Chapter 6 - Reflection and Transmission of Plane Waves

Abstract

The SH and qP-qSV cases illustrate the physics of wave propagation in anisotropic anelastic media. In general, the reflected and transmitted waves are inhomogeneous, i.e., equiphase planes do not coincide with equiamplitude planes. The reflected wave is homogeneous only when the symmetry axis is perpendicular to the interface. If the transmission medium is elastic and the incident wave is homogeneous, the transmitted wave is inhomogeneous of the elastic type, i.e., the attenuation vector is perpendicular to the Umov-Poynting vector. The angle between the attenuation vector and the slowness vector may exceed 90°, but the angle between the attenuation and the Umov-Poynting vector is always less than 90° . If the incidence medium is elastic, the attenuation of the transmitted wave is perpendicular to the interface. The relevant physical phenomena are not related to the propagation direction (slowness vector), but rather to the energy-flow direction (Umov-Poynting vector) – for instance, the characteristics of the elastic type inhomogeneous waves, the existence of critical angles and the fact that the amplitudes of the reflected and transmitted waves decay in the direction of energy flow despite the fact that they grow in the direction of phase propagation. The applications of the theory includes propagation at fluid/solid interfaces, Rayleigh surface waves and propagation through a set of layers.