Monte Carlo simulation of radiative energy transfer in continuous elastic random media-three-component envelopes and numerical validation

Abstract

We present Monte Carlo solutions of the 3-D radiative transfer (RT) equations for energy transport in elastic media with randomly fluctuating velocity and density. It includes mode conversions from P- to S-wave energy and vice versa and considers angular-dependent scattering patterns following from the Born approximation. Synthesis of the space-time distribution of seismic energy emitted from point sources with arbitrary radiation patterns can be achieved. The method offers a unique way to model complete mean square envelopes of high-frequency wavefields in the presence of random heterogeneity starting from the first P-wave onset until the late S-wave coda. Validation of the method is achieved through a comparison of mean square envelopes from an isotropic P-wave radiation point source with full 3-D wavefield simulations for the whole envelope shape and with the analytical Markov approximation for small lapse times. RT yields accurate envelope shapes even for parameter ranges where strong and direction-dependent scattering occurs. Peak amplitudes, envelope broadening and coda decay at long lapse times are correctly modelled. A breakdown of RT with Born scattering coefficients only occurs in the vicinity of a point source: waveform modelling shows that even for a pure compressional source, some per cent of shear wave energy are generated by near-source scattering that are not explained within the framework of Born approximation. © 2008 The Authors Journal compilation © 2008 RAS.