP) and autoregressive (AR) approaches. The MED is performed by maximizing an entropy norm with respect to the coefficients of a linear operator that deconvolves the seismic trace. By comparison, the approach presented here maximizes the norm with respect to the missing frequencies of the reflectivity series spectrum. This procedure reduces to a nonlinear algorithm that is able to carry out the deconvolution of band‐limited data, avoiding the inherent limitations of linear operators. The proposed method is illustrated under a variety of synthetic examples. Field data are also used to test the algorithm. The results show that the proposed method is an effective way to process band‐limited data. The FMED and the LP arise from similar conceptions. Both methods seek an extremum of a particular norm subjected to frequency constraints. In the LP approach, the linear programming problem is solved using an adaptation of the simplex method, which is a very expensive procedure. The FMED uses only two fast Fourier transforms (FFTs) per iteration; hence, the computational cost of the inversion is reduced.
Inversion of induced polarization data
Authors: Oldenburg Douglas W. , Li Yaoguo
Published: October 2002

We develop three methods to invert induced polarization (IP) data. The foundation for our algorithms is an assumption that the ultimate effect of chargeability is to alter the effective conductivity when current is applied. This assumption, which was first put forth by Siegel and has been routinely adopted in the literature, permits the IP responses to be numerically modeled by carrying out two forward modelings using a DC resistivity algorithm. The intimate connection between DC and IP data means that inversion of IP data is a two‐step process. First, the DC potentials are inverted to recover a background conductivity. The distribution of chargeability can then be found by using any one of the three following techniques: (1) linearizing the IP data equation and solving a linear inverse problem, (2) manipulating the conductivities obtained after performing two DC resistivity inversions, and (3) solving a nonlinear inverse problem. Our procedure for performing the inversion is to divide the earth into rectangular prisms and to assume that the conductivity σ and chargeability η are constant in each cell. To emulate complicated earth structure we allow many cells, usually far more than there are data. The inverse problem, which has many solutions, is then solved as a problem in optimization theory. A model objective function is designed, and a “model” (either the distribution of σ or η)is sought that minimizes the objective function subject to adequately fitting the data. Generalized subspace methodologies are used to solve both inverse problems, and positivity constraints are included. The IP inversion procedures we design are generic and can be applied to 1-D, 2-D, or 3-D earth models and with any configuration of current and potential electrodes. We illustrate our methods by inverting synthetic DC/IP data taken over a 2-D earth structure and by inverting dipole‐dipole data taken in Quebec.
Viscoelastic finite‐difference modeling
Authors: Robertsson Johan O. A. , Blanch Joakim O. , Symes William W.
Published: October 2002

Real earth media disperse and attenuate propagating mechanical waves. This anelastic behavior can be described well by a viscoelastic model. We have developed a finite‐difference simulator to model wave propagation in viscoelastic media. The finite‐difference method was chosen in favor of other methods for several reasons. Finite‐difference codes are more portable than, for example, pseudospectral codes. Moreover, finite‐difference schemes provide a convenient environment in which to define complicated boundaries. A staggered scheme of second‐order accuracy in time and fourth‐order accuracy in space appears to be optimally efficient. Because of intrinsic dispersion, no fixed grid points per wavelength rule can be given; instead, we present tables, which enable a choice of grid parameters for a given level of accuracy. Since the scheme models energy absorption, natural and efficient absorbing boundaries may be implemented merely by changing the parameters near the grid boundary. The viscoelastic scheme is only marginally more expensive than analogous elastic schemes. The efficient implementation of absorbing boundaries may therefore be a good reason for also using the viscoelastic scheme in purely elastic simulations. We illustrate our method and the importance of accurately modeling anelastic media through 2-D and 3-D examples from shallow marine environments.
THE GULF GRAVIMETER
Authors: Wyckoff R. D.
Published: October 2002

The design features of the Gulf gravimeter are presented accompanied by a brief discussion of general gravimeter design problems. In addition to the description of the unastatized instrument which is the type finally selected for commercial development, brief consideration is given to two astatized instruments including a bifilar gravimeter the construction of which was carried to completion.
Apparent resistivity curves in controlled‐source electromagnetic sounding directly reflecting true resistivities in a layered earth
Authors: Das Umesh C.
Published: October 2002

Conversion of the measured voltages in direct current resistivity sounding methods into apparent resistivity [Formula: see text] is a useful step since [Formula: see text] data provide information about the subsurface resistivity variations with depth. This resistivity information then helps select a model for inverting the sounding data. In the controlled‐source electromagnetic method (CSEM), conversion of the measured electric and magnetic fields into apparent resistivity values has not been popular. This attitude may be attributed to the difficulties in the inversion of the resistivity of a half‐space from the electromagnetic (EM) field components as well as to the nonunique nature of the inversion giving two resistivity values for a single measurement. Two measured components—the vertical magnetic field [Formula: see text] and the tangential electric field [Formula: see text] as a result of a vertical magnetic dipole source—are combined to derive an exact apparent resistivity in a way similar to that used in direct current resistivity methods. Conversion of the measured [Formula: see text] and [Formula: see text] field components into apparent resistivity is found to be simple and can be carried out on a programmable pocket calculator. Theoretical apparent resistivity curves for frequency‐domain electromagnetic sounding show features similar to magnetotelluric (MT) and direct current dipole‐dipole apparent resistivity curves.