Acoustic imaging methods often ignore multiple scattering. This leads to false images in cases where multiple scattering is strong. Marchenko imaging has recently been introduced as a data-driven way to deal with internal multiple scattering. Given the increasing interest in non-reciprocal materials, both for acoustic and electromagnetic applications, a modification to the Marchenko method is proposed for imaging such materials. A unified wave equation is formulated for non-reciprocal materials, exploiting the similarity between acoustic and electromagnetic wave phenomena. This unified wave equation forms the basis for deriving reciprocity theorems that interrelate wave fields in a non-reciprocal medium and its complementary version. Next, these theorems are reformulated for downgoing and upgoing wave fields. From these decomposed reciprocity theorems, representations of the Green's function inside the non-reciprocal medium are derived in terms of the reflection response at the surface and focusing functions inside the medium and its complementary version. These representations form the basis for deriving a modified version of the Marchenko method to retrieve the wave field inside a non-reciprocal medium and to form an image, free from artefacts related to multiple scattering. The proposed method is illustrated at the hand of the numerically modeled reflection response of a horizontally layered medium.
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