Direct and inverse dynamic problems of poroelasticity

Kh. Kh. Imomnazarov ; A. E. Kholmurodov ; A. T. Omonov

Vestnik Tomskogo gosudarstvennogo universiteta. Matematika i mehanika, no. 75 (2022), pp. 87-99

Résumé

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.

Détail

Keywords: direct problem, poroelasticity, distributed source, inverse problem, fundamental solution.