Reflection and refraction of SH plane waves at the interface between two inhomogeneous half-spaces

The reflection and refraction of SH plane wave at the interface between two inhomogeneous half-spaces are studied in this paper, where the distributions of shear modulus and mass density all obey the parabolic functions. Based on the fundamental solution of the wave equation, the general formulations of incident wave, reflected wave and transmitted wave are given. Substituting the formulations into the boundary condition at the interface, the unknown coefficients are obtained, where the absolute values of these coefficients represent the amplitudes of reflected wave and transmitted wave. A series of parametric discussion are made to exhibit the effect on the reflection and refraction by wave number, incident angle and material properties.