Acoustic imaging in a shallow ocean with a thin ice cap

This paper considers the determination, from scattered sound, of a distribu ted 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 held over a line. In this paper we consider the case where the wavenumber, k, is small. Under t hese circumstances, we obtain a representation for the solution to the dire ct problem, and prove the uniqueness and existence of the direct scattering problem. The inverse problem is formulated as a regularized minimization p roblem. Numerical examples illustrating the procedure are presented.