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

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 𝛺 𝑘 , 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 𝛺 𝑓 = ⋃ 𝑘=1 3 𝛺 𝑓,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 𝛺 𝑓,1 and 𝛺 𝑓,3 have the 𝜀periodic structure and the domain 𝛺 𝑓,2 has the 𝛿-periodic structure with 𝜀 = 𝛿 𝑟 , 0 < 𝑟 < 1.At the common boundaries of the 'liquid-solid' area, the usual continuity condition of continuum mechanics holds.The main goal of the study is the numerical implementations using finite element method (FEM) for the analysis of wave propagation in 𝛺.The impact of the study on the composites field offers valuable insights into materials' behavior under dynamic loading conditions, improving the composite structures across industries.

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