Geodesic
Comparative analysis of the error of the single scattering approximation when solving one inverse problem in two-dimensional and three-dimensional cases
Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 2, pp. 151-165

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{DVMG_2021_21_2_a2,
     author = {P. A. Vornovskikh and I. V. Prokhorov},
     title = {Comparative analysis of the error  of the single scattering approximation when solving one inverse problem in two-dimensional and three-dimensional cases},
     journal = {Dalʹnevosto\v{c}nyj matemati\v{c}eskij \v{z}urnal},
     pages = {151--165},
     publisher = {mathdoc},
     volume = {21},
     number = {2},
     year = {2021},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a2/}
}
TY  - JOUR
AU  - P. A. Vornovskikh
AU  - I. V. Prokhorov
TI  - Comparative analysis of the error  of the single scattering approximation when solving one inverse problem in two-dimensional and three-dimensional cases
JO  - Dalʹnevostočnyj matematičeskij žurnal
PY  - 2021
SP  - 151
EP  - 165
VL  - 21
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a2/
LA  - ru
ID  - DVMG_2021_21_2_a2
ER  - 
%0 Journal Article
%A P. A. Vornovskikh
%A I. V. Prokhorov
%T Comparative analysis of the error  of the single scattering approximation when solving one inverse problem in two-dimensional and three-dimensional cases
%J Dalʹnevostočnyj matematičeskij žurnal
%D 2021
%P 151-165
%V 21
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a2/
%G ru
%F DVMG_2021_21_2_a2
P. A. Vornovskikh; I. V. Prokhorov. Comparative analysis of the error  of the single scattering approximation when solving one inverse problem in two-dimensional and three-dimensional cases. Dalʹnevostočnyj matematičeskij žurnal, Tome 21 (2021) no. 2, pp. 151-165. http://geodesic.mathdoc.fr/item/DVMG_2021_21_2_a2/