Imaging overturned waves by plane-wave migration in tilted coordinates (ps.gz 2498K) (pdf 599K) (src 11765K)
Shan G. and Biondi B.
We image overturned waves by decomposing the source and receiver wavefields into plane-waves. For each plane-wave, we extrapolate the source and receiver wavefields in a tilted coordinate system and cross-correlate them to obtain Common Image Gathers (CIGs). The tilting angle for the coordinate system is determined by the propagation direction of the plane wave. In tilted coordinates, the propagation direction is close to the extrapolation direction, so we can image steeply dipping reflectors and overturned waves with the one-way wave equation. We can also obtain robust, dip-dependent angle-domain CIGs (ADCIGs) by the same method employed in reverse-time migration. These gathers provide moveout information and thus are very important for velocity analysis on steeply dipping reflectors. Since plane-wave migration needs no padding and the extrapolation is one-way wave equation based, our method is very efficient. We demonstrate our method on the Marmousi model by computing the Green's function for a point source on the surface. We also apply our method to a North Sea real dataset with overturned events.
Adaptive phase-ray wavefield extrapolation (ps.gz 2994K) (pdf 936K) (src 30172K)
Shragge J. and Sava P.
Riemannian wavefield extrapolation (RWE) is a generalization of downward continuation to coordinate systems that closely conform to the orientation of extrapolated wavefields. If the coordinate system overturns, so does the computed wavefield, despite being extrapolated with a one-way solution to the acoustic wave-equation. This allows for accurate imaging of structures of arbitrarily steep dips with simple operators equivalent to standard extrapolators. An obvious question for RWE is which is an optimal coordinate system for a given velocity model. One option is to compute ray coordinates as a solution to the wide-band eikonal equation in a smoothed velocity model. However, this solution ignores the natural variability and frequency dependence of wavepaths in cases of complicated velocity models, for example under salt bodies. The solution advocated in this paper is a recursive bootstrap procedure where a frequency-dependent coordinate system is computed on-the-fly at every step from the gradient of the monochromatic wavefield phase of the preceding few steps, coupled with standard RWE.
Updating ray-coordinate systems with phase-rays (ps.gz 17160K) (pdf 1783K) (src 46637K)
Shragge J. and Biondi B.
Riemannian wavefield extrapolation (RWE) casts the problem of wavefield extrapolation in a framework independent of a particular coordinate system Sava and Fomel (2003). A practical implementation of RWE, though, requires specifying the computation domain on which to perform extrapolation. One judicious choice is a rayfield where the natural extrapolation direction is stepping in time along an individual ray. Rays in simple media are characterized by smooth curves, and are regularly distributed and (usually) triplication-free. ...
Aliasing in prestack wavefield continuation migration (ps.gz 1143K) (pdf 446K) (src 3682K)
Artman B., Shragge J., and Biondi B.
With the widespread adoption of wavefield continuation methods for prestack migration, the concept of operator aliasing warrants revisiting. While zero-offset migration is unaffected by spatial aliasing due to the migration operator, this is not the case for prestack migration. This problem arises in any situation where sources and receivers are not collocated at every sampling point. Once anti-aliasing criteria have been calculated, aliased energy may be prevented from entering the image space by using a source function of appropriate band-width, or band-limiting the energy of the contributing data. As shot-profile migration is the most accurate and expensive imaging algorithm, data axes are commonly subsampled to save cost. We analyse the costs and benefits of implementing anti-aliasing measures to remediate unequal sampling intervals. While some bandwidth of the output image is lost in this process, it will attend to aliasing problems that will be most apparent in the shallow overburden and steeply dipping reflectors. Despite the loss in resolution, any proposed method still enjoys better bandwidth than source-receiver migration with the same data.
Ocean-bottom hydrophone and geophone coupling (ps.gz 4309K) (pdf 1020K) (src 36455K)
Rosales D. A. and Guitton A.
