WAVE PROPAGATION IN THE ANISOTROPIC INHOMOGENEOUS HALF-PLANE

This study presents closed-form solutions for free-field motions in an anisotropic continuously inhomogeneous half-plane that includes contributions of incident waves as well as of waves reflected from the traction free horizontal surface. A state of plane strain holds and both pressure and vertically polarized shear waves are considered. Anisotropic material characteristics vary quadratically with respect to the depth coordinate. The method of solution is a hybrid approach based on the plane wave decomposition technique, augmented by appropriate functional transformation relations for the displacement vector. The existence of a unique analytical solution as, a superposition of the incident P- or SV-wave and the corresponding reflected P- and SV-waves is proved under some restrictions on the incident wave direction. The simulation study reveals the influence of the material inhomogeneity and anisotropy on the displacement free field wave motion.