The inverse scattering problem by an elastic inclusion
This work addresses a niche problem in inverse scattering for elastic materials, offering an incremental algorithmic improvement.
The authors tackle the inverse elastic scattering problem for an inclusion in 2D, proposing an iterative method that linearizes only the far-field equations. Numerical results demonstrate feasibility, but no concrete performance numbers are provided.
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.