Geodesic
On a~problem of reconstructing the bottom configuration of a~fluctuating ocean
Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 2, pp. 99-110.

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We formulated and investigate an inverse problem for nonstationary radiative transfer equation in application to the acoustic map making of the sea bottom with the use of side-scan sonars. In the single scattering approximation, we obtain a formula for determining the function that describes the small deviation of the surface from the bottom from a medium level.
Keywords: radiative transfer equation, inverse problems, bottom configuration, single-scattering approximation. 
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I. V. Prokhorov; A. A. Sushchenko; V. A. Kan. On a~problem of reconstructing the bottom configuration of a~fluctuating ocean. Sibirskij žurnal industrialʹnoj matematiki, Tome 18 (2015) no. 2, pp. 99-110. http://geodesic.mathdoc.fr/item/SJIM_2015_18_2_a9/

[1] Matvienko Yu. V., Voronin V. A., Tarasov S. P., Sknarya A. V., Tutynin E. V., “Puti sovershenstvovaniya gidroakusticheskikh tekhnologii obsledovaniya morskogo dna s ispolzovaniem avtonomnykh neobitaemykh podvodnykh apparatov”, Podvodnye issledovaniya i robototekhnika, 8:2 (2009), 4–15

[2] Bogorodskii A. V., Yakovlev G. V., Korepin E. A., Dolzhikov A. K., Gidroakusticheskaya tekhnika issledovaniya i osvoeniya okeana, Gidrometeoizdat, L., 1984

[3] Ageev A. L., Igumnov G. A., Kostousov V. B., Agafonov I. B., Zolotarev V. V., Madison E. A., “Sintezirovanie apertury mnogokanalnogo gidrolokatora bokovogo obzora s kompensatsiei traektornykh nestabilnostei”, Podvodnye issledovaniya i robototekhnika, 2:14 (2012), 13–26

[4] Prokhorov I. V., Zolotarev V. V., Agafonov I. B., “Zadacha akusticheskogo zondirovaniya vo fluktuiruyuschem okeane”, Dalnevostochnyi mat. zhurn., 11:1 (2011), 76–87 | MR | Zbl

[5] Kovtanyuk A. E., Prokhorov I. V., Suschenko A. A., Agafonov I. B., Zolotarev V. V., “O problemakh postroeniya i uluchsheniya kachestva gidrolokatsionnykh izobrazhenii morskogo dna”, Sib. elektron. mat. izvestiya, 8 (2011), S124–S134

[6] Prokhorov I. V., Suschenko A. A., “Issledovanie zadachi akusticheskogo zondirovaniya morskogo dna metodami teorii perenosa izlucheniya”, Akusticheskii zhurn., 61:3 (2015), 400–408 | DOI | MR

[7] Prokhorov I. V., Sushchenko A. A., “Imaging based on signal from side-scan sonar”, Appl. Mech. Materials, 756 (2015), 678–682 | DOI

[8] Isimaru A., Rasprostranenie i rasseyanie voln v sluchaino-neodnorodnykh sredakh, Mir, M., 1981

[9] Bal G., “Kinetics of scalar wave fields in random media”, Wave Motion, 43 (2005), 132–157 | DOI | MR | Zbl

[10] Mendus V. I., Postnov G. A., “Ob uglovom raspredelenii vysokochastotnykh dinamicheskikh shumov okeana”, Akusticheskii zhurn., 39:6 (1993), 1107–1116

[11] Andreeva I. B., “Sravnitelnye otsenki poverkhnostnogo, donnogo i ob'emnogo rasseyaniya zvuka v okeane”, Akusticheskii zhurn., 41:5 (1995), 699–705 | MR

[12] Lavrentev M. M., Romanov V. G., Vasilev V. G., Mnogomernye obratnye zadachi dlya differentsialnykh uravnenii, Nauka, Novosibirsk, 1969

[13] Romanov V. G., “Formula obrascheniya v zadache integralnoi geometrii na ellipsoidakh”, Mat. zametki, 46:4 (1989), 124–126 | MR | Zbl