Locating an obstacle in a 3D finite depth ocean using the convex scattering support

We consider an inverse scattering problem in a 3D homogeneous shallow ocean. Specifically, we describe a simple and efficient inverse method which can compute an approximation of the vertical projection of an immersed obstacle. This reconstruction is obtained from the far-field patterns generated by illuminating the obstacle with a single incident wave at a given fixed frequency. The technique is based on an implementation of the theory of the convex scattering support [S. Kusiak, J. Sylvester, The scattering support, Commun. Pure Appl. Math. (2003) 1525-1548]. A few examples are presented to show the feasibility of the method.