We compare two methods for combining hydrophone and geophone components for an ocean-bottom seismic experiment to eliminate the receiver ghosts associated with this type of seismic acquisition. One approach is in the time domain, the other in the frequency domain. Both approaches are compared with the 2D OBS data over the Mahogany field in the Gulf of Mexico. The receiver ghosts are eliminated more efficiently with the frequency domain method, because this method combines the data in two different steps: i) calibration, and ii) deghosting.
Surface boundary condition for one-way wave equation shot-profile migration (ps.gz 924K) (pdf 531K) (src 2328K)
Valenciano A. A., Tisserant T., and Biondi B.
The one-way approximation to the full wave equation has been widely used for imaging the earth's interior Claerbout (1985). This approximation ignores back-scattering in the wavefield but usually works well with surface seismic data. In the shot-profile migration scheme, two one-way wave equations need to be solved. One downward extrapolates the source wavefield and the other downward extrapolates the receiver wavefield. By using an imaging condition, the subsurface image is formed Claerbout (1971). Usually, the initial surface boundary condition for downward extrapolating the source wavefield is chosen to be an impulse convolved with a wavelet at the shot position. However, downward extrapolation with the one-way wave equation requires boundary conditions on the surface, z=0, at all locations and all times. Since horizontal (or high-propagation-angle) ...
Improving the amplitude accuracy of downward continuation operators (Part 2) (ps.gz 303K) (pdf 447K) (src 1971K)
Vlad I. and Tisserant T.
One-way wavefield continuation methods correctly account for traveltimes, but the amplitude and phase of the images they produce can still be improved. Zhang et al. present theoretical formulations of amplitude-improving corrections for shot-profile migration. Vlad et al. (2003) show concrete ways of implementing Zhang's theory for both finite-difference and mixed-domain extrapolators, with applications to constant-velocity, ...
Least-squares joint imaging of multiples and primaries applied to 3-D field data (ps.gz 1644K) (pdf 1369K) (src 6945K)
In this paper I outline the extension to 3-D of the Least-squares Joint Imaging of Multiples and Primaries (LSJIMP) method for simultaneously separating multiples and primaries and combining their information. I apply LSJIMP to a 3-D field dataset and demonstrate that the method cleanly removes surface-related multiples from the data while preserving the prestack amplitude signature of the primaries. LSJIMP compares favorably to least-squares Radon demultiple, both in terms of computational performance and result quality.
Multidimensional multiple attenuation in complex geology: illustration on the Sigsbee2B dataset (ps.gz 11440K) (pdf 2381K) (src 35445K)
A pattern-based multiple attenuation technique is tested on the Sigsbee2B dataset. The results of multiple removal are analyzed in the image space after migration to better understand the impact of this process on the primaries. When an accurate model of the primaries (signal) and the multiples (noise) exist for the estimation of the noise and signal annihilation filters (i.e., non-stationary multidimensional prediction-error filters), this method removes the multiples extremely well while preserving the primaries. When the model of the multiples is provided by the Spitz approximation, which consists in convolving the data with the noise annihilation filters to get a signal model, good results are obtained if 3D filters are utilized.
Subtraction of surface-related multiples: adaptive subtraction vs. pattern recognition (ps.gz 2611K) (pdf 784K) (src 15188K)
Two multiple subtraction techniques are tested on a 2D synthetic dataset. The first technique is adaptive subtraction, where the signal is assumed to have minimum energy. The second technique is pattern recognition, where the signal and noise are assumed to have different multivariate spectra. Overall, the pattern based technique leads to a better subtraction of the multiples.
Attenuation of diffracted multiples with an apex-shifted tangent-squared radon transform in image space (ps.gz 2334K) (pdf 859K) (src 38499K)
Alvarez G., Biondi B., and Guitton A.
