Geodesic
On the problem of determining the scattering coefficient in frequency modulated sounding of a medium
Dalʹnevostočnyj matematičeskij žurnal, Tome 22 (2022) no. 2, pp. 263-268 
P. A. Vornovskikh; E. V. Ermolaev; I. V. Prokhorov. On the problem of determining the scattering coefficient in frequency modulated sounding of a medium. Dalʹnevostočnyj matematičeskij žurnal, Tome 22 (2022) no. 2, pp. 263-268. http://geodesic.mathdoc.fr/item/DVMG_2022_22_2_a23/
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Voir la notice de l'article provenant de la source Math-Net.Ru

Within the framework of the kinetic model of the transfer of linear frequency modulated radiation in a scattering medium, an inverse problem is formulated, which consists in determining the volume scattering coefficient of sound. Additional information in the problem is the frequency-averaged angular distribution of the radiation flux density at a given point in space. An analytical solution of the inverse problem is obtained in the single scattering approximation.

[1] P. A. Vornovskikh, A. Kim, I. V. Prokhorov, “The applicability of the approximation of single scattering in pulsed sensing of an inhomogeneous medium”, Computer Research and Modeling, 12:5 (2020), 1063–1079 | DOI

[2] 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”, Dal’nevost. Mat. Zh., 21:2 (2021), 151–165 | MR

[3] C. S. Clay, H. Medwin, Acoustical Oceanography: Principal and Applications, John Wiley and Sons New, York, 1977

[4] A. Ishimaru, Wave Propagation and Scattering in Random Media, Academic Press, New York, 1978 | MR

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

[6] G. Bal, “Inverse transport theory and applications”, Inverse Problems, 25:5 (2009), 025019 | MR

[7] I. V. Prokhorov, A. A. Sushchenko, “Studying the problem of acoustic sounding of the seabed using methods of radiative transfer theory”, Acoustical Physics, 61:3 (2015), 368–375 | DOI

[8] S. Acosta, “Time reversal for radiative transport with applications to inverse and control problems”, Inverse Problems, 29 (2013), 085014 | DOI | MR

[9] I. V. Prokhorov, I. P. Yarovenko, “Determination of Refractive Indices of a Layered Medium under Pulsed Irradiation”, Optics and Spectroscopy, 124:4 (2018), 567–574 | DOI

[10] M. Bellassoued, Y. Boughanja, “An inverse problem for the linear Boltzmann equation with a time-dependent coefficient”, Inverse Problems, 35 (2019), 085003 | DOI | MR

[11] W. Dahmen, F. Gruber, O. Mula, “An adaptive nested source term iteration for radiative transfer equations”, Math. Comp, 89 (2020), 1605–1646 | DOI | MR

[12] Q. Li, W. Sun, “Applications of kinetic tools to inverse transport problems”, Inverse Problems, 36 (2020), 035011 | DOI | MR

[13] I. V. Prokhorov, I. P. Yarovenko, “Determination of the Attenuation Coefficient for the Nonstationary Radiative Transfer Equation”, Computational Mathematics and Mathematical Physics, 61:12 (2021), 2088–2101 | DOI | MR

[14] L. Florescu, V. A. Markel, J. C. Schotland, “Single-scattering optical tomography: simultaneous reconstruction of scattering and absorption”, Phys. Rev. E., 81 (2010), 016602 | DOI

[15] A. Kleinboehl, J. T. Schofield, W. A. Abdou, P. G. J. Irwin, de R. J. Kok, “A single-scattering approximation for infrared radiative transfer in limb geometry in the Martian atmosphere”, Journal of Quantitative Spectroscopy and Radiative Transfer, 112:10 (2011), 1568–1580 | DOI