Iterative direct and inverse scattering in multilayered elastic background media.

Abstract

This work is concerned with the modeling of elastic wave scattering by solid- or fluid-filled inclusions buried in multilayered elastic background media. A general framework, encompassing both direct and inverse problems, is developed based on vector integral equations for elastic scattering. The entire medium, comprising inclusion plus background, is probed by a time-harmonic body force and the field scattered by the inclusion is computed (direct problem) or observed (inverse problem) at some known receiver locations. The scattering framework developed is independent of the problem geometry and the transmitter–receiver characteristics. A Born approximation for inhomogeneous background is invoked (i) in the direct problem to obtain a closed-form expression for the scattered field, and (ii) in the inverse problem to linearize for the inclusion multiparameters. To circumvent the limitations of the Born approximation, both direct and inverse scattering are tackled iteratively. In the case of direct scattering, a recursive algorithm that recovers the Born series is developed. In the case of inverse scattering, a two-step iterative inversion procedure alternating direct and inverse modeling to improve on the resolution and accuracy of the reconstruction is proposed. The aim is to calculate a better estimate of the inclusion given a better estimate of the actual field inside the inclusion. Preliminary simulations results are presented.