The general theory of viscoelasticity, which accounts for elastic as well as anelastic linear behavior of materials, predicts that two types of S waves propagate in anelastic earth materials. The particle motion for an inhomogeneous plane S wave of type I is elliptical in the plane defined by the directions of propagation and attenuation, while the particle motion for an inhomogeneous plane S wave of type II is linear perpendicular to this plane. The general theory predicts that an S-wave incident upon a plane boundary perpendicular to the plane defined by the directions of propagation and attenuation generates S waves only of the same type. General characteristics of the type-II S waves reflected and refracted at plane anelastic boundaries are:
velocities and maximum attenuations which depend on the angle of incidence and frequency,
maximum energy flow at a different velocity and in a different direction than phase propagation,
energy flow across the boundary due to interaction of the incident and reflected waves.
The general theory predicts these characteristics for the waves whenever a plane type-II S wave interacts with a plane anelastic boundary such as a soil-bedrock, crust-mantle, or core-mantle interface. None of these characteristics are predicted for the plane SH waves described by elasticity theory.