Modeling elastic anisotropy resulting from the application of triaxial stress
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Elastic wave velocities in rocks vary with stress due to the presence of discontinuities and microcracks within the rock. We analytically derived a model to account for stress dependency of seismic velocities when a rock is subjected to triaxial stresses. We first considered 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 triaxial stresses, cracks tend to close depending on their orientation with respect to the applied stresses. For small stresses, the model predicts ellipsoidal anisotropy and expresses the ratios of Thomsen’s parameters ϵ/γ in the three orthogonal planes of symmetry as a function of the compliance and Poisson’s ratios. It also establishes relationships between anisotropy parameters and stress ratios. Deriving the model for larger stresses shows that such results still hold for stresses as high as approximately 40 MPa. There is a reasonable agreement between the model predictions and laboratory measurements made on a sample of Penrith sandstone, although crack opening in the direction of maximum stress should be taken into account for larger stresses. The proposed model could be used to differentiate stress-induced anisotropy from fracture-induced anisotropy. Besides, if the cause of anisotropy is known, then this model could enable one to determine P-wave anisotropy from S-wave anisotropy.
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