Analysis of Phase Velocity and Polarization Features for Elastic Waves in TTI Media

Abstract

Phase velocity and polarization direction are the important parameters for studying seismic wave propagation and describing medium properties, which play essential roles in theory and application. We assume that the symmetry axis of tilted transverse isotropy (TTI) media lies in XOZ plane in the observation coordinates system and directly derive an analytic expression for phase velocity and polarization direction in TTI media in this system. Based on the Thomson dimensionless anisotropic parameters and weak anisotropy approximation theory, we also derive the approximate expressions of phase velocity for elastic waves, polarization direction for qP wave and qSV wave. Theoretical analysis and numerical examples indicate that the change of velocity for qP wave and qSH wave is gentle, and the change of velocity for qSV wave is dramatic. The errors of approximate values of phase velocity are small, so the approximate expression is a good approximation for precise phase velocity. The polarization direction of SH wave is the function of propagation angle and tilted angle of symmetry axis instead of anisotropic parameters. The polarization directions of SH wave is not only perpendicular to propagation direction, but also perpendicular to the direction of symmetry axis. The polarization directions of qP wave and qSV wave are neither parallel nor perpendicular to propagation direction except some special directions, and changes with the angle of symmetry axis in TTI media. For both precise and approximate expressions, the polarization directions of qP wave and qSV wave are always perpendicular. In a given range of errors, the weak anisotropy approximation and analytic expressions match well.