Ocean bathymetry as an inverse problem for the radiative transfer equation

We consider the bathymetry problem which is based on the mathematical model of the acoustic signal propagation in a fluctuating medium. Solution of the direct problem for determination of the flux density is obtained in the double scattering approximation. The inverse problem is formulated as determination of the function describing deviation from a reference value. As a solution to the problem, a non-linear differential equation is obtained with some assumptions for the directivity pattern of the receiving antenna. A numerical analysis of the bathymetry problem is conducted, and the influence of a double scattering signal on the reconstruction of the bathymetric function is investigated.