A direct imaging method for inverse elastic scattering by unbounded rigid rough surfaces

TL;DR

This paper introduces a direct imaging method for reconstructing unbounded rigid rough surfaces in elastic scattering problems using near-field data, demonstrating efficiency, accuracy, and robustness through numerical experiments.

Contribution

The paper presents a novel direct imaging algorithm that uses only inner products of near-field data to recover unbounded rough surfaces in elastic scattering.

Findings

The method is computationally efficient.

The inversion scheme is accurate even with noisy data.

Numerical experiments confirm robustness and effectiveness.

Abstract

This paper is concerned with the inverse time-harmonic elastic scattering problem of recovering unbounded rough surfaces in two dimensions. We assume that elastic plane waves with different directions are incident onto a rigid rough surface in a half plane. The elastic scattered field is measured on a horizontal straight line segment within a finite distance above the rough surface. A direct imaging algorithm is proposed to recover the unbounded rough surface from the scattered near-field data, which involves only inner products between the data. Numerical experiments are presented to show that the inversion scheme is not only efficient but also accurate and robust with respect to noise.