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

We consider the ray limit of propagating ultrasound waves in three-dimensional bodies made from an 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 analyse the long time equilibrium distribution focussing 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 [Phys. Rev. E 78, 066212 (2008)].