Porosity and elastic anisotropy of rocks under tectonic stress and pore-pressure changes

Abstract

Elastic properties of rocks depend on tectonic stress. Using the theory of poroelasticity as a constraint, we analyze features of these dependencies related to changes in rock pore-space geometry. We develop a formalism describing elastic moduli and anisotropy of rocks as nonlinear functions of confining stress and pore pressure. This formalism appears to agree with laboratory observations. To a first approximation, elastic moduli and seismic velocities as well as porosity depend only on the difference between the confining tectonic stress and pore pressure. However, in general, both the confining stress tensor and the pore pressure must be taken into account as independent variables. The stress-dependent geometry of the pore space fully controls the stress-induced changes in elastic moduli and seismic velocities. Specifically, the compliant porosity plays the most important role, despite the fact that in many rocks the compliant porosity is a very small part of total porosity. Changes in compliant porosity with pressure and stress explain the often observed behavior of elastic moduli: in the low compressive stress regime — say, below 50 to 100 MPa — moduli increase rapidly and then taper exponentially into a flat and linear increase with increasing load. Taking into account the strain of the compliant pore space, we introduce a tensor quantity defining the sensitivity of elastic moduli of rocks to the difference between confining stress and pore pressure. We call it the stress sensitivity tensor. This tensor is an important physical characteristic directly related to elastic nonlinearity of rocks. The stress sensitivity tensor governs the changes in elastic anisotropy of a drained poroelastic system as it depends upon the applied load.