Acoustic imaging in a shallow ocean with a thin ice cap

Abstract

This paper considers the determination, from scattered sound, of a distributed inhomogeneity in a shallow, two-dimensional, ocean with a thin ice cap. Assuming that we know the acoustic properties of the ice cap, we determine the unknown inhomogeneity by sending in incident waves from point sources in prescribed locations, and detect the total acoustic field over a line. In this paper we consider the case where the wavenumber, k, is small. Under these circumstances, we obtain a representation for the solution to the direct problem, and prove the uniqueness and existence of the direct scattering problem. The inverse problem is formulated as a regularized minimization problem. Numerical examples illustrating the procedure are presented.