We propose to attenuate diffracted multiples with an apex-shifted tangent-squared Radon transform in angle domain common image gathers (ADCIG). Usually, where diffracted multiples are a problem, the wavefield propagation is complex and the moveout of primaries and multiples in data space is irregular. In our method, the complexity of the wavefield is handled by the migration provided reasonably accurate migration velocities are used. As a result, the moveout of the multiples is well behaved in the ADCIGs. For 2D data, our apex-shifted tangent-squared Radon transform maps the 2D image space into a 3D model space cube whose dimensions are depth, curvature and apex-shift distance. Well-corrected primaries map to or near the zero curvature plane and specularly-reflected multiples map to or near the zero apex-shift plane. Diffracted multiples map elsewhere in the cube according to their curvature and apex-shift distance. Thus, specularly reflected as well as diffracted multiples can be attenuated simultaneously. We illustrate our approach with a segment of a 2D seismic line over a large salt body in the Gulf of Mexico. We show that ignoring the apex shift compromises the attenuation of the diffracted multiples, whereas our approach attenuates both the specularly-reflected and the diffracted multiples without compromising the primaries.
Migration of surface-related multiples: tests on the Sigsbee2B dataset (ps.gz 3957K) (pdf 996K) (src 15308K)
Shan G. and Guitton A.
We present a theory to generate pseudo-primary shot gathers from multiple and primary reflections by performing a surface-consistent cross-correlation. The estimated pseudo-primaries exhibit the same kinematics as the original dataset with few transformation artifacts. We demonstrate that pseudo-primaries can accurately estimate missing traces as long as the gaps are within the acquisition spread. Pseudo-primaries can also help to extrapolate the data outside the acquisition spread. The image obtained by migrating the pseudo-primary gathers shows that multiple migration can provide valuable information under complex geology.
3-D Angle-domain common-image gathers for migration velocity analysis (ps.gz 1027K) (pdf 693K) (src 6038K)
Biondi B. and Tisserant T.
Angle-Domain Common Image Gathers (ADCIGs) are an essential tool for Migration Velocity Analysis (MVA). We present a method for computing ADCIGs in 3-D from the results of wavefield-continuation migration. The proposed methodology can be applied before or after the imaging step in a migration procedure. When computed before imaging, 3-D ADCIGs are functions of the offset ray parameters ;we derive the geometric relationship that links the offset ray parameters to the aperture angle and the reflection azimuth .When computed after imaging, 3-D ADCIGs are directly produced as functions of and . The mapping of the offset ray parameters into the angles depends on both the local dips and the local interval velocity; therefore, the transformation of ADCIGs computed before imaging into ADCIGs that are function of the actual angles is difficult in complex structure. In contrast, the computation of ADCIGs after imaging is efficient and accurate even in presence of complex structure and a heterogeneous velocity function. On the other hand, the estimation of the offset ray parameters is less sensitive to velocity errors than the estimation of the angles .When ADCIGs that are functions of the offset ray parameters are adequate for the application of interest (e.g. ray-based tomography), the computation of ADCIGs before imaging might be preferable. Errors in the migration velocity cause the image point in the angle domain to shift along the normal to the apparent geological dip. By assuming stationary rays (i.e. small velocity errors), we derive a quantitative relationship between this normal shift and the traveltime perturbation caused by velocity errors. This relationship can be directly used in a MVA procedure to invert depth errors measured from ADCIGs into migration velocity updates. In this paper, we use it to derive an approximate 3-D Residual Moveout (RMO) function for measuring inconsistencies between the migrated images at different and .We tested the accuracy of our kinematic analysis on a 3-D synthetic data set with steeply dipping reflectors and a vertically varying propagation velocity. The tests confirm the accuracy of our analysis and illustrate the limitations of the straight-rays approximation underlying our derivation of the 3-D RMO function.
Residual move-out analysis with 3-D angle-domain common-image gathers (ps.gz 518K) (pdf 642K) (src 1155K)
Tisserant T. and Biondi B.
We describe a method to update the velocity model from the residual move-out information contained in 3-D angle-domain common-image gathers. The 3-D angle-domain common-image gathers computed after wave-equation migration are functions of the aperture angle and the reflection azimuth angle. We perform a velocity error analysis by semblance using 2-D and 3-D residual move-out functions. Both functions enable us to update the velocity model. The 3-D function leads to a better estimation of the velocity error in the case of 3-D events.
Sensitivity kernels for wave-equation migration velocity analysis (ps.gz 3985K) (pdf 665K) (src 12586K)
Sava P. and Biondi B.
