Stress-induced anisotropy model for triaxially stressed rocks

Abstract

Elastic wave velocities in rocks vary with stress due to the presence of discontinuities and microcracks within the rock. In this paper, we analytically derive a model for seismic anisotropy caused by small triaxial stresses. We first consider a linearly isotropic elastic medium permeated by a distribution of cracks with random orientations. The geometry of cracks is not specified; instead, their behavior is defined by a ratio B of their normal to tangential excess compliances. When this isotropic rock is subjected to small triaxial stresses, crack closure occurs perpendicular to the applied stresses. This effect is modeled using Sayers and Kachanaov (1995) non-interactive approximation. The model predicts ellipsoidal anisotropy and also expresses the ratios of Thomsen’s parameters ε/γ as a function of the compliance and Poisson’s ratios in the three orthogonal planes of symmetry. A reasonable agreement was obtained when comparing the model predictions to laboratory measurements for small stresses (up to 20 MPa). These results could be used to differentiate stress-induced anisotropy from that caused by aligned fractures. Besides, if the cause of anisotropy is known, then this model could enable one to fully estimate the elasticity tensor from log data.