2024 , Volume 29, № 3, p.38-51

Purpose. Mathematical modelling of the processes of acoustic sounding of the marine bottom using side-scan sonar mounted on autonomous unmanned underwater vehicles. Development of new extrapolation algorithms for processing the measured signal to improve the quality of seabed images.

Methodology. As a mathematical model, the nonstationary radiative transfer equation in an unbounded region with diffuse reѕection conditions on the boundaries is considered. An inverse problem is formulated, which includes ҥnding for the coefficient of bottom scattering under some redeҥnition conditions. Using some simplifying restrictions, the problem is reduced to an integral equation of the ҥrst kind, which has an explicit solution in the narrow beam approximation. For an approximate solution of the obtained equation, it is proposed to use the data of measurements by antennas with radiation patterns of different widths. Then the solution of the radiation transfer equation is extrapolated to the region of small values of the parameter characterizing the width of the radiation pattern. An explicit formula is used to ҥnd the bottom scattering coefficient for the extrapolated solution of the direct problem. Extrapolation algorithms of the ҥrst and second order are considered.

Findings. A series of numerical experiments revealed that the developed algorithms are very effective if the condition on the accuracy of measurements are satisҥed. The limitations associated with the accuracy of the original data, especially affect the quality of images when using higher order extrapolation formulas.