Understanding the Anisotropy

Abstract

The relation between the particle displacement and the strain field is introduced. Then, stress field is related to the particle velocity by the equation of motion. Based on that, Hooke's law provides a way to link stress and strain fields through elastic parameters characterizing the medium. Finally, Christoffel equation is obtained and T is presented by Thomsen. Its plane wave solutions for solid of transverse isotropy of vertical symmetry axis (TIV). Since the transverse isotropy or hexagonal symmetry is the simplest anisotropy case of widespread geophysical applicability, the author then describes transverse isotropy (TIV) by five elastic parameters, using the main notations introduced by Thomsen in 1986. For ray tracing purposes, the difference between the phase and group velocities is clarified in order to numerically derive the change in ray velocity due to anisotropy.