The success of migration velocity analysis methods is strongly dependent on the characteristics of the linearized tomographic operator that is inverted to estimate velocity updates. To study the properties of wave-equation migration velocity analysis, we analyze its sensitivity kernels. Sensitivity kernels describe the dependence of data space elements to small changes of model space elements. We show that the sensitivity kernels of wave-equation MVA depend on the frequency content of the recorded data and on the background velocity model. Sensitivity kernels computed assuming the presence of a salt body in the background velocity show that these kernels are drastically different from idealized ``fat rays''. Consequently sensitivity kernels cannot be approximated by artificial fattening of geometrical rays. Furthermore, our examples illustrate the potential of finite-frequency MVA as well as the frequency-dependent nature of illumination for subsalt regions.
Diffraction-focusing migration velocity analysis with application to seismic and GPR data (ps.gz 9108K) (pdf 1170K) (src 28571K)
Sava P., Biondi B., and Etgen J.
We propose a method for estimating interval velocity using the kinematic information in diffractions. We extract velocity information from migrated diffracted events by analyzing their residual focusing in physical space (depth and midpoint) using prestack residual migration. The results of this residual-focusing analysis are fed to a linearized inversion procedure that produces interval velocity updates. Our inversion procedure employs a wavefield-continuation operator linking perturbations of interval velocities to perturbations of migrated images, based on the principles of Wave Equation Migration Velocity Analysis (WEMVA) introduced in recent years. We measure the accuracy of the migration velocity by using a diffraction-focusing criterion, instead of the criterion of flatness of migrated common-image gathers that is commonly employed in Migration Velocity Analysis (MVA). This new criterion enables us to extract velocity information from events that would be challenging to use with conventional MVA methods, and thus makes our method a powerful complement to conventional MVA methods. We demonstrate our method with synthetic and real Ground-Penetrating Radar data.
Velocity uncertainty in tomography (ps.gz 6368K) (pdf 915K) (src 15294K)
Clapp R. G.
The conventional method for migration velocity analysis scans over one (or possibly multiple) move-out parameter(s) ang the offset or angle axis. The appropriate move-out parameter is then selected based on what produces the best coherence. The coherence as a function of the scanning parameter provides important information on how confident we are of our given move-out measure. In this paper, the move-out parameter selection is set up as an inverse problem and multiple, equi-probable move-out fields are generated. These various realization of move-out are then used to update the velocity model and migrated image. Early results are promising.
First-order lateral interval velocity estimates without picking (ps.gz 990K) (pdf 400K) (src 23384K)
Guitton A., Claerbout J., and Lomask J.
A new method for estimating interval velocities without picking is proposed. The first step applies a normal move-out correction with a v(z) stacking velocity to common mid-point gathers. The second step estimates local stepouts at every offset and time for each gather. Local stepouts across offset are then integrated to obtain local time shifts. The integration is done in the Fourier domain for increased speed. Finally the interval velocity is estimated in the space by fitting the time shifts with a tomographic inversion procedure based on a straight rays geometry. This approach is tested on a Gulf of Mexico dataset with flat geology where recovery of lateral velocity variations across faults is demonstrated.
Velocity estimation for seismic data exhibiting focusing-effect AVO (Part 4) (ps.gz 70K) (pdf 204K) (src 383K)
Focusing-effect AVO (FEAVO) can be eliminated by migrating with a velocity model obtained by Wave-Equation Migration Velocity Analysis (WEMVA). For this specific problem, WEMVA requires the extraction of an image perturbation that contains all and only the FEAVO effects. Such an image perturbation can be generated by using a ``discriminate-focus-filter-mask'' strategy. A simplified version of the first step of this approach was implemented with acceptable results. A simple, effective and cheap FEAVO detector was also conceived and implemented.
Robust moveout without velocity picking (ps.gz 967K) (pdf 574K) (src 2121K)
Wolf K., Rosales D., Guitton A., and Claerbout J.
At every point in a CMP gather, a local estimate of RMS velocity is:
Regularized inversion for subsalt imaging: real data example (ps.gz 1901K) (pdf 702K) (src 3580K)
Clapp M. L. and Clapp R. G.
