Reflection and transmission coefficients of a fracture in transversely isotropic media

We obtain the reflection and transmission coefficients at a fracture in transversely isotropic media, whose symmetry axis is perpendicular to the fracture surface. We consider dissimilar upper and lower media. The fracture is modeled as an interface with boundary discontinuities in the displacement and the particle velocity. The stress components are proportional to the displacement and velocity discontinuities through the specific stiffnesses and specific viscosities, respectively. The stiffness introduces frequency-dependence and phase changes in the fracture response and the viscosity is related to the energy loss. We also calculate the energy balance at the fracture and the dissipated energy. The theory is illustrated by computing the reflection coefficient of a fracture present in the Antarctic ice cap. In this case, the reflection coefficient decreases with increasing incidence angle and then approaches 1 at grazing angle.