Reflection and refraction of elastic wave at VTI-TTI media interface

Abstract

We explore the physical phenomenon of acoustic waves induced at the interface between two different anisotropic rock media. Specifically, one medium is a transversely isotropic medium with a vertical axis of symmetry (VTI medium) and the other one is a transversely isotropic medium with a tilt axis of symmetry (TTI medium). By solving the Kelvin-Christoffel equation, an eighth-order polynomial is established for reflection and refraction angles, which is confirmed from Snell’s law. Three types of analytical expressions of the polarization coefficients of the induced waves are obtained corresponding to different incident angle regions. An effective algorithm has been developed for numerical analysis of the polarization coefficients. Applying characteristic anisotropic parameters reported in the literature, the influencing factors on reflection and refraction coefficients are analyzed, e.g., the anisotropy, the tilt-angle of rock-layer, and the incident-angle. The calculated reflection and refraction coefficients have been rechecked for energy conservation.