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Wavefield Extrapolation Imaging

Wavefield extrapolation in laterally-varying tilted TI media (ps.gz 183K) (pdf 131K) (src 352K)
Shan G. and Biondi B.
A new wavefield extrapolation method has been developed that allows the propagation of waves in an anisotropic medium. The anisotropic medium considered here is transversely isotropic (TI) with an axis of symmetry. Our method applies an asymmetric explicit correction filter after the normal isotropic extrapolation operator. It is stable and suitable for laterally varying TI media. This new scheme is useful to extrapolate wavefields in a vertical transversely isotropic (VTI) medium in tilted coordinates. The explicit correction operator, designed by a weighted least-square method, is stable and accurate for the desired wavenumbers. Impulse responses from this scheme and the anisotropic phase-shift method are compared to illustrate the algorithm.
High-order kernels for Riemannian wavefield extrapolation (ps.gz 8181K) (pdf 1153K) (src 19667K)
Sava P.
High-order kernels for Riemannian wavefield extrapolation (RWE) are developed and demonstrated by impulse responses for models which are difficult or impossible to handle with Cartesian downward continuation. Those kernels improve the accuracy of extrapolation, particularly for situations when the Riemannian coordinate systems does not match closely the general direction of wave propagation (e.g. triplicating wavefields and migration from topography).
Incorporating topography into wave-equation imaging through conformal mapping (ps.gz 2664K) (pdf 725K) (src 28073K)
Shragge J. and Sava P.
Conformal mapping is a technique used widely in applied physics and engineering fields to facilitate numerical solution of boundary value problems involving solution domains characterized by complex geometry. The predominant reason for applying a conformal mapping procedure is to transform an irregular solution domain to one of symmetric geometry. The conformal map transform has the property that the angle between neighboring arc segments is (locally) conserved under the mapping. Accordingly, in the context of wave-equation imaging under topography, conformal mapping can transform an irregular, topographically-influenced solution domain to a regular computational mesh. In this paper, we demonstrate that the use of the conformal mapping transform coupled with Riemannian wavefield extrapolation generates an orthogonal coordinate system and the governing wavefield contination equation required for wave-equation migration directly from a topographic surface. We illustrate the potential of this approach by migrating a 2-D prestack data set acquired on a geologic model of thrust belt.

Inversion and Optimization

Regularized inversion for imaging: Effect on the data space (ps.gz 379K) (pdf 227K) (src 10774K)
Clapp M. L.
Imaging in areas of complex subsurfaces is difficult due to poor illumination. This poor illumination is partially caused by seismic energy being directed outside of the survey bounds. Imaging in areas with poor illumination can be improved by using Regularized Inversion with model Preconditioning (RIP). RIP helps compensate for poor illumination by regularizing amplitudes in the image. By compensating for the lost energy, RIP in essence expands the data space.
Bound constrained optimization: Application to the dip estimation problem (ps.gz 3761K) (pdf 948K) (src 7734K)
Guitton A.
A bound constrained optimization algorithm called L-BFGS-B is presented. It combines a trust region method with a quasi-Newton update of the Hessian and a line-search. This algorithm is tested on the non-linear dip estimation problem. Results show that the optimization algorithm converges effectively toward a model with bounds. Furthermore, bounds improve the estimated dips where plane-waves with different slopes overlap (e.g., with aliased data). When no constraints are applied, the algorithm is of comparable speed to a conjugate gradient solver.
Target-oriented computation of the wave-equation imaging Hessian (ps.gz 621K) (pdf 397K) (src 1267K)
Valenciano A. A. and Biondi B.
A target-oriented strategy can be applied to explicitly compute the wave-equation imaging Hessian. This approach allows us to study the characteristics of the Hessian for different acquisition and subsurface geometries (low illumination, faults, etc.). Results on the Sigsbee and the Marmousi model show that in complex areas, a diagonal approximation of the Hessian might be insufficient to obtain the correct position and amplitudes of the reflectors.

