A non-iterative sampling method for inverse elastic wave scattering by rough surfaces

TL;DR

This paper introduces a non-iterative sampling method for detecting rough surfaces in inverse elastic wave scattering, extending previous techniques from the Helmholtz to the Navier equation, with demonstrated numerical effectiveness.

Contribution

It develops a novel non-iterative sampling technique for inverse elastic wave scattering by rough surfaces, generalizing earlier Helmholtz-based methods to the Navier equation.

Findings

Effective surface detection demonstrated through numerical examples

Method extends previous Helmholtz equation techniques to Navier equation

Non-iterative approach reduces computational complexity

Abstract

Consider the two-dimensional inverse elastic wave scattering by an infinite rough surface with a Dirichlet boundary condition. A non-interative sampling technique is proposed for detecting the rough surface by taking elastic wave measurements on a bounded line segment above the surface, based on reconstructing a modified near-field equation associated with a special surface, which generalized our pervious work for the Helmholtz equation (SIAM J. IMAGING. SCI. 10(3)(2017), 1579-1602) to the Navier equation. Several numerical examples are carried out to illustrate the effectiveness of the inversion algorithm.