Propagation of SH waves in 2-D random media: from ballistic to diffusive behavior

Random inhomogeneities in the earth can highly influence the characteristics of propagating seismic waves. They exist at all scales and can become an important source of epistemic uncertainty in the ground motion estimation. Despite several works have evaluated these effects, few of them have verified the accuracy of their numerical solutions or controlled the propagation regime they were simulating. In this work we present a comprehensive study of SH wave propagation in 2D random media, which covers from ballistic to diffusive behaviors. In order to understand and identify the interaction of these regimes, we analyzed the coherent and incoherent components of the wavefield. The random media consist in correlated density and velocity fluctuations described by von Kármán autocorrelation function with a Hurst coefficient of 0.25 and a correlation length a=500 m. The Birch correlation coefficient which relates density to velocity fluctuations takes 4 possible values between 0.5 and 1, and the standard deviation of the perturbations is either 5% or 10%. Spectral element simulations of SH wave propagation excited by a plane wave are performed for normalized wavenumbers (ka) up to 5. By measuring the amplitude decay of the coherent wave we obtain the scattering attenuation, which is then compared with theoretical predictions from the mean field theory. Similarly, mean intensities from synthetic waveforms are also compared with those from radiative transfer theory. Both sets of comparisons show excellent agreement between numerical and theoretical predictions. Addionally, we perform statistical analyses on the fluctuations of the ballistic peak which exhibits a transition from log-normal to exponential distribution. These two types of distribution characterize the ballistic and diffusive behaviors, respectively, which means that after certain propagation distances the quasi-ballistic peak is composed mainly by multiply-diffused components. Such critical distance is of the order of the scattering mean free path and offers an alternative method to measure this parameter. Finally, we pay particular attention on the attenuation of the quasi-ballistic peak, which in the forward scattering regime appears to decay exponentially over a length scale known as the transport mean free path.