Stress-dependent elastic anisotropy of sandstones

Elastic wave velocities in sandstones vary with stress due to the presence of discontinuities such as grain boundaries and microcracks within the rock. In the presence of non-hydrostatic stress fields the elastic wave velocities in sandstones often show significant stress-induced anisotropy. The elastic anisotropy due to any discontinuities within the rock can be written in terms of a second-rank and a fourth-rank tensor which quantify the effect on the elastic wave velocities of the orientation distribution and normal and shear compliances of the discontinuities. This allows elastic wave velocity measurements to be inverted to obtain the components of these tensors. Application of the method to ultrasonic velocity measurements made in a triaxial loading frame shows that a simple theory using only the second-rank tensor allows the P-wave stress-induced anisotropy to be predicted to reasonable accuracy from the S-wave anisotropy and vice versa, thus confirming the correctness of the underlying model. Deviations between the measurements and the predictions of this simplified theory are used to determine the ratio of the normal to shear compliance of the discontinuities. The discontinuities are found to be more compliant in shear than in compression.