FAR EASTERN BRANCH OF THE RUSSIAN ACADEMY OF SCIENCES
INSTITUTE OF APPLIED MATHEMATICS KHABAROVSK DIVISION
Far Eastern Mathematical Journal
On the problem of determining the scattering coefficient in frequency modulated sounding of a medium |
P.A. Vornovskikh, E.V. Ermolaev, I.V. Prokhorov |
2022, issue 2, P. 263-268 DOI: https://doi.org/10.47910/FEMJ202237 |
Abstract |
| 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. |
Keywords: radiative transfer equation, linear frequency modulated sounding, scattering coefficient, inverse problem |
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References |
| [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. [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. [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. [5] G. Bal, “Kinetics of scalar wave fields in random media", Wave Motion, 43, (2005), 132-157. [6] G. Bal, “Inverse transport theory and applications", Inverse Problems, 25:5, (2009), 025019. [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. [8] S. Acosta, “Time reversal for radiative transport with applications to inverse and control problems", Inverse Problems, 29, (2013), 085014. [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. [10] M. Bellassoued, Y. Boughanja, “An inverse problem for the linear Boltzmann equation with a time-dependent coefficient", Inverse Problems, 35, (2019), 085003. [11] W. Dahmen, F. Gruber, O. Mula, “An adaptive nested source term iteration for radiative transfer equations", Math. Comp, 89, (2020), 1605-1646. 512 [12] Q. Li, W. Sun, “Applications of kinetic tools to inverse transport problems", Inverse Problems, 36, (2020), 035011. [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. [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. [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. |