Localization of Low Frequency Elastic Waves

Abstract

We consider the propagation of compressional (P) and vertical shear (SV) waves in a plane-stratified medium with a stochastic microstructure. For such a medium, localization theory applies: waves are exponentially attenuated with propagation distance solely by the mechanism of random multiple scattering. We compute here the localization length and another deterministic length, called the equilibration length, which is associated with the equilibration of shear and compressional energy on transmission through a large slab. These characteristic lengths are seen to be reciprocals of the Lyapunov exponents for this system. We also provide expressions for the probability density of P to SV wave energy on transmission through a large slab, and for the fraction of energy which is mode converted on backscatter from a random half-space.KeywordsLyapunov ExponentLocalization LengthIncident FieldPositive Lyapunov ExponentPropagator MatrixThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.