Reflection and refraction at the interface between distinct generally anisotropic half spaces for three-dimensional plane quasi-P waves

In this paper, reflection and refraction phenomena are studied for a three-dimensional plane quasi-P wave incident at the interface between distinct triclinic half spaces. A method has been developed to find the analytical expressions of all the phase velocities of reflected and transmitted quasi-P (qP), quasi-SV (qSV), and quasi-SH (qSH) waves. Closed form expressions for the amplitude ratios of reflection and transmission coefficients of qP, qSV, and qSH waves are also obtained. These expressions are computed numerically for a given set of data and the velocity distributions and variation of reflection and transmission coefficients with polar and azimuthal angle of incidence are shown graphically using two-dimensional single and double axes graphs. Surface plots of velocity variations of different reflected and transmitted waves are drawn to analyze the combined effect of incident polar and azimuthal angle on velocity distribution. Numerical results presented indicate that anisotropy effects on the reflection and transmission coefficients are significantly different in the three-dimensional case compared to the two-dimensional case. Certain published work has been derived as special cases to illustrate the present technique. Software in MATLAB has been designed to analyze the reflection/transmission phenomena with present geometry in simpler elastic media, such as monoclinic, transversely isotropic, isotropic, etc.