An acoustic imaging method for layered non-reciprocal media

Given the increasing interest for non-reciprocal materials, we propose a novel acoustic imaging method for layered non-reciprocal media. The method we propose is a modification of the Marchenko imaging method, which handles multiple scattering between the layer interfaces in a data-driven way. We start by reviewing the basic equations for wave propagation in a non-reciprocal medium. Next, we discuss Green's functions, focusing functions, and their mutual relations, for a non-reciprocal horizontally layered medium. These relations form the basis for deriving the modified Marchenko method, which retrieves the wave field inside the non-reciprocal medium from reflection measurements at the boundary of the medium. With a numerical example we show that the proposed method is capable of imaging the layer interfaces at their correct positions, without artefacts caused by multiple scattering.