Radiation propagation in the ocean is described using mathematical model based on the radiation transfer equation. 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 the deviation from a reference value. As a solution for the inverse problem, a nonlinear differential equation is obtained with some assumptions on the radiation pattern of the receiving antenna. A numerical algorithm is developed and computational experiments are carried out with various types of seabed surfaces. The effect of double scattering on the seabed topography restoration is analyzed.
The problem of determining the sea bottom surface using a model that describes the process of radiation transfer in a randomly inhomogeneous medium was investigated. In the case of single scattering approximation, a pulsed source and the reflective properties of the reconstructable boundary obey Lambert's cosine law. As a result, a solution of the inverse problem is obtained in the form of a nonlinear differential equation for a curve function describing the bottom profile. An algorithm for solving the inverse problem based on explicit and implicit numerical schemes is developed. Using synthetic data, computational experiments were conducted comparing two approaches to solving the problem. An analysis of the effect of volume scattering on the restoration of the sea bottom surface was carried out using different methods for solving the nonlinear differential equation.
The kinetic model of radiation transfer, based on the non-stationary transfer equation, is considered. The explicit solution of the inverse problem, which consists of determining the volume scattering coefficient in a weakly scattering medium, is obtained in the single-scattering approximation and point-pulse source, when the dimensions of the diffusers are comparable with the scale of sensing. The solution of the direct problem for determining the received signal considering two-fold volume scattering is obtained. Analysis of the adequacy of the solution in the single-scattering approximation is carried out.