SEP-82 (1994)

Velocity estimation and multiple suppression

Velocity-stack inversion using L norms

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Nichols D.
Velocity-stack inversion is the process of creating a model in velocity space 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. Superior velocity space images, with a better separation of primaries and multiples, 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.

Velocity analysis of the Mobil AVO dataset

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Ecker C. and Lumley D. E.
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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Amplitude-preserved multiple suppression

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Lumley D., Nichols D., and Rekdal T.
Water-bottom and pegleg multiples can contaminate primary reflections and distort AVO amplitude information. We develop an inversion method for suppressing multiple reflections while simultaneously preserving amplitudes along primary reflections. An iterative time-domain conjugate gradient scheme is used to find a velocity scan which ``fits'' its associated CMP gather to within a few percent misfit energy, when a hyperbolic forward modeling operator is applied to that inverted velocity scan. This ensures that most amplitude and AVO information is preserved in the transform pair. A primary velocity trend is then automatically picked in the scan by a Monte Carlo method, and a mask is designed on this basis to isolate multiple energy in velocity space. An estimate of the multiple reflection energy is generated by forward modeling the masked velocity scan. An amplitude-preserved multiple-suppressed CMP gather is then obtained by subtracting the estimated multiples from the input CMP gather. Current test results with the Mobil AVO dataset are very encouraging.

AVO estimation using surface-related multiple prediction

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Levin S. A.
In this work I explore the use of surface multiple prediction in enhancing AVO estimation. Multiple reflections from a proposed reflection event are predicted using surface-related multiple prediction and compared to the actual data to identify anomalous amplitude behavior.

Estimating a pseudounitary operator for velocity-stack inversion

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E. Lumley D.
I estimate a pseudounitary operator for enhancing an iterative conjugate-gradient (CG) inversion of CMP data to derive a best-fitting model in velocity-stack space. The amplitude balance of the operator is approximated with a simple time- and offset-variant operator weighting function. The spectral balance of the operator is tuned with a finite-aperture finite-fold approximation to the continuous integral rho filter. Convergence of the CG inversion and separation of multiple and primary velocity-stack energy is improved by application of the pseudounitary operator weights. Application of the rho filter improves the first few CG iterations, but counterintuitively slows or reverses convergence in subsequent iterations.

Prestack migration velocity analysis using wavefront synthesis

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Ji J.
Common-reflection-point (CRP) gathers provide important clues in various migration velocity analysis schemes (Al-Yahya, 1987; Etgen, 1990). Conventionally, CRP gathers are obtained by prestack migration of shot records or constant-offset sections. This paper introduces a way to generate a CRP gather for residual velocity analysis using wavefront synthesis imaging. Compared to CRP gathers obtained by other prestack migrations, those obtained by wavefront synthesis imaging provide a better resolution residual velocity panel. As a result, we can easily determine and get more reliable residual velocity, which is very important in inverting it into the true interval velocity of a medium.

The quest for anisotropic moveout

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Karrenbach M. and Muir F.
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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Three-dimensional seismology

AVS as a 3-D seismic data visualizing platform

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Clapp R. G., Biondi B., and Karrenbach M.
In an effort to increase SEP's ability to work with 3-D prestack data sets we have continued the development of our integrated 3-D seismic visualizer using Advanced Visual Systems (AVS) as our integrating platform. To the capacity of displaying SEP data sets, we have added the ability to simultaneously display non-seismic 3-D geophysical and geological data. The main thrust of our work has been the integration of GOCAD model building tool into AVS. To achieve this goal we have developed a few AVS modules to convert GOCAD surface into AVS geometry objects. In addition, we have begun integrating SEP batch programs into our AVS environment. Specifically, we have added an interactive wave modeler, which can be viewed simultaneously.

Depth migration of complex surfaces with GOCAD: Study of the curvature of a triangulated surface

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Berlioux A.
The depth migration of time-migrated surfaces by demigration with GOCAD is inaccurate in the case of complex surfaces, such as folded horizons, in areas where the curvature of the surface reverses its sign. I believe this problem can be avoided by cutting the original complex surface into pieces for which the depth migration is accurate. To do so, I propose an algorithm to study the sign of the curvature of the GOCAD surface in order to divide it up properly before performing the depth migration. Putting the depth-migrated pieces back together, I should then obtain a depth-migrated surface more representative of the true geology than the direct depth-migrated surface.

