Mode-resolved travel-time statistics for elastic rays in three-dimensional billiards

Abstract

We consider the ray limit of propagating ultrasound waves in three-dimensional bodies made from a homogeneous, isotropic, elastic material. Using a Monte Carlo approach, we simulate the propagation and proliferation of elastic rays using realistic angle-dependent reflection coefficients, taking into account mode conversion and ray splitting. For a few simple geometries, we analyze the long-time equilibrium distribution, focusing on the energy ratio between compressional and shear waves. Finally, we study the travel time statistics, i.e., the distribution of the amount of time a given trajectory spends as a compressional wave, as compared to the total travel time. These results are intimately related to recent elastodynamics experiments on Coda-wave interferometry by Lobkis and Weaver. © 2012 American Physical Society.