Anisotropy pattern arising from application of a triaxial stress to a dry isotropic rock

Abstract

Elastic wave velocities in rocks vary with stress due to the presence of discontinuities and microcracks within the rock. We analytically derive a model for seismic anisotropy caused by small triaxial stresses applied on a linearly isotropic elastic medium permeated by a distribution of cracks with random orientations. This 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. We apply this model to fully estimate the elasticity tensor from log or VSP data and infer P-wave anisotropy from S-wave anisotropy in an area where the anisotropy is known to result from anisotropy of stresses. Besides, this model could be used to differentiate stress-induced anisotropy from that caused by aligned fractures.