35 Partial differential equations -- 35Q Equations of mathematical physics and other areas of application 35Q35 PDEs in connection with fluid mechanics 35Q74 PDEs in connection with mechanics of deformable solids
Summary: ``In the present paper we consider elastic and poroelastic media having a common interface. We derive the macroscopic mathematical models for seismic wave propagation through these two different media as a homogenization of the exact mathematical model at the microscopic level. They consist of seismic equations for the each component and boundary conditions at the common interface, which separates different media. To do this we use the two-scale expansion method in the corresponding integral identities, defining the weak solution. Our results we illustrate with the numerical implementations of the inverse problem for the simplest model.''