An analytic model for the stress-induced anisotropy of dry rocks

One of the main causes of azimuthal anisotropy in sedimentary rocks is anisotropy of tectonic stresses in the earth's crust. We have developed an analytic model for seismic anisotropy caused by the application of a small anisotropic stress. We first considered an isotropic linearly elastic medium (porous or nonporous) permeated by a distribution of discontinuities with random (isotropic) orientation (such as randomly oriented compliant grain contacts or cracks). The geometry of individual discontinuities is not specified. Instead, their behavior is defined by a ratio B of the normal to tangential excess compliances. When this isotropic rock is subjected to a small compressive stress (isotropic or anisotropic), the number of cracks along a particular plane is reduced in proportion to the normal stress traction acting on that plane. This effect is modeled using the Sayers-Kachanov noninteractive approximation. The model predicts that such anisotropic crack closure yields elliptical anisotropy, regardless of the value of the compliance ratio B. It also predicts the ratio of Thomsen's anisotropy parameters epsilon/gamma as a function of the compliance ratio B and Poisson's ratio of the unstressed rock. A comparison of the model predictions with the results of laboratory measurements indicates a reasonable agreement for moderate magnitudes of uniaxial stress (as high as 30 MPa). These results can be used for differentiating stress-induced anisotropy from that caused by aligned fractures. Conversely, if the cause of anisotropy is known, then the anisotropy pattern allows one to estimate P-wave anisotropy from S-wave anisotropy.