New numerical method of solving the acoustical scattering equation with applications to seismic wave equation tomography

Jerry M. Harris; Feng Yin

doi:10.1117/12.187479

23 September 1994 New numerical method of solving the acoustical scattering equation with applications to seismic wave equation tomography

Jerry M. Harris, Feng Yin

Author Affiliations +

Proceedings Volume 2301, Mathematical Methods in Geophysical Imaging II; (1994) https://doi.org/10.1117/12.187479
Event: SPIE's 1994 International Symposium on Optics, Imaging, and Instrumentation, 1994, San Diego, CA, United States

Abstract

We present a new moment method of solving the acoustical scattering equation, and then apply this method to non-linear wave equation tomography. We describe the formulation, the implementation, and numerical testing of the method. The main characteristic of this method is that a bilinear basis function is used instead of a pulse basis function to evaluate the Green function, total field, and scattering potential at any arbitrary point of the image region. In this way, the integral equation may be discretized to arbitrary fineness in order to increase the accuracy of the computations. From simulation tests, we find that this method is accurate and the number of unknowns can be greatly reduced. Finally, we utilize this method in solving a non-linear wave equation inverse problem. The simulation results show that this method is effective and very useful for both forward and inverse problems.

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Jerry M. Harris and Feng Yin "New numerical method of solving the acoustical scattering equation with applications to seismic wave equation tomography", Proc. SPIE 2301, Mathematical Methods in Geophysical Imaging II, (23 September 1994); https://doi.org/10.1117/12.187479

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