2009 Volume 62 Issue 4 Pages 397-419
We overview the models for calculating velocity anisotropy in rocks in terms of the preferred orientations of cracks and minerals in rocks. We also discuss about wave propagation in anisotropic media. The P- and the S-wave velocities in rocks are affected by voids and cracks in rocks as well as the elastic properties of the constituent minerals. To understand the elastic properties of rocks, we start from the basic definitions and equations of the theory of elasticity for continuum homogeneous media. The elastic constants or elastic compliances are derived from an approach based on thermodynamics of solids. We derive the elastic constants or elastic compliances of materials from thermodynamics of solids. Then we see several approaches for calculating seismic wave velocities in composite media, where pieces of the second material are embeded into a matrix of the first material. For voids and cracks, the second material is gas or liquid in most of the actural cases in the Earth's crust. The most important anistropy in eath sciences is the transverse isotropy (TI) where seismic wave velocities are given as functions of the angle from the symmetry axis. For calculating seismic velocity anisotropy of rocks, we consider two anisotropies produced by preferred orientation of anisotropic minerals and oriented cracks. In the last, we dicuss about the crack density parameter that is one of the most important parameters for describing seismic anisotropy due to cracks and voids in a rock.
