A new approach to reflection-transmission between viscoelastic half-spaces

Reflection and transmission of time-harmonic waves at the welded boundary between linear, viscoelastic, isotropic half-spaces is examined. A basis consisting of inhomogeneous waves is considered, for wave fields obeying Snell’s law; the basis elements are parameterized by the component k∥ of the wave vector parallel to the interface; incident and reflected-transmitted waves are expressed as superpositions of incoming and outgoing inhomogeneous waves. The characterization of incoming and outgoing inhomogeneous waves through the phase, the amplitude, and the mean energy intensity is shown to provide nonequivalent mathematical models for reflection and transmission. On the basis of the general properties of the energy flux, the energy criterion is regarded as the appropriate one. The resulting approach is developed in connection with the reflection-transmission process. In particular, the incoming or outgoing character of any inhomogeneous wave is shown to depend on k∥. In correspondence with such a dependence, jump discontinuities of the reflection and transmission coefficients are shown to occur.