Mathematical models of seismics in composite media: elastic and poro-elastic components

Abstract

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 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. We illustrate our results with the numerical implementations of the inverse problem for the simplest model.

Keywords

• Acoustics
• two-scale expansion method
• full wave field inversion
• numerical simulation