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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2023 Volume 20, Issue 2, Pages 1079–1092 (Mi semr1630)

Computational mathematics

Localization of discontinuity surfaces of the scattering coefficient according to the time-angular distribution of the radiation flux density

P. A. Vornovskikhab, I. V. Prokhorova

a Institute of Applied Mathematics FEB RAS, str. Radio, 7, Vladivostok, 690041, Russia
b Far Eastern Federal University, 10 Ajax Bay, Russky Island, Vladivostok, 690922, Russia

Abstract: In the paper the inverse problem for the nonstationary radiative transfer equation is formulated and investigated. It consists in determining the discontinuity surfaces of the scattering coefficient by the time-angular distribution of the radiation flux density at a given point in space. A numerical method for localizing the lines of discontinuity of the required coefficient in any plane is proposed. On a number of numerical experiments applied to high-frequency acoustic sounding of an inhomogeneous fluctuating ocean, the operability of the algorithm is demonstrated and its shortcomings due to the measurement data error are indicated.

Keywords: radiative transfer equation, inverse problem, scattering coefficient, function discontinuity surfaces.

UDC: 517.958

MSC: 35Q60

Received November 1, 2022, published November 16, 2023

DOI: doi.org/10.33048/semi.2023.20.067



© Steklov Math. Inst. of RAS, 2025