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Imaging complex structures with first-arrival traveltimes (ps.gz 902K) (pdf 781K) (src 2356K)
Bevc D.
I present a layer-stripping Kirchhoff migration algorithm which is capable of obtaining accurate images of complex structures by downward continuing the data and imaging from a lower datum. I use eikonal traveltimes in a Kirchhoff datuming algorithm for the downward continuation. After downward continuation, I perform Kirchhoff migration. The method alternates steps of datuming and imaging. Because traveltimes are computed for each step, the adverse effects of caustics, headwaves, and multiple arrivals do not develop. In principal, this method only requires the same number of traveltime calculations as a standard migration. Tests on the Marmousi data set produce excellent results.
3-D prestack depth migration of common-azimuth data (ps.gz 48K) (pdf 64K) (src 910K)
Biondi B. and Palacharla G.
We extended the common-azimuth 3-D prestack migration method presented in a previous report () to the important case of imaging common-azimuth data when the velocity field varies laterally. This generalization leads to an efficient mixed space-wavenumber domain algorithm for 3-D prestack depth migration of common-azimuth data. We implemented the method using a split-step scheme, and applied it to the migration of two synthetic data sets: the first data set was generated assuming a vertical velocity gradient, the second one assuming a velocity gradient with both a vertical and a horizontal component. Common-azimuth migration correctly imaged the reflectors in both cases.
The time and space formulation of azimuth moveout (ps.gz 582K) (pdf 643K) (src 1639K)
Fomel S. and Biondi B. L.
Azimuth moveout (AMO) transforms 3-D prestack seismic data from one common azimuth and offset to different azimuths and offsets. AMO in the time-space domain is represented by a three-dimensional integral operator. The operator components are the summation path, the weighting function, and the aperture. To determine the summation path and the weighting function, we derive the AMO operator by cascading dip moveout (DMO) and inverse DMO for different azimuths in the time-space domain. To evaluate the aperture, we apply a geometric approach, defining AMO as the result of cascading prestack migration (inversion) and modeling. The aperture limitations provide a consistent description of AMO for small azimuth rotations (including zero) and justify the economic efficiency of the method.
Migration from a non-flat datum via reverse-time extrapolation (ps.gz 335K) (pdf 281K) (src 4089K)
Palacharla G.
Land surveys usually have elevation changes, and this irregular topography distorts seismic data. For large topography changes and near-surface velocity comparable to subsurface velocity, static-corrections are inadequate, wavefield extrapolation is required in this situation. I present a scheme for doing migration directly from the irregular datum. The scheme can also be used for redatuming data collected at a non-flat datum to a flat datum. The reverse-time migration method is used to do the extrapolation, because it is a boundary-value problem, which naturally accommodates an irregular topography. It can handle steep dips and a general velocity model. After describing the reverse-time algorithm, I apply it to a post-stack example and show that static shifts are inadequate but migration from a non-flat datum produces a good image. I also outline the shot-profile implementation and its extension to 3-D.
Prestack migration by split-step DSR (ps.gz 407K) (pdf 366K) (src 730K)
Popovici A. M.
This document was generated using the LaTeX2HTML translator Version 97.1 (release) (July 13th, 1997) Copyright © 1993, 1994, 1995, 1996, 1997, Nikos Drakos, Computer Based Learning Unit, University of Leeds. The command line arguments were:
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Evaluating the Stolt stretch parameter (ps.gz 94K) (pdf 108K) (src 251K)
Fomel S.
The Stolt migration extension to a varying velocity case (Stolt stretch) implies describing a vertical heterogeneity by a constant parameter (W). This paper exploits the connection between modified dispersion relations and traveltime approximations to derive an explicit expression for W. The expression provides theoretically the highest possible accuracy within the Stolt stretch framework. Applications considered include optimal partitioning of the velocity distribution for the cascaded migrations and extension of the Stolt stretch method to transversally isotropic models.


