LOCALIZATION AND MODE CONVERSION FOR ELASTIC-WAVES IN RANDOMLY LAYERED MEDIA .2.

This paper is Part II of a two part work in which we derive localizati on theory for elastic waves in plane-stratified media, a multimode pro blem complicated by the interconversion of shear and compressional wav es, both in propagation and in backscatter. We consider the low freque ncy limit, i.e., when the randomness constitutes a microstructure. In Part I, we set up the general suite of problems and derived the probab ility density and moments for the fraction of reflected energy which r emains in the same mode (shear or compressional) as the incident field . Our main mathematical tool was a limit theorem for stochastic differ ential equations with a small parameter. In this part we use the limit theorem of Part I and the Oseledec theorem, which establishes the exi stence of the localization length and other structural information, to compute: the localization length and another deterministic length, ca lled the equilibration length, which gives the scale for equilibration of shear and compressional energy in propagation; and the probability density of the ratio of shear to compressional energy in transmission through a large slab. This last quantity is shown to be asymptoticall y independent of the incident field. We also extend the results to the small fluctuation, rather than the low frequency case.