Far Eastern Mathematical Journal

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Comparative analysis of the error of the single scattering approximation when solving one inverse problem in two-dimensional and three- dimensional cases

Vornovskikh P.A., Prokhorov I.V.

2021, issue 2, P. 151-165 DOI: https://doi.org/10.47910/FEMJ202113

Abstract

The inverse problem for the nonstationary radiative transfer equation is considered, which consists in finding the scattering coefficient for a given time-angular distribution of the solution to the equation at a certain point. To solve this problem, the single scattering approximation in the pulsed sounding mode is used. A comparative analysis of the error in solving the inverse problem in the single scattering approximation for two-dimensional and three-dimensional models describing the process of high-frequency acoustic sounding in a fluctuating ocean is carried out. It is shown that in the two-dimensional case the error of the approximate solution significantly exceeds the error in the three-dimensional model.

Keywords: radiative transfer equation, pulsed ocean sounding, scattering coefficient, inverse problem, Monte Carlo methods

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References

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