Reflection and refraction of three dimensional plane quasi-P waves at a corrugated surface between distinct triclinic elastic half spaces

Abstract

The present work deals with the reflection and transmission of three-dimensional plane quasi-P (qP) waves at a corrugated surface between distinct triclinic elastic half spaces. A method has been developed to find the analytical expressions of all the three phase velocities of qP, quasi-SV (qSV) and quasi-SH (qSH) waves in three dimensions. Closed form expressions in three-dimensions for the amplitude ratios of reflection and transmission coefficients of qP, qSV and qSH waves are obtained. Graphs for reflection and transmission coefficients are drawn for different polar and azimuthal angles. These reflection and transmission coefficients are computed numerically and shown graphically for fixed values of relevant parameters. Graphical user interface software in MATLAB has been designed to generalize the result of the study, by allowing one to choose arbitrary suitable values for relevant parameters. It is found that reflection and transmission coefficients are significantly different in three dimensional case compared to the two dimensional case.