Linearized inversed scattering in the presence of caustics

A. P.E. ten Kroode; D.-J. Smit; Arie Verdel

doi:10.1117/12.187493

23 September 1994 Linearized inversed scattering in the presence of caustics

A. P.E. ten Kroode, D.-J. Smit, Arie Verdel

Proceedings Volume 2301, Mathematical Methods in Geophysical Imaging II; (1994) https://doi.org/10.1117/12.187493
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

In modern high frequency inversion of acoustic scattering data, standard ray theoretic methods play an important role, since the inversion operation is usually formulated in terms of traveltimes and amplitude functions computed along the rays. In this approach one formulates the inversion procedure in terms of a Fourier-integral operator acting on the scattering data. It is well known that this Fourier-integral operator reproduces the most singular part of the scattering potential, provided that there are no multiple ray paths between any two points in the medium. This rules out many practical situations in which caustics in the ray field are present. We show that under a relatively mild condition the inversion technique mentioned above can be extended to allow for caustics. We also present an explicit inversion formula.

Citation Download Citation

A. P.E. ten Kroode, D.-J. Smit, and Arie Verdel "Linearized inversed scattering in the presence of caustics", Proc. SPIE 2301, Mathematical Methods in Geophysical Imaging II, (23 September 1994); https://doi.org/10.1117/12.187493

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