Velocity Analysis

Velocity uncertainty: Non-linearity and the starting guess (ps.gz 9726K) (pdf 1434K) (src 61287K)
Clapp R. G.
The last few years have seen a significant increase in research assessing risk. Several papers deal with assessing risk from a geostatistical framework Gambus-Ordaz et al. (2002); Shanor et al. (2002). The general methodology is to create equi-probable models based on simplified covariance descriptions and probability functions. Each point ...
The effect of model covariance description on global seismology tomography problems (ps.gz 242K) (pdf 997K) (src 15270K)
Clapp R. G. and Wilson C. K.
Global seismology tomography faces a different set of problems than those faced in typical oil exploration tomography projects. Energy travels at significantly wider range of angles in global seismology and the velocity-depth ambiguity of reflection based seismology is not present. On the other hand, global seismologists have orders of magnitude less data. ...
The influence of multiples and imaging approximations on focusing-effect AVA detection and removal (ps.gz 2967K) (pdf 612K) (src 6935K)
Vlad I.
Focusing-effect AVA (FEAVA) consists of anomalous amplitudes due to transmission effects. In multiple-free synthetic datasets, whether simple or complex, the focusing is removed by migration with the correct velocity and an operator adjoint to that used in modeling. In multiple-affected synthetic datasets, migration with the correct velocity but with an operator less accurate than that used in modeling is only partially sucessful in removing FEAVA. There are numerical experiments which can distinguish whether this is due to the presence of multiples, to lack of imaging operator accuracy, or to lack of imaging-modeling adjointness.
An educated guess on the Vp/Vs ratio (ps.gz 276K) (pdf 247K) (src 2291K)
Rosales D. A.
Data processing of converted waves generally yields estimated values for both P velocity and S velocity in the area of study. These values are usually seen in the form of two parameters: 1) the multiplication of both velocity fields, and 2) the ratio of both velocity fields. Traditionally the ratio of the P and S velocities, which is known as the $$ value, is the result of an extensive combined analysis on the PS data and the single P-mode data. Knowledge of $$ is important not only for seismic processing but also ...


Multiple suppression in the image space: A Mahogany field example (ps.gz 5572K) (pdf 837K) (src 26293K)
Rosales D. A. and Sava P.
Stolt residual migration (SRM) is an effective technique for image processing after migration. It allows us to reconstruct an image corresponding to a velocity different from the original migration velocity. Furthermore, multiple attenuation in the image space (MAIS) is a powerful technique for seismic data processing after migration. Combining these two techniques makes it possible to remove multiples in the image space without accurately knowing the velocity model. The PZ section of the Mahogany field serves as a field data example to demonstrate the advantage of this combined methodology.
Analytical traveltimes for arbitrary multiples in constant velocity (ps.gz 72K) (pdf 130K) (src 148K)
Liner C. and Vlad I.
Levin and Shah (1977) compute analytical traveltimes for internal multiples generated by a single-CMP seismic survey over a 2-D, two-layer, constant-velocity Earth. Their expression treats the specific case of a single reflection from the bottom of the second layer, preceded and followed by a number of bounces inside the first layer. To obtain the traveltimes, they use the method of images, computing successive images of the source through successive reflections towards the receivers, then computing an image of the receiver through the last reflector. The traveltime is obtained by ...