Multi-azimuth velocity estimation (ps.gz 134K) (pdf 147K) (src 459K)
Clapp R. G. and Biondi B.
It is well known that the inverse problem of estimating interval velocities from reflection data is poorly constrained in 2-D. We show that the interval velocity estimation problem in 3-D is much better constrained when the velocity function is estimated by jointly inverting the data collected along multiple offset-azimuth, even when the azimuth range is fairly limited. We extend to 3-D the linear operator presented by () for relating stacking velocities with interval velocities. We then apply a Singular Value Decomposition (SVD) analysis to the derived operator. This analysis suggests that methods that take advantage of the azimuth range in the data should yield better velocity functions than currently used velocity estimation methods that neglect the additional information provided by multi-azimuth coverage.
Tomographic velocity estimation with planewave synthesis imaging (ps.gz 939K) (pdf 966K) (src 19527K)
Ji J.
In areas with structurally complex geology, tomographic velocity analysis is required to estimate velocities. This paper describes a tomographic velocity analysis algorithm which uses planewave synthesis imaging as a prestack migration. In reflection tomography, prestack migration is required for both event picking and traveltime error computation. Traveltime errors are often measured in the form of residual moveout (RMO) velocity in common surface location (CSL) gathers after prestack depth migration. It is shown that we can measure the residual moveout (RMO) velocity accurately with the help of reflector-dependent planewave synthesis imaging.
Velocity structure of the methane hydrate formation at the Blake Outer Ridge (ps.gz 951K) (pdf 1288K) (src 4939K)
Ecker C.
Seismic analysis of data from the Blake Outer Ridge indicates the presence of hydrate-bearing sediments overlaying gas-saturated sediments in this region. In an attempt to determine possible lateral and vertical variations of the hydrate and gas sediments, I performed a 2-D velocity analysis along two approximately perpendicular seismic lines. Subsequent determination of the seafloor and BSR reflection coefficients along one of the lines resulted in additional zero offset P-wave velocity and density constraints. Combining these with the average interval velocity model of this line, I performed a 1-D elastic amplitude modeling of zero offset reflections using the Thompson-Haskell reflectivity method. The results suggest that regions showing a continuous bottom simulating reflection are characterized by a thick hydrate layer that has an average velocity of 2.1 km/s overlaying low-velocity ($$ 1.6 km/s) sediments of considerable thickness. This result agrees well with results discussed in SEP80. In regions of discontinuous BSR, a less pronounced velocity contrast is visible, probably indicating a decrease in the hydrate concentration of the sediments.


