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.
Ocean remote sensing problem is studied as an inverse problem for the model of sound propagation based on the nonstationary radiative transfer equation with a Lambertian boundary condition. The sea bottom scattering coefficient is determined by using signal measured in a side scan sonar. Numerical solution to the inverse problem is analyzed depended on different number of remote sensing angles and on different radiation pattern widths. The volumetric scattering effect in the sea bottom reconstruction is demonstrated.
The kinetic model, describing sound propagation in the ocean with diffuse reflection by Lambert's cosine law on the bottom surface, is considered. The inverse problem of bottom scattering reconstruction is formulated. The inverse problem is reduced to solving the Fredholm integral equation of the first kind. An iterative algorithm is developed. Numerical experiments for reconstruction of the seabottom scattering coefficient depending on different width of directivity pattern 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.
Authors study a problem of determining the bottom topography of a fluctuating ocean using the data of side-scan sonars. Based on a kinetic model of acoustic radiative transfer authors obtain a formula for determining a function describing small deviations of the bottom surface from a middle level. Numerical experiments have been done on modeling data that demonstrate the accuracy of the obtained formula.