The research of bathymetry problem by simulation propagation of an acoustic signal in a fluctuating medium using the equation of radiative transfer has completed. The inverse problem of identifying a function describing the seabottom profile was formulated. In the double-scattering approximation and the narrow directivity pattern of the receiving antenna, the solution of the direct problem has obtained. As a solution of the inverse problem according to single-scattering approximation, a nonlinear differential equation in the сartesian coordinate system (solution1) and ordinary differential equation in the polar coordinate system are obtained (solution2). The regularization of Solution2 was investigated. Numerical analysis of the influence of the double-scattering approximation on the solution are carried out.
Based on the mathematical model of the propagation of an acoustic signal in a fluctuating medium, the inverse problem is formulated, which includes determination a function that describes the deviation of the bottom level from the average specified horizontal plane. In the single-scattering approximation and the narrow directivity pattern of the receiving antenna, the solution of the direct problem is obtained. As a solution to the inverse problem, a nonlinear differential equation is obtained for a function describing the deviation of the bottom relief. A numerical analysis of the solution of the equation is carried out. The dependence of the reconstruction of the lower surface on the curvature of the function describing the relief is shown.
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