Amplitude-preserved processing and analysis of the Mobil AVO data set[*] (ps.gz 3474K) (pdf 3051K) (src 68651K)
Lumley D. E., Nichols D., Ecker C., Rekdal T., and Berlioux A.
Mobil Oil has released a comprehensive seismic and well-log data set from the North Sea to benchmark AVO techniques. We present our results on amplitude-preserved data processing and analysis of the Mobil AVO data. First, we apply a source and receiver consistent amplitude balancing to the seismic data, which reduces source and receiver amplitude variance from about 8% and 15% respectively, to within a few percent scatter. Next, we apply a time-domain conjugate-gradient multiple-suppression technique to remove multiple reflection energy and simultaneously preserve and enhance primary-reflection AVO amplitudes. We perform unmigrated AVO analyses and find that the multiple-suppressed data correlate better with the well-log data than the unprocessed data. A prestack migration/inversion of the multiple-suppressed data shows a clear improvement over unmigrated AVO analysis, and reveals an undrilled graben block in the center of the line that exhibits a positive hydrocarbon indicator anomaly.
Amplitude preserving AMO from true amplitude DMO and inverse DMO (ps.gz 99K) (pdf 129K) (src 8051K)
Chemingui N. and Biondi B.
Starting from the definition of Azimuth Moveout (AMO) as the cascade of DMO and inverse DMO at different offsets and azimuths, we derive an amplitude-preserving function for the AMO operator. This amplitude function is based on the FK definition of DMO and the definition of its true inverse. Similar to Liner's formalism of a true inverse for Hale's DMO, we derive an asymptotically true inverse for Black/Zhang's DMO and Bleinstein's Born DMO. A numerical test is given that compares amplitude preservation using kinematically equivalent DMO operators cascaded with their true inverses. We define amplitude-preserved processing as the preservation of the offset-dependent reflectivity after AMO transformation, where the reflectivity is considered to be proportional to the peak amplitude of each event. We found that an AMO operator defined using Zhang's DMO cascaded with its true inverse best reconstructs data amplitudes after transformation to a new offset and azimuth. The new amplitude function represents an amplitude-preserving azimuth moveout.
Angle-dependent reflectivity recovery by planewave synthesis imaging (ps.gz 168K) (pdf 170K) (src 427K)
Ji J.
In this paper I compared imaging conditions of three different prestack migrations in terms of angle-dependent reflectivity recovery. The imaging conditions compared are shot profile migration with conventional imaging condition, de Brduin's imaging condition, and planewave synthesis imaging. The conventional imaging condition can be applied to any reflector geometry and to arbitrary velocity, but it recovers only diagonal component of the reflectivity matrix. de Bruin's imaging condition recovers full reflectivity matrix but has difficulty in implementing for arbitrary reflector geometry and under variable velocity. Planewave synthesis imaging takes advantages from both conventional and de Bruin's imaging condition.
Amplitude preserving offset continuation in theory Part 1: The offset continuation equation (ps.gz 111K) (pdf 97K) (src 124K)
Fomel S.
This paper concerns amplitude-preserving kinematically equivalent offset continuation (OC) operators. I introduce a revised partial differential OC equation as a tool to build OC operators that preserve offset-dependent reflectivity in prestack processing. The method of characteristics is applied to reveal the geometric laws of the OC process. With the help of geometric (kinematic) constructions, the equation is proved to be kinematically valid for all offsets and reflector dips in constant velocity media. In the OC process, the angle-dependent reflection coefficient is preserved, and the geometric spreading factor is transformed in accordance with the laws of geometric seismics independently of the reflector curvature.
Amplitude-preserved low velocity noise suppression (ps.gz 3898K) (pdf 3339K) (src 17175K)
Urdaneta H.
Low velocity noise can contaminate reflections and distort AVO amplitude information. I explore different inversion methods for suppressing low velocity noise while simultaneously preserving amplitudes along reflections. A velocity-stack inversion process is used for recreating models in velocity space that can reconstruct the reflections and the low velocity noise. Velocity-stack inversion is the process of creating a velocity space model that can correctly reconstruct the measured data. This is usually implemented by minimizing the L2 norm of the data misfit and the L2 norm of the model. Better velocity space images, with a better separation of the reflections and the low velocity noise, can be created by minimizing a different norm of the data misfit and a different norm of the model length. Norms closer to the L1 norm appear to be better at rejecting impulsive noise and creating a spiky model. Current tests with the CORPOVEN 3-component dataset show very encouraging results.

Resevoir monitoring

Seismic monitoring of reservoir fluid flow: Fundamental theory and examples[*] (ps.gz 320K) (pdf 306K) (src 823K)
E. Lumley D.
Time-lapse 3-D seismic monitoring of subsurface rock property changes incurred during reservoir fluid-flow processes is an emerging new diagnostic technology for optimizing hydrocarbon production. I discuss the physical theory relevant for three-phase fluid flow in a producing oil reservoir, and rock physics transformations of fluid-flow pressure, temperature and pore-fluid saturation values to seismic P-wave and S-wave velocity. I link fluid-flow physical parameters to seismic reflection data amplitudes and traveltimes through elastic wave equation modeling and imaging theory. I demonstrate with synthetic and field data examples that changes in fluid flow can be monitored and imaged from repeated seismic surveys acquired at varying production calendar times.
4-D seismic monitoring of an active steamflood (ps.gz 922K) (pdf 815K) (src 34837K)
E. Lumley D.
3-D migrations of time-lapse seismic monitor data acquired during steam injection show dramatic and complex changes in the reservoir zone over a wide area, compared to baseline seismic data recorded prior to steam injection. Anticipated large decreases in seismic P-wave velocity Vp near the injection well correlate with the presence of a hot desaturated steam zone. Unanticipated large increases in Vp in an annulus around the steam zone may correspond to a high-pressure cold oil front, in which residual free gas in pore space crosses the bubble point and dissolves into liquid oil. Horizontal and vertical anisotropy in flow directions inferred from these seismic observations correlate with two temperature monitor wells, and in situ measurements of upper and lower reservoir permeability. Since the pressure front propagates out from the injector an order of magnitude faster than either the thermal or steam fronts, monitoring it may be useful for predicting future fluid-flow paths of heated oil, months in advance of actual production.

