Multiple scattering of high‐frequency seismic waves in the deep Earth: Modeling and numerical examples

Abstract

We apply the modern theory of radiative transfer to the modeling of the global propagation of high‐frequency seismic waves in the Earth. This theory stems from an exact statistical treatment of the wave equation and incorporates rigorously the effects of multiple scattering. The statistical mean time between scattering events (the mean free time) and the typical correlation length of the random fluctuations (the scale length) are introduced as the fundamental parameters of the theory. The integro‐differential equation of transport describes statistically the propagation of energy in phase space and can be conveniently solved by means of Monte Carlo simulations. We provide a general description of the method, stressing the important modifications required to adapt it to global propagation. The theory is applied to the modeling of PKP precursors, probably the best documented examples of wave scattering at the global scale. Guided by recent results of Hedlin et al. [1997], we solve the transfer equation in a variety of Earth models presenting exponentially correlated fluctuations of elastic parameters superimposed upon PREM. The validity of Born approximation is tested in a series of random media with mean free time and scale length in the 100–3200 s and 4–24 km ranges, respectively. For errors in coda envelope amplitude bound by 20%, the Born approximation can be safely applied in media with mean free times larger than about 400 s, relatively independent of the scale length. This corresponds to rather moderate (<0.5% RMS) perturbations, thus severely limiting the range of validity of Born approximation.