Inverting waveforms for velocities in the presence of caustics

William Woodbury Symes

doi:10.1117/12.187492

23 September 1994 Inverting waveforms for velocities in the presence of caustics

William Woodbury Symes

Proceedings Volume 2301, Mathematical Methods in Geophysical Imaging II; (1994) https://doi.org/10.1117/12.187492
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

Transmission caustics cause velocity estimation techniques based on straightforward analysis of image volume moveout to fail. For example, the differential semblance objective function is smooth and quasi-convex when the incident wavefield is free of caustics, but loses these properties when caustics are present. The reason for this phenomenon is closely related to that identified by Geoltrain and Brac for the inadequacy of Kirchhoff migration based on first arrival times for complex velocity structure. controlled illumination of the subsurface, introduced by Rietvold and Berkhout to improve imaging, given an adequate macromodel, also suggests a new approach to image volume moveout analysis for macromodel estimation. In particular, the differential semblance objective function again becomes, through controlled illumination, a smooth quasi-convex function of the macromodel, hence suitable for optimization using variants of Newton's method. The transmission inversion problem provides a simple framework within which to illustrate the controlled illumination reformulation of differential semblance and its effectiveness.

Citation Download Citation

William Woodbury Symes "Inverting waveforms for velocities in the presence of caustics", Proc. SPIE 2301, Mathematical Methods in Geophysical Imaging II, (23 September 1994); https://doi.org/10.1117/12.187492

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