Factorization method for near-field inverse scattering problems in elastodynamics

TL;DR

This paper introduces a factorization method for solving near-field inverse scattering problems in elastodynamics, enabling the recovery of obstacle location and shape from boundary measurements with demonstrated numerical accuracy.

Contribution

It develops a novel factorization-based inversion algorithm for elastodynamic scattering, specifically addressing near-field data and obstacle reconstruction.

Findings

Numerical examples in 2D confirm the method's validity.

The algorithm accurately recovers obstacle shape and location.

The approach effectively handles elastic wave data on a spherical surface.

Abstract

Consider a time-harmonic elastic point source incident on a bounded obstacle which is embedded in an open space filled with a homogeneous and isotropic elastic medium. This paper is concerned with the inverse problem of recovering the location and shape of the obstacle from near-field data generated by infinitely many incident point source waves at a fixed energy. The incident point sources and the receivers for recording scattered signals are both located on a spherical closed surface, on which an outgoing-to-incoming operator is defined for facilitating the factorization of the near-field operator. Numerical examples in 2D are presented to show the validity and accuracy of the inversion algorithm.