Chapter 3 - Isotropic anelastic media

Abstract

The effects of the space dimension are considered in this chapter, revealing other properties of wave fields. The attenuation vector plays a role at the same level as the wavenumber vector. Snell law, for instance, implies continuity of the tangential components of both vectors at the interface of discontinuity. For inhomogeneous viscoelastic waves, the angle between the propagation and attenuation directions must be less than π/2. Furthermore, the energy does not propagate in the direction of the slowness vector, and the particle motion is elliptical in general. For homogeneous plane waves, the energy-velocity vector is equal to the phase-velocity vector. The last part of the chapter analyzes the viscoelastic wave equation expressed in terms of fractional time derivatives, provides expressions for the reflection and transmission coefficients corresponding to a partially welded interface, and illustrates the concept of the transfer function.