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Singular value decomposition of the velocity-reflector depth tradeoff, Part 2: High-resolution analysis of a generic model

Stork, Christof (1992) Singular value decomposition of the velocity-reflector depth tradeoff, Part 2: High-resolution analysis of a generic model. Geophysics, 57 (7). pp. 933-943. ISSN 0016-8033. doi:10.1190/1.1443306.

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The symmetries of a block circulant matrix significantly reduce the computational expense of the singular value decomposition (SVD) of the variable velocity inverse problem for a generic reflection seismology model. As a result, the decomposition does not suffer from edge effects or parameterization artifacts that are associated with small model spaces. Using this approach, we study the eigenvector and eigenvalue characteristics for a generic model of a size as large as is used with a variety of iterative inversion techniques (>100 000 parameters). Singular value decomposition of the raypath inverse problem of a discretized generic seismic model having one reflector indicates that the eigenvalue distribution for the inverse problem is nonuniform, with a large concentration near 0 and a gap near 0.4. All but the long horizontal wavelength reflector‐depth variations cannot be uniquely resolved from velocity variations. Lateral velocity variations serve to significantly reduce the ability of seismic data to resolve reflector depth for most of the horizontal wavelength components shorter than twice the cable length. As a result, automatic velocity analysis methods may not be able to resolve reflector variations when the velocity field is allowed to take on an arbitrary structure.

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Additional Information:© 1992 Society of Exploration Geophysicists. Received: 18 January 1991; Revised: 9 December 1991. A course taught by Ted Madden first introduced me to eigenvectors and eigenvalues. Discussions with Francis Muir and John Toldi helped stimulate me to take advantage of the symmetries of a block circulant matrix. This paper is an outgrowth of thesis work done at the California Institute of Technology, in which I laboriously discovered the computational limitations of SVD. The inspiration of my thesis advisor, Robert W. Clayton, helped me become interested in this problem. Support from Amoco and Rob Clayton's Presidental Young Investigator's Award enabled me to pursue this work at Caltech. I thank the sponsors of the Stanford Exploration Project. I am also grateful for the efforts of the Associate Editor and reviewers in the review process.
Group:Seismological Laboratory
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Amoco Production CompanyUNSPECIFIED
Issue or Number:7
Record Number:CaltechAUTHORS:20170829-092022349
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Official Citation:Christof Stork (1992). ”Singular value decomposition of the velocity‐reflector depth tradeoff, Part 2: High‐resolution analysis of a generic model.” GEOPHYSICS, 57(7), 933-943.
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:80894
Deposited By: Tony Diaz
Deposited On:29 Aug 2017 19:30
Last Modified:15 Nov 2021 19:39

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