Interpolation and PEF

Searching the Sea of Galilee (ps.gz 990K) (pdf 868K) (src 5832K)
Fomel S. and Claerbout J. F.
We applied the inverse linear interpolation method to process a bottom sounding survey data set from the Sea of Galilee in Israel. Non-Gaussian behavior of the noise led us to employ a version of the iteratively reweighted least squares (IRLS) technique. The IRLS enhancement of the method was able to remove the image artifacts caused by the noise at the cost of a loss in the image resolution. Untested alternatives leave room for further research.
The interpolation of a 3-D data set by a pair of 2-D filters (ps.gz 151K) (pdf 138K) (src 1037K)
Schwab M. and Claerbout J. F.
Seismic 3-D field data is often recorded as a set of relatively sparse and often irregular 2-D lines. Under the assumption that the data consists of the superposition of local plane waves, such data can be interpolated by prediction-error techniques using a set of two 2-D filters instead of the conventional single 3-D filter. The two 2-D prediction-error filters are found by two independent linear minimization problems along sets of parallel linearly-independent lines. A third linear minimization yields the missing data. Fortunately, such an approach avoids the nonlinear minimization that is required when trying to find simultaneously the missing data and the 3-D filter on a sparse 3-D data set.
Multigrid nonlinear SeaBeam interpolation (ps.gz 154K) (pdf 146K) (src 351K)
Crawley S.
A multigrid nonlinear algorithm was applied to the April 18 SeaBeam data set to fill in the large regions of missing data, obtaining an image superior to those obtained with linear methods, and more quickly than is possible with a normal, single grid nonlinear interpolation. The model may be chosen to contain any number of points; here models with gradually increasing numbers of points are solved for in succession, each providing the initial guess for the next. The algorithm is unstable in some cases, but in general converges quickly to a detailed solution.
An example of inverse interpolation accelerated by preconditioning (ps.gz 81K) (pdf 72K) (src 2475K)
Crawley S.
This document was generated using the LaTeX2HTML translator Version 97.1 (release) (July 13th, 1997) Copyright © 1993, 1994, 1995, 1996, 1997, Nikos Drakos, Computer Based Learning Unit, University of Leeds. The command line arguments were:
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Flying over the Ocean Southeast of Madagascar (ps.gz 657K) (pdf 606K) (src 10686K)
Ecker C. and Berlioux A.
Satellite measurements from the Southwest Indian Ridge provide information about the local ocean topography along both ascending and descending tracks. We present a weighted least-squares approach to combine the information given along these two measurement directions, thus obtaining a dense altitude coverage. High-frequency, spiky noise along the tracks is eliminated by additional weighting of the derivatives of the initial residuals. After having obtained the optimal altitude fit to the crossing data, we illuminate the local seafloor features using a set of first-order derivative filters. The results show high image resolution, indicating effective noise removal.
2-D phase unwrapping (ps.gz 1864K) (pdf 1520K) (src 7309K)
Chemingui N., Clapp R. G., and Claerbout J.
We present a method for unwrapping the phase of a satellite data set that maps Mt.Vesuvius in Italy. The method finds a solution for a partial differential equation by redefining the problem as a system of regressions that we solve using linear inversion techniques with iterated reweighting. We show three different techniques for eliminating the noise bursts from the raw data and fitting it to a linear model. The first process is a two-step solution in which the data is first cleaned up and then fitted to a model by phase unwrapping. In the second approach, starting from a raw noisy data, we solve the inversion problem as a system of regressions using iterative weighting based on the residual. The third technique attempts to resolve a discontinuity in the data by solving a different system of regressions with weights based on the model. In the three processes, the inversion successfully unwrapped the phase of the radar image and produced an altitude map of the volcano region. We were able to accelerate the convergence of the solution by a smart preconditioning substitution. This transformation changes the problem-formulation variable using a leaky integration operator as a preconditioner. The substitution reduced the number of iterations in the least square-inversion by two orders of magnitude and provided a solution after very few iterations. The method, however, did not help resolve a presumed discontinuity in the model, and we may have to determine an optimal function for the iterated reweighting.
Tying well information and seismic data (ps.gz 53K) (pdf 57K) (src 108K)
Berlioux A.
Well log information and seismic data for a given horizon may not tie properly. I address the problem by formulating a least-square inverse problem for a synthetic dataset. The aim of my regression equations is to find a model with a regular grid by simultaneously linear interpolating the well data and mapping the trend of the seismic information. I have scaled the second regression equation to decrease the dominance of the seismic over the well data. First I determine a prediction-error filter (PEF) from the seismic data and then run a conjugate gradient solver with the PEF to create the final map of the horizon. With this new method, the final map matches the wells more accurately.
Compensating for irregular sampling and rugged topography (ps.gz 121K) (pdf 122K) (src 284K)
Bevc D.
Artifacts arise when irregularly sampled data are input to a Kirchhoff datuming algorithm. The irregular sampling occurs because of uneven sampling of the recording surface and rugged topography. To ameliorate these artifacts, I combine wave-equation datuming with model-space filtering to resample data onto a regular grid. The filtering can be a simple Laplacian operator or a nonstationary prediction error filter with unknown filter coefficients. Synthetic examples demonstrate that the method is successful for unevenly sampled data along a flat datum. The best result is achieved by using a Laplacian filter in the inversion.
Trace balancing with PEF plane annihilators (ps.gz 37K) (pdf 49K) (src 71K)
Crawley S.
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Noise removal

