Abstract <p>The inverse problem for the nonstationary integro-differential equation of high-frequency acoustic radiative transfer is considered. It consists in determining the surfaces of discontinuity of the volume scattering coefficient from the time-angular distribution of the flux density at a given point in three-dimensional space. Numerical algorithms for solving the inverse problem are proposed. They are based on the introduction of special indicator functions that explicitly indicate the location of the lines of discontinuity of the scattering coefficient in a given plane. The process of ultrasonic sounding in the marine environment was simulated by the Monte Carlo methods, the efficiency of the algorithms for localizing scattering inhomogeneities was demonstrated, and the effect of incompleteness of the initial data on the quality of tomographic images was analyzed numerically.</p>