The propagation of inhomogeneous waves in an orthotropic viscoelastic medium

Abstract The present article deals with the propagation of inhomogeneous waves in an orthotropic viscoelastic medium. For chosen directions of propagation and a real finite inhomogeneity parameter, a complex slowness vector is specified to define the propagation of an inhomogeneous incident wave. Then, the reflection and transmission of plane waves at a plane interface between two orthotropic viscoelastic half-spaces are discussed. In this incidence, horizontal slowness determines the slowness vectors for all reflected and transmitted waves. For each reflected and transmitted wave, the corresponding slowness vector is resolved to define its phase direction, phase velocity and attenuation angle. Appropriate boundary conditions on this wave field determine the amplitude ratios for reflected and transmitted waves relative to the incident wave. The numerical examples are provided to show the effect of the inhomogeneity of the incident wave on the propagation characteristic as well as the reflection and transmission coefficients. The existence of homogeneous, inhomogeneous incident waves also is investigated.