Near-field imaging of an unbounded elastic rough surface with a direct imaging method

TL;DR

This paper introduces a direct imaging method for reconstructing unbounded elastic rough surfaces from near-field data, providing a fast, accurate, and noise-robust solution to the inverse scattering problem.

Contribution

A novel direct imaging algorithm for elastic rough surface reconstruction using a Helmholtz-Kirchhoff identity, with theoretical analysis and numerical validation.

Findings

The method is fast and computationally efficient.

It demonstrates high accuracy in surface reconstruction.

The approach is robust to noisy data.

Abstract

This paper is concerned with the inverse scattering problem of time-harmonic elastic waves by an unbounded rigid rough surface. A direct imaging method is developed to reconstruct the unbounded rough surface from the elastic scattered near-field Cauchy data generated by point sources. A Helmholtz-Kirchhoff-type identity is derived and then used to provide a theoretical analysis of the direct imaging algorithm. Numerical experiments are presented to show that the direct imaging algorithm is fast, accurate and robust with respect to noise in the data.