The inverse scattering problem by an elastic inclusion

TL;DR

This paper presents a new iterative method for solving the inverse elastic scattering problem involving an inclusion in a 2D elastic medium, utilizing boundary and far-field integral equations.

Contribution

It introduces a linearized iterative approach to solve the nonlinear integral equations derived from Betti's formula for elastic scattering.

Findings

Numerical results demonstrate the method's feasibility.

The approach effectively reconstructs the inclusion boundary.

The method converges with reasonable computational effort.

Abstract

In this work we consider the inverse elastic scattering problem by an inclusion in two dimensions. The elastic inclusion is placed in an isotropic homogeneous elastic medium. The inverse problem, using the third Betti's formula (direct method), is equivalent to a system of four integral equations that are non linear with respect to the unknown boundary. Two equations are on the boundary and two on the unit circle where the far-field patterns of the scattered waves lie. We solve iteratively the system of integral equations by linearising only the far-field equations. Numerical results are presented that illustrate the feasibility of the proposed method.