Mach-wave Properties in Scattering Media with Random Heterogeneities

Abstract:

We investigate the properties of Mach-waves, generated by super-shear ruptures, in scattering media with random heterogeneities. To simulate the Mach-wave, we use kinematic earthquake source descriptions that include fault-regions over which the rupture propagates at super-shear speed. The local slip rate is modeled with the regularized Yoffe function, assuming constant rise time. We generate various realizations of 3D random media by characterizing the heterogeneities of medium parameters using the Von Karman function. We adopt six different characterizations of the medium from combinations of three correlation lengths (0.5 km, 2 km, 5 km) and two standard deviations (5%, 10%). Simulations in a homogeneous medium serve as a reference case. The ground-motion simulations (maximum resolved frequency of 5 Hz) are conducted by solving the elasto-dynamic equations of motions using generalized finite-difference method. The seismic wavefield is sampled at numerous locations within R_JB(Joyner-Boore distance) ranging between 10-40 km, with focus on the Mach-cone region, to study the properties and evolution of the Mach-waves in the scattering media.

We find that seismic scattering in random media significantly diminishes the coherence of the Mach-wave away from the source. Investigating peak ground velocities (PGV) to quantify the scattering effects, we observe that mean PGV in the medium with the largest correlation length and standard deviation is significantly smaller (by about a factor of 1.5 to 2.5 with increasing R_JB distance) compared to the reference case. Correlation length, rather than standard deviation, appears to control the scattering of the Mach wave. Our analysis of Fourier amplitude spectra shows that the seismic energy is redistributed among the three ground-motion components, with an increase of high frequency content in the vertical component. Based on our simulations of Mach-wave properties in scattering media, we hypothesize that local super-shear ruptures may be more common in nature then reported, but are very difficult to detect due to the strong seismic scattering.