Predicting stress‐induced velocity anisotropy in rocks

Abstract

A simple transformation, using measured isotropic [Formula: see text] and [Formula: see text] versus hydrostatic pressure, is presented for predicting stress‐induced seismic velocity anisotropy in rocks. The compliant, crack‐like portions of the pore space are characterized by generalized compressional and shear compliances that are estimated from the isotropic [Formula: see text] and [Formula: see text]. The physical assumption that the compliant porosity is crack‐like means that the pressure dependence of the generalized compliances is governed primarily by normal tractions resolved across cracks and defects. This allows the measured pressure dependence to be mapped from the hydrostatic stress state to any applied nonhydrostatic stress. Predicted P‐ and S‐wave velocities agree reasonably well with uniaxial stress data for Barre Granite and Massillon Sandstone. While it is mechanically similar to methods based on idealized ellipsoidal cracks, the approach is relatively independent of any assumed crack geometry and is not limited to small crack densities.