Application of Finite Element Method for Solving Seismoacoustic Modeling Problems in Poroelastic Composite Media

M. Nurtas1,2,Email

F. Tokmukhamedova1,Email

A. Ydyrys1,Email

Zh. Zhantaev2

S. Nurakynov2

B. Iskakov2

A. Altaibek1,2

B. Matkerim3

1Department of Mathematical and Computer Modelling, International Information Technology University, 34/1 Manas Street, 050040, Almaty, Kazakhstan.
2Institute of Ionosphere, 117 Gardening Community IONOSPHERE, 050020, Almaty, Kazakhstan.
3Department of Computer Science, Faculty of Mechanics and Mathematics, Al-Farabi Kazakh National University, 71 Al-Farabi Avenue, 050040, Almaty, Kazakhstan.

Abstract

The present study is devoted to solving the problem of seismic and acoustic wave propagation in the porous media for composite domains. For simplicity, simple geometry was selected, where domain Ω in consideration consists of three different domains Ωk,k=1,2,3 with different physical and geometrical properties. The wave propagation in the solid skeleton Ω_s of Ω is governed by the Lame's equations. The fluid dynamics in the liquid domain Ωf= ⋃3k=1Ωf,k is governed by the Stokes equations. To model the geometry, we postulate that there are two small parameters: the dimensionless size of pores ε and the dimensionless size of fractures δ and ε≤δ, where ε=l/L is the dimensionless pore size, l is the average size of pores. Domains Ωf,1 and Ωf,3 have the ε-periodic structure and the domain Ωf,2 has the δ-periodic structure with ε=δr,0

Application of Finite Element Method for Solving Seismoacoustic Modeling Problems in Poroelastic Composite Media