MATRIX METHOD OF THE PROPAGATION THEORY OF ELASTIC WAVES IN STRATIFIED POROELASTIC MEDIUM

Abstract

The classic poroelastic theory of Biot, developed in the 1950's, describes the propagation of elastic waves through a porous media containing a fluid. This theory has been extensively used in many fields dealing with porous media: seismic exploration, oil gas reservoir characterization, environmental geophysics, earthquake seismology, etc. In this work, it was used the Ursin formalism to create an effective method for the analysis of propagation of elastic waves through a stratified 3D porous media, where the parameters of the media are characterized by piece-wise constant functions of only one spatial variable, depth. In addition, it was considered that the source and the receiver could be localized in any point of the medium. Therefore, it was showed that the method is useful to construct the explicit solution of the Biot's equations, and this method can be a base to the development of an efficient computational algorithm. Keywords: stratified poroelastic medium, Biot's theory, formalism of Ursin, mathematical modeling, explicit solution.