Relevance of Matrix Isotropy Assumption to Elasticity in Porous Anisotropic Rocks

The poroelastic theory of Gassmann (1951) is widely used in fluid substitution problems of seismic monitoring in media considered as isotropic. It is not commonly appreciated that this author also dealt with anisotropic porous media, but of a special type. In his simplified theory the grain constituent is assumed isotropic, and only the rock skeleton is anisotropic. Because anisotropy in sedimentary rocks is very common , the purpose of this presentation is to compare the relative contributions of the anisotropies of the rock skeleton and of the constituent matrix to the overall anisotropy of a fluid saturated rock. The results clearly show the essential contribution of the skeleton anisotropy. As a consequence assuming an isotropic matrix is quite reasonable. In practice, in fluid substitution problems in anisotropic rocks this considerably reduces the number of characteristic elastic parameters to be estimated for the grain constituent, namely from 6 in the general theory to 1 in the simplified anisotropic theory. Finally this work a posteriori justifies the matrix isotropy assumption in the simplified anisotropic model of Gassmann.