Numerical Investigation of an Analytic Solution of a Multi-dimensional Lippman-Schwinger Seismic Inverse Problem
✍ Scribed by David B. Gray; George A. McMechan
- Publisher
- Elsevier Science
- Year
- 1995
- Tongue
- English
- Weight
- 676 KB
- Volume
- 119
- Category
- Article
- ISSN
- 0021-9991
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✦ Synopsis
The analytic solution of the Lippman-Schwinger seismic inverse problem in three spatial dimensions, assuming a point source and a constant-density earth model, is valid in the spatial zero frequency limit. It is expressed as a two-dimensional inverse Fourier transform followed by an inverse Laplace transform. For the case of laterally homogeneous velocity, the analytic solution is correct when applied to a forward solution of the wave equation for a single-interface velocity model. Error surfaces of the non-linear, iterative, leastsquares inversions corresponding to multiple, constant-velocity, horizontal layers have an absolute minimum at or near the location of the solution parameters for zero and low frequencies. The error surface for a scattered wavefield dataset generated by 3D finitedifference modeling combined with a priori constraints, produces nearly correct solutions for a range of low frequencies. Thus, this approach has potential for applicability to field data. (1995 Academic Press, Inc.