Weak Elastic Anisotropy in a Cracked Rock

Crack and textural fabrics have significant control over the development of mechanical anisotropy in a rock. Bedding in sedimentary rocks, cleavage in slates, preferred orientation of anisotropic minerals and anisotropic distribution of microcracks can all contribute to elastic anisotropy. Using Kachanov's (1992, 1993) formulation we analyzed the effects of an axisymmetric system of microcracks on seismic anisotropy. The elastic behavior of such a cracked rock is transversely isotropic, and its seismic properties can be characterized by the three Thomsen parameters. In this study we calculated the parameters ɛ, δ and γ under dry and saturated conditions. We derived analytic expressions for the model proposed by Sayers & Kachanov (1995), which assumes that the contribution from the fourth rank crack density tensor is negligible. This model predicts that the elliptic anisotropy condition ɛ=δ is obeyed in a dry rock. Guided by microstructural observations we adopted a two-parameter axisymmetric distribution to characterize the crack density, which predicts that δ and γ in a fluid saturated rock are related to ɛ in a nonlinear manner. All three Thomsen parameters are sensitively dependent on the crack density difference. While our model shows basic agreement with some of the laboratory data on seismic anisotropy in saturated shale, there are discrepancies which suggest that the petrofabric associated with preferred orientation of clay minerals and elastic anisotropy of the rock matrix may have considerable influence which should not be neglected in model. Preliminary comparison with borehole log data suggests rock physics tests which may be useful for interpreting the shear wave anisotropy observations.