Inverse elastic scattering by random periodic structures

Abstract

This paper investigates an inverse scattering problem of time-harmonic elastic waves incident on a rigid random periodic structure. A novel and efficient numerical method is proposed to quantify the randomness, i.e., to reconstruct key statistical properties of random structures from boundary measurements of the scattering data. This method consists of two ingredients, the Monte Carlo technique for sampling the probability space and a continuation method with respect to the wavenumber. Unlike existing methods, this approach does not require a priori knowledge of the randomness and can handle a wide range of random structures, including non-Gaussian processes with extremely high levels of complexity. To illustrate the accuracy and effectiveness of the proposed method, numerical examples involving Gaussian and non-Gaussian processes with various covariances are provided.