Near-field imaging for an obstacle above rough surfaces with limited aperture data

Abstract

This paper is concerned with the scattering and inverse scattering problems for a point source incident wave by an obstacle embedded in a two-layered background medium. It is a nontrivial extension of the previous theoretical work on the inverse obstacle scattering in an unbounded structure [Commun. Comput. Phys., 26 (2019), 1274-1306]. By the potential theory of boundary integral equations, we derive a novel integral equation formula for the scattering problem, then the well-posedness of the system is proved. Based on the singularity analysis of integral kernels, we presented a numerical method for the integral equations. Furthermore, we developed a reverse time migration method for the corresponding composite inverse scattering problem with the limited aperture data. Numerical experiments show that the proposed method is effective to recover the support of an unknown obstacle and the shape, location of the surfaces.