An efficient algorithm for solving the inverse problem of locating the interfaces using the frequency sounding data

Authors:
Alexandre Timonov;Michael V. Klibanov
Affiliations:
Department of Mathematics, University of North Carolina at Charlotte, Charlotte, North Carolina;Department of Mathematics, University of North Carolina at Charlotte, Charlotte, North Carolina
Venue:
Journal of Computational Physics
Year:
2002

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Abstract

We consider the inverse coefficient problem of locating the interface positions arising in frequency sounding of layered media. Such a problem is of particular interest in the exploration of geophysics, underwater acoustics and electromagnetics, optical sensing, and so forth. We found that a simplified algorithm can be constructed to determine the approximate positions of interfaces. Unlike the conventional non-linear least squares, this algorithm does not require the time-consuming constrained optimisation. Instead, the predictor-corrector method is applied to solve numerically the auxiliary Cauchy problem for a Riccati equation. The feasibility of this algorithm is demonstrated in computational experiments with a model problem of electromagnetic frequency sounding of layered media.