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.
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 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.
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.
The kinetic model, describing sound propagation in a randomly inhomogeneous medium with diffuse reflection by Lambert's cosine law on the bottom surface, is considered. Based on it the inverse problem of bottom scattering reconstruction is formulated. An explicit solution is deduced by using a narrow receiving directivity pattern and a pointwise isotropic source. Numerical experiments for the analysis of the impact of the finite pulse and the finite receiving directivity pattern on the received signal are done.
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.
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