Imaging the subsurface where seismic illumination is poor is a difficult exercise. Conventional imaging techniques such as migration are insufficient. Better results can be obtained from regularized least-squares inversion methods that use migration operators in a conjugate-gradient minimization. We demonstrate this regularized inversion using downward continuation migration and regularization along offset ray parameters (reflection angles) on a real 2-D seismic line. The result is cleaner than the migration result and has filled in some amplitude information where poor illumination caused gaps. We discuss a regularized inversion that uses common azimuth migration and the same type of regularization to image a real 3-D subsurface around a salt body.
AVA effects of regularized least-squares inversion (ps.gz 62K) (pdf 197K) (src 195K)
Clapp M. L.
As we search for hydrocarbons in areas where the earth's subsurface is too complex to accurately image with migration algorithms, we find ourselves turning to imaging techniques such as least-squares. My version of least-squares inversion imaging uses a downward continuation operator to produce offset ray parameter gathers (equivalent to angle gathers) and a regularization operator that is a derivative along the angle axis. The regularization operator stabilizes the inversion and helps to fill in illumination gaps. Essentially, I assume that any large, sudden changes in amplitude along the reflection angle axis are caused by poor illumination. This methodology is effective for reducing artifacts and helping to compensate for poor illumination. However, there is still the question of how this regularization will affect any real amplitude variation with angle (AVA) that should be seen in the model. In this paper, I address the question of how the derivative type regularization operator affects expected AVA in a simple model with no illumination problems. I experiment with various numbers of iterations and various strengths of regularization. Overall, I find that this operator, as implemented in this paper, can have a minor effect on the true AVA due to edge effects. However, it does not affect all possible AVA information, so I remain hopeful that the derivative-type regularization operator can be modified to allow us to trust AVA information from models produced by my regularized least-squares inversion.
Target-oriented shot-profile one-way wave equation inversion (ps.gz 136K) (pdf 217K) (src 356K)
Valenciano A. A. and Biondi B.
Least-squares shot-profile inversion could improve image amplitudes while remaining consistent with the data. This could be done efficiently by approximating the scalar two-way wave-equation operator by two one-way wave-equation operators: one for the source wavefield and the other for the receiver wavefield. In addition, a target-oriented scheme could help reduce the computation time. Instead of recursively computing the Green functions at each depth step for each inversion iteration, the Green functions from the surface to a target and from the target to the surface could be calculated and stored in the first iteration. In the subsequent iterations, the Green functions are retrieved from the disk.
Conjugate-guided-gradient (CGG) method for robust inversion and its application to velocity-stack inversion (ps.gz 3157K) (pdf 1166K) (src 8149K)
This paper proposes a modified conjugate-gradient (CG) method, called the conjugate-guided-gradient (CGG) method, as an alternative iterative inversion method that is robust and easily manageable. The CG method for solving least-squares (LS) (i.e. L2-norm minimization) problems can be modified to solve for a different norm or different minimization criteria by guiding the gradient vector appropriately. The guiding can be achieved by iteratively weighting either the residual vector or the gradient vector during iteration steps. Weighting the residual vector can guide the solution to the minimum Lp-norm solution, and weighting the gradient vector can guide the solution to one constrained by a priori information imposed in the model space. In both cases, the minimum solutions are found in a least-squares sense along the gradient direction guided by the weights. Therefore, the solution found by the CGG method can be interpreted as the LS solution located in the guided gradient direction. I applied the CGG method to the velocity stack inversion, and the results suggest that the CGG method gives a far more robust model estimation than the standard L2-norm solution, with results comparable to, or better than, an L1-norm IRLS (Iteratively Reweighted LS) solution.
Dynamic programming and trace alignment: Part 2 (ps.gz 2148K) (pdf 595K) (src 18072K)
Liner C. and Clapp R. G.
Dynamic programming is an effective tool for finding a solution for certain types of relatively small, non-linear problems. In biology, dynamic programming is used for pairwise alignment of amino acid sequences Needleman and Wunsch (1970). In electrical engineering, it is used for error correction in wireless communication and speech recognition Hosom et al. (1999) among many other things. ...
