Numerical observation of the equipartition regime in a 3D random elastic medium, and discussion of the limiting parameters

At long lapse times in the weakly scattering regime, the energy of the coda in a randomly fluctuating isotropic medium is equipartitioned between P and S modes. This behavior is well understood mathematically and physically for full spaces. For realistic domains, analytical results are more scarce and numerical simulations become a valuable tool. This paper discusses, based on numerical simulations of wave propagation in a 3D randomly heterogeneous elastic medium, the transition to an equipartitioned regime of the wave field. Both the time to transition and the value of the ratio of energies after transition are evaluated. Several influencing parameters are discussed, either physical (ratio of background P- and S- velocities, propagation length, variance of the heterogeneities) or numerical (influence of Perfectly Matched Layers). Setting up of a localization regime, inefficient mixture of body waves and small propagation length compared to the transport mean free paths are identified as constraining for the transition toward an equipartition regime.