The paper gives a detailed analysis of the bathymetry problem, which is the study of sea-bottom relief. Optical and acoustic methods for obtaining bathymetric data are considered. The inverse problem consisting of the search of a function that simulates the seabed profile is formulated and solved based on the kinetic model. Much attention is given to the acoustic method. A solution to the direct problem in the acoustic approach was obtained in the case of a double scattering approximation with some restrictions of the receiving antenna pattern. Numerical experiments for the inverse problem solution showed a significant effect of double scattering on the seabed reconstruction in the case of focusing surfaces.
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.
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.
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