Factorization method for inverse time-harmonic elastic scattering with a single plane wave

TL;DR

This paper introduces a one-wave factorization method for inverse elastic scattering that efficiently recovers convex polygonal scatterers using minimal data, without needing forward solvers, and is applicable to both compressional and shear waves.

Contribution

It develops a novel one-wave factorization approach for elastic scattering that is independent of classical methods and applicable with limited data.

Findings

The method successfully recovers convex polygonal scatterers.

It applies to both compressional and shear wave data.

The approach does not require forward solvers.

Abstract

This paper is concerned with the factorization method with a single far-field pattern to recover an arbitrary convex polygonal scatterer/source in linear elasticity. The approach also applies to the compressional (resp. shear) part of the far-field pattern excited by a single compressional (resp. shear) plane wave. The one-wave factorization is based on the scattering data for a priori given testing scatterers. It can be regarded as a domain-defined sampling method and does not require forward solvers. We derive the spectral system of the far-field operator for rigid disks and show that, using testing disks, the one-wave factorization method can be justified independently of the classical factorization method.