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This article is cited in 6 scientific papers (total in 6 papers)
MECHANICS
Direct and inverse dynamic problems of poroelasticity
Kh. Kh. Imomnazarova, A. E. Kholmurodovb, A. T. Omonovc a Institute of Computational Mathematics and
Mathematical Geophysics SB RAS, Novosibirsk, Russian Federation
b Karshi State University, Karshi, Uzbekistan
c Tashkent State
Economic University, Tashkent, Uzbekistan
Abstract:
In applied problems related to propagation of elastic waves, it is often necessary to take into account porosity, fluid saturation of the media, and the hydrodynamic background. Real geological media are multiphase, electrically conductive, fractured, porous, etc. When propagating, seismic waves dissipate due to the absorption of energy. In this paper, the wave propagation process occurs in terms of partial densities of phases, stress tensor, pore pressure, and velocities of the corresponding phases. In the first section, for completeness, the presentation presents a quasilinear system of equations of the poroelasticity theory [1-3]. In the second section, the corresponding linear system of equations of the poroelasticity theory for a homogeneous medium is obtained. In the third section, we construct a fundamental solution for the system of equations of the poroelasticity theory obtained in the second section. In the final section, the inverse poroelasticity problem of determining the distributed source in a half-space using additional information about the free surface mode is considered.
Keywords:
direct problem, poroelasticity, distributed source, inverse problem, fundamental solution.
Received: 11.08.2020
Citation:
Kh. Kh. Imomnazarov, A. E. Kholmurodov, A. T. Omonov, “Direct and inverse dynamic problems of poroelasticity”, Vestn. Tomsk. Gos. Univ. Mat. Mekh., 2022, no. 75, 87–99
Linking options:
https://www.mathnet.ru/eng/vtgu903 https://www.mathnet.ru/eng/vtgu/y2022/i75/p87
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