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

SUMMARY 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.