On an inverse elastic wave imaging scheme for nearly incompressible materials

TL;DR

This paper introduces a two-stage inverse elastic wave imaging method for nearly incompressible materials, efficiently reconstructing scatterer locations and shapes using minimal incident waves and rigorous mathematical analysis.

Contribution

It develops a novel two-stage algorithm for reconstructing elastic scatterers with rigorous analysis, requiring only two incident waves of different wavenumbers.

Findings

Effective reconstruction of scatterer locations and shapes

Requires only two incident waves for the process

Numerical tests demonstrate high efficiency and accuracy

Abstract

This paper is devoted to the algorithmic development of inverse elastic scattering problems. We focus on reconstructing the locations and shapes of elastic scatterers with known dictionary data for the nearly incompressible materials. The scatterers include non-penetrable rigid obstacles and penetrable mediums, and we use time-harmonic elastic point signals as the incident input waves. The scattered waves are collected in a relatively small backscattering aperture on a bounded surface. A two-stage algorithm is proposed for the reconstruction and only two incident waves of different wavenumbers are required. The unknown scatterer is first approximately located by using the measured data at a small wavenumber, and then the shape of the scatterer is determined by the computed location of the scatterer together with the measured data at a regular wavenumber. The corresponding mathematical principle with rigorous analysis is presented. Numerical tests illustrate the effectiveness and efficiency of the proposed method.