Estimating a 2D stationary PEF on sparse data (ps.gz 974K) (pdf 378K) (src 13722K)
Lomask J.
A stationary 2D PEF and missing data are simultaneously estimated on sparse data where the 2D PEF is never fully on known data. This PEF is estimated using non-linear conjugate gradients. A weight is applied to the residual to use only fitting equations where a prescribed minimum number of the PEF coefficients are on known data. The minimum parameter is then reduced and a new 2D PEF is estimated using the previous PEF as a starting solution. This process is repeated and the 2D PEF is gradually built up. This method is tested on the Madagascar satellite data. Using increasingly sparse data, the sparse 2D PEF compares favorably to the 2D PEF estimated on the dense data even when 67 percent of the data is unknown.
Midpoint-offset vs. source-receiver coordinates for PEF-based interpolation (ps.gz 356K) (pdf 423K) (src 1026K)
Curry W.
There are two obvious choices of coordinates to use when interpolating seismic data: cmp-offset and source-receiver. A multi-scale prediction-error filter (PEF) based interpolation works well on both sets of coordinates for a 2D prestack land dataset, although the cmp-offset coordinates appear to be preferable. By using reciprocity in source-receiver space, a pair of 2D PEFs may interpolate the data with more efficiency and practical applicability to 3D data.

Rock Properties Estimation

Bounds on transport coefficients of porous media (ps.gz 48K) (pdf 353K) (src 53K)
Berryman J. G.
Transport coefficients such as electrical conductivity, thermal conductivity, fluid permeability, etc., can all be treated in mathematically equivalent terms. So an analytical formulation of conductivity bounds by Bergman and Milton can be used in a different way to obtain rigorous bounds on, for example, the real thermal conductivity (which is the particular transport coefficient chosen for the present study) of a fluid-saturated porous material. These bounds do not depend explicitly on the porosity, but rather on two formation factors - one associated with the pore space and the other with the solid frame. The results are then applicable to other physical properties such as fluid permeability. In particular, the formation factors are measures of the microstructure (actually of the tortuosities) of the porous medium, and are therefore the same dimensionless numbers for all these transport processes within the same porous material.
Bounds on geomechanical constants for a model of heterogeneous reservoirs (ps.gz 58K) (pdf 257K) (src 38K)
Berryman J. G.
A well-known result due to Hill provides an exact expression for the bulk modulus of any multicomponent elastic composite whenever the constituents are isotropic and the shear modulus is uniform throughout. Although no precise analog of Hill's result is available for the opposite case of uniform bulk modulus and varying shear modulus, it is shown here that some similar statements can be made for shear behavior of random polycrystals composed of laminates of isotropic materials. This model is intended to incorporate characteristics that mimic geomechanical properties of heterogeneous earth reservoirs, including local layering due to sedimentary processes. In particular, the Hashin-Shtrikman-type bounds of Peselnick, Meister, and Watt for random polycrystals composed of hexagonal (transversely isotropic) grains are applied to our model of polycrystals of laminates. An exact product formula relating the Reuss estimate of bulk modulus and an effective shear modulus (of laminated grains composing the system) to products of the eigenvalues for quasi-compressional and quasi-uniaxial shear eigenvectors also plays an important role in the analysis of the overall shear behavior of the random polycrystal. When the bulk modulus is uniform in such a system, the equations are shown to reduce to a simple form that depends prominently on the uniaxial shear eigenvalue - as expected from physical arguments concerning the importance of uniaxial shear in these systems. Applications of the analytical results presented here include benchmarking of numerical procedures used for studying elastic behavior of complex composites, and estimating coefficients needed in up-scaled equations for elasticity and/or poroelasticity of heterogeneous reservoirs.

Cluster Computing

Fault tolerant parallel SEPlib (ps.gz 15K) (pdf 71K) (src 8K)
Clapp R. G.
In the past few years, several papers have been written dealing with SEP's attempts to run on Beowulf style clusters. The initial work involved the use of the Open Multi-Processing (OMP) library Biondi et al. (1999). As we increased the number of nodes at SEP, we switched to, or added on support for, MPI to many of our programs Sava and Clapp (2002). This proved to be a somewhat successful ...
A Python solver for out-of-core, fault tolerant inversion (ps.gz 24K) (pdf 75K) (src 26K)
Clapp R. G.
In the last ten years SEP has seen a progression in the way it does inversion. Earlier version of Claerbout (1999) coded the conjugate gradient loop within a FORTRAN 77 main program. Later, with the adoption of FORTRAN 90, the solver became a subroutine, operators were in modules, and ...

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