Regularizing Madagascar: PEFs from the data space? (ps.gz 976K) (pdf 412K) (src 3099K)
The Madagascar seasat dataset presents a problem where data are collected along crossing tracks. These tracks are not straight, and appear to be irregular in the model space. Previous methods assumed that the data were regularly sampled in the model space coordinate system. I warp the model space to look more like the data space, so that prediction-error filters can be estimated in the more regularly-sampled data space. I try two different approaches to this problem on the warped space, one where the data is single-valued and fixed, while the other is multivalued and allowed to vary. The former method works very well, while the second one works well.
Improved image segmentation for tracking salt boundaries (ps.gz 194K) (pdf 296K) (src 3979K)
Lomask J., Biondi B., and Shragge J.
Normalized cut image segmentation can be used to track salt boundaries within an iterative velocity analysis scheme. To overcome the formidable computational expense and storage requirements of normalized cut image segmentation, three cost saving approaches are proposed. First, pixels are sampled from windows centered at powers of 2. This greatly increases the sparseness of the weight matrix. Second, initial solutions are provided to subsequent segmentations for multiple segmentation passes in iterative velocity analysis. Third, an iterative multi-scale approach would be necessary for tracking of the bright salt events in large 3D cubes.
Analytical flattening with adjustable regularization (ps.gz 9590K) (pdf 1626K) (src 23593K)
Lomask J. and Guitton A.
We add an adjustable regularization parameter to the analytical flattening method which integrates dips in the Fourier domain. The regularization penalizes roughness in depth in the integration result which, in turn, insures that the flattening result is monotonic and continuous. This preserves the data which is necessary for multiple flattening passes or for undoing the flattening result. Because we preform the integration in the Fourier domain, this method is still highly efficient. 2D field gathers and a stacked section are provided as examples. This can easily be extended to 3D, allowing adjustable regularization along shot gathers.
Shot-profile migration of GPR data (ps.gz 370K) (pdf 178K) (src 28871K)
Shragge J., Irving J., and Artman B.
Multi-offset ground-penetrating radar data possess a number of important advantages over constant-offset data, and are becoming increasingly popular within the GPR community. With the availability of these data comes the opportunity to experiment with state-of-the-art seismic imaging techniques. Here, we consider the application of shot-profile migration, a prestack scalar wave-equation imaging method, to 2-D multi-offset GPR data. With this method, source and receiver wavefields of individual shot records are propagated separately and combined at depth with application of an imaging condition. Receiver wavefields are comprised of recorded traces, and source wavefields are modeled from point sources at the transmitter locations. The complete migrated image is the sum of all overlapping shot-record migrations.
Migration methods for passive seismic data (ps.gz 2119K) (pdf 1469K) (src 4402K)
Artman B., Draganov D., Biondi B., and Wapenaar K.
Passive seismic imaging is based on the fact that by cross-correlating the transmission responses of a medium, one can reconstruct its reflection response. Here, we show a method to directly migrate the transmission responses measured at the surface, based on the shot-profile migration. We also show that the results from direct migration of passive data and from migration of the simulated reflection response are identical. At the end, we also show comparisons between the behavior of the results from the migration process and the simulated reflection responses.
Teleseismic imaging with wave equation migration (ps.gz 617K) (pdf 303K) (src 258 M)
Wilson C. K., Shragge J., and Artman B.
Images of the lithosphere from three-component seismic arrays recording wavefields generated by teleseismic earthquakes (30- 90 epicentral distance) reveal important aspects of lithospheric structure. Unfortunately, interpretation of these images remains ambiguous due to improper reflector mapping and amplitude restoration. We introduce the shot-profile representation of wave equation migration as a novel way to cast the teleseismic imaging problem. We show results from two synthetic datasets using both forward- and backscattered modes to demonstrate the strength of this imaging scheme. To demonstrate the techniques effictiveness with real data, we present preliminary images from the forward-scattered P-to-S mode from data collected across the Proterozoic Cheyenne suture near Laramie, Wyoming.