Prestack imaging

Coherent partial stacking by offset continuation of 2-D prestack data

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Chemingui N. and Biondi B.
Previously, we introduced a new partial-migration operator named Azimuth Moveout (AMO), that rotates the azimuth and shifts the offset of 3-D prestack data. The restriction of this operator to the 2-D case defines a new operator for offset-continuation that has many applications on its own. We apply the 2-D AMO on the synthetic Marmousi data set to reduce its size by coherent partial stacking prior to prestack migration. We show that AMO transformation eliminates the dip filtering action of CMP stacking and preserves the complex geology of the model. We derive a time-space formulation of the 2-D AMO by stationary phase approximation to its Fourier domain definition. The expression for the traveltime curve is used for a Kirchhoff-style implementation, with care taken to avoid aliasing.

Berryhill's ``pure migration'' = Gardner's PSI

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Popovici A. M.
Kinematically, Berryhill's ``pure migration'' or nonimaging shot-record migration is equivalent to dip moveout (DMO) before normal moveout (NMO) followed by Gardner's Prestack Imaging (PSI). The two processes have the same effect on a point diffractor in midpoint, offset, and time coordinates, compressing the Cheops pyramid surface to the same curve. The two methods produce the same kinematic result, although from a computational point of view, Berryhill's method is much faster.

Tomography and datuming

Shortest-path calculation of first arrival traveltimes by expanding wavefronts

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Urdaneta H. and Biondi B.
A new approach to computing traveltimes and ray paths by solving the shortest path problem is presented. The technique is based on a partitioning of the shortest path optimization problem into smaller problems. We recursively evaluate the solution on expanding wavefronts instead of finding the global shortest paths from the source. To solve the local minimization, we apply a modified version of the Bellman-Ford optimization algorithm because of its suitability for a parallel implementation in three dimensions.

Datuming velocity from traveltime tomography

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Bevc D.
Near-surface velocity anomalies cause kinematic and focusing effects which can be ameliorated by wave-equation datuming and layer replacement. The trick is to find the correct datuming velocity. When the anomalies are shorter in lateral extent than the cable length, residual times picked from deep non-hyperbolic events can be used for traveltime tomography. The optimal reconstruction is obtained by constraining the model to the near surface and by estimating the inverse covariance matrix with a prediction error filter. Downward continuation with the traveltimes from this model, followed by upward continuation with a replacement velocity, removes most of the unwanted distortions.

Computing tomographic resolution matrices using Arnoldi's iterative inversion algorithm

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Berryman J. G.
Resolution matrices are useful in seismic tomography because they allow us to evaluate the information content of reconstructed images. Techniques based on the multiplicity of equivalent exact formulas that may be used to define the resolution matrices have been used previously by the author to design algorithms that avoid the need for any singular value decomposition of the ray-path matrix. An explicit procedure is presented for computing both model and data resolution matrices using Arnoldi's algorithm for iterative inversion in seismic tomography. Arnoldi's method differs from the Lanczos scheme by including explicit reorthogonalization of basis vectors. Some convenient notation is introduced to permit ready comparison of Arnoldi's method with the Lanczos approach. Arnoldi's method requires greater storage of basis vectors but completely overcomes the lack of basis vector orthogonality, which is the major practical limitation of the Lanczos method.

Inverse theory

A simple example of a null space and how to modify it

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Nichols D.
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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Spectral preconditioning

(ps.gz 19K) (pdf 23K) (src 4K)
Claerbout J. and Nichols D.
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:
latex2html -dir /net/sepwww/public/docs/sep82/jon2/paper_html index.ltx. ...

Preconditioning the wave equation

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Karrenbach M.
The solution of systems of equations can employ preconditioning of the involved operators. This preconditioning process aims at accelerating convergence and requires some estimate of the solution or of the operator behavior. I outline a preconditioning operation for use with wave equations having the aim of increasing the region of stability of the evolution equation.

Infomatics

Birth of a C++ Project

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Schwab 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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What's new in SEPLIB?

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Nichols D., Karrenbach M., and Urdaneta H.
The CD-ROM version of this report is distributed with a new version of the SEP software ``SEPLIB'' on it. The new version has a more robust Input/Ouput (I/O) system that is extendible to support new types of I/O. It also unifies the behavior of all input and output files. The distribution contains experimental support for a geometry database to permit the use of non-uniformly sampled data.

SEP goes World Wide Web

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Karrenbach M., Claerbout J., and Berlioux A.
User friendly navigation software (MOSAIC) for the Internet, the World Wide Web (WWW), recently became publically available. This software understands the standardized mark-up language for electronic online documents (HTML). This presents a unique opportunity for increasing SEP's visibility in the scientific community and will also give sponsors easy access to research results. We see it as a unique complement to our past electronic publishing efforts, which have been restricted to CDROM, and we hope that this makes it easier to disseminate our research results and views on electronic publishing.