Enhanced random noise removal by inversion (ps.gz 200K) (pdf 229K) (src 5746K)
Abma R.
Noise attenuation by prediction filtering breaks down in the presence of high-amplitude noise when the prediction filter is corrupted by noise and the filter response to the noise overwhelms the signal. Spurious events are generated and the amplitude of the signal is reduced by prediction filtering under these circumstances. To reduce these undesired effects, the separation of signal and noise is posed as an inversion problem. The inversion process preserves signal amplitudes and attenuates spurious events.
Enhanced prestack noise removal (ps.gz 121K) (pdf 111K) (src 388K)
Abma R.
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Variational structure of inverse problems in wave propagation and vibration (ps.gz 90K) (pdf 126K) (src 59K)
Berryman J. G.
Practical algorithms for solving realistic inverse problems may often be viewed as problems in nonlinear programming with the data serving as constraints. Such problems are most easily analyzed when it is possible to segment the solution space into regions that are feasible (satisfying all the known constraints) and infeasible (violating some of the constraints). Then, if the feasible set is convex or at least compact, the solution to the problem will normally lie on the boundary of the feasible set. A nonlinear program may seek the solution by systematically exploring the boundary while satisfying progressively more constraints. Examples of inverse problems in wave propagation (traveltime tomography) and vibration (modal analysis) are presented to illustrate how the variational structure of these problems may be used to create nonlinear programs using implicit variational constraints.

Wave propagation

Errors in SEP-81 (ps.gz 14K) (pdf 16K) (src 1K)
Nichols D.
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SEP World-Wide Web update (ps.gz 96K) (pdf 77K) (src 145K)
Berlioux A. and Claerbout J.
This document was generated using the LaTeX2HTML translator Version 97.1 (release) (July 13th, 1997) Copyright © 1993, 1994, 1995, 1996, 1997, Nikos Drakos, Computer Based Learning Unit, University of Leeds. The command line arguments were:
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CD-ROM versus The Web (ps.gz 12K) (pdf 14K) (src 4K)
Claerbout J. and Schwab M.
SEP has learned how to deliver reproducible research on CD-ROM. Publication via the Internet's World Wide Web may in the future offer a more flexible and efficient alternative.
SEP AVS User Guide (ps.gz 357K) (pdf 249K) (src 885K)
Clapp R. G.
The last 10 years has seen a steady increase in the number of 3-D seismic surveys. This increase has led to a push to develop innovative tools to deal with the unique challenges that 3-D data present. SEP has chosen to work within the framework provided by Advanced Visual Systems (AVS) for its 3-D work. This paper attempts to summarize current status of SEP's AVS environment; provide some useful hints when problems are encountered running AVS; and give a brief overview of where we are headed in the near future.

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