Imaging oceanic thermohaline structure with reflection seismology (ps.gz 838K) (pdf 391K) (src 1.9M)
Guitton A. and Vlad I.
Temperature and salinity contrasts between volumes of seawater can generate reflections that are recorded before the water-bottom arrival on marine seismic data. While explorationists commonly mute them without observing them, seawater reflections are of interest to researchers of ocean dynamics. Yilmaz (2001), at page 1809, maintains that such reflections are due to density contrasts. Holbrook et al. (2003) ...
Seismic waves in finely layered VTI media: Poroelasticity, Thomsen parameters, and fluid effects on shear waves (ps.gz 211K) (pdf 1879K) (src
Berryman J. G.
Layered earth models are well justified by experience, and provide a simple means of studying fairly general behavior of the elastic and poroelastic characteristics of seismic waves in the earth. Thomsen's anisotropy parameters for weak elastic and poroelastic anisotropy are now commonly used in exploration, and can be conveniently expressed in terms of the layer averages of Backus. Since our main interest is usually in the fluids underground, it would be helpful to have a set of general equations relating the Thomsen parameters as directly as possible to the fluid properties. This end can be achieved in a rather straightforward fashion for these layered earth models, and the present paper develops and then discusses these relations. Furthermore, it is found that, although there are five effective shear moduli for any layered VTI medium, one and only one effective shear modulus for the layered system contains all the dependence of pore fluids on the elastic or poroelastic constants that can be observed in vertically polarized shear waves in VTI media. The effects of the pore fluids on this effective shear modulus can be substantial. An increase of shear wave speed on the order of 10% is shown to be possible when circumstances are favorable, which occurs when the medium behaves in an undrained fashion, and the shear modulus fluctuations are large (resulting in strong anisotropy). These effects are expected to be seen at higher frequencies such as sonic and ultrasonic waves for well-logging or laboratory experiments, or at seismic wave frequencies for low permeability regions of reservoirs, prior to hydrofracing. Results presented are strictly for velocity analysis.
Poroelastic fluid effects on shear for rocks with soft anisotropy (ps.gz 73K) (pdf 234K) (src 106K)
Berryman J. G.
A general analysis of poroelasticity for vertical transverse isotropy (VTI) shows that four eigenvectors are pure shear modes with no coupling to the pore-fluid mechanics. The remaining two eigenvectors are linear combinations of pure compression and uniaxial shear, both of which are coupled to the fluid mechanics. After reducing the problem to a system, the analysis shows in a relatively elementary fashion how a poroelastic system with isotropic solid elastic frame but with anisotropy introduced through the poroelastic coefficients interacts with the mechanics of the pore fluid and produces shear dependence on fluid properties in the overall poroelastic system. The analysis shows, for example, that this effect is always present (though sometimes small in magnitude) in the systems studied, and can be quite large (up to a definite maximum increase of 20 per cent) in some rocks - including Spirit River sandstone and Schuler-Cotton Valley sandstone.
Electric fields created at the seismic source - a new electroseismic phenomenon (ps.gz 166K) (pdf 306K) (src 488K)
Electroseismic data may show two different forms of source-related energy. The first is the electroseismic direct field which is produced at any impact source. It is approximately an electric dipole created by the asymmetrical pressure field of the impact. The second field is the electric field created by the impact of a mass on a metal hammer plate. The impact moves the hammer plate within the earth's magnetic field, and creates an electric field described by Lorentz's equation. Both show no moveout, and the amplitude pattern of a dipole. The direct field may be differentiated from the Lorentz field, however, by its reversed polarity on opposite sides of the shot point.
Parallel datasets in SEPlib (ps.gz 22K) (pdf 81K) (src
Clapp R. G.
The extension of SEPlib to handle parallel datasets has many unintended similarities to the parallel data capability of HDF (). A parallel dataset is a composition of several datasets with a master file describing the relationship between the various parts. All programming with the parallel dataset library is done through the superset library (). To handle parallel datasets with minimal changes to coding style requires a more abstract definition for IO than simple SEPlib or SEP3d allows. ...