A Description of Seismic Acoustic Wave Propagation in Porous Media via Homogenization
Anvarbek Mukatovich Meirmanov · SIAM Journal on Mathematical Analysis · 2008
We consider a linear system of differential equations describing the joint motion of an elastic porous body and a fluid occupying the porous space. A rigorous justification is performed for the homogenization procedures under various conditions imposed on the physical parameters as the dimensionless size of the pores tends to zero, while the porous body is geometrically periodic and the process's characteristic time is sufficiently small. Such models describe the propagation of seismic acoustic waves. In the present paper, we derive the homogenized equations, which are different types of nonstandard wave equations depending on the relations between the physical parameters. The proofs are based on Nguetseng's two-scale convergence method of homogenization in periodic structures.