The seamount on a sloping seabed problem (Q2754435)

The authors study an inverse problem in underwater acoustics. An object is partially buried on a sloping seabed. The inverse problem is to determine the shape of the object from measurements of the reflections of point sources on a plane. The mathematical model leads to an inverse problem for the Helmholtz equation in a locally perturbed wedge region. The authors derive formally a representation of the Green's function in the unperturbed wedge region. A uniqueness theorem for the inverse problem is formulated and a proof is sketched following closely ideas of Kirsch and Kreß. Then the authors propose an iterative algorithm for solving the inverse problem based on some kind of linearization.NEWLINENEWLINEFor the entire collection see [Zbl 0961.00018].