Correct interpretation and processing of seismic data must integrate a correct description of the mechanical behavior of rocks, taking into account facts such as the presence of anisotropy and porosity with or without a saturating fluid. This work discusses elasticity of porous media of arbitrary anisotropy type, with emphasis on the study of deformation states and the associated elastic constants. The stress-strain law is represented in seven dimensions. Dynamic parameters (i.e., the six stress components and fluid pressure) are linked with kinematical parameters (i.e., the six strain components and the local increase of fluid content) by a 7D poroelastic tensor. The model is based on the following mechanical interpretation: each eigenvector (eigenstrain) of the poroelastic tensor defines a fundamental deformation state of the medium and the seven eigenvalues (eigenstiffnesses) representthe genuine poroelastic parameters. The set of seven eigenstrains and corresponding eigenstiffnesses constitute the eigensystem of the poroelastic medium. Complete characterization of the eigensystems corresponding to different types of anisotropies encountered in geologic media is achieved. The first six eigenstrains do not differ substantially from the six eigenstrains in elastic nonporous media, which are well documented in the literature. In contrast, the next result is the existence of a seventh eigenstrain characterized by reduction of the total volume of the porous medium associated with an increase in fluid content. Finally, the analysis is applied to experimental data on a rock sample of Pfalz sandstone, considered as an arbitrarily anisotropic porous medium. Thus, more complex mechanical behaviors of rocks can be introduced naturally, including viscoelastic rheology (already published), frequency dependence, nonlinearity, and even hysteresis, as has been done recently in nonporous media.
Modeling of craton stability using a viscoelastic rheology
