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Reflection and refraction of type-II S waves in elastic and anelastic media

U.S. GEOLOGICAL SURVEY, 345 MIDDLEFIELD ROAD, MENLO PARK, CALIFORNIA 94025

Abstract

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:

1. (a) velocities and maximum attenuations which depend on the angle of incidence and frequency,
   
2. (b) maximum energy flow at a different velocity and in a different direction than phase propagation,
   
3. (c) 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.

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