Coherence of Mach fronts during heterogeneous supershear earthquake rupture propagation: Simulations and comparison with observations

We study how heterogeneous rupture propagation affects the coherence of shear and Rayleigh Mach wavefronts radiated by supershear earthquakes. We address this question using numerical simulations of ruptures on a planar, vertical strike-slip fault embedded in a three-dimensional, homogeneous, linear elastic half-space. Ruptures propagate spontaneously in accordance with a linear slip-weakening friction law through both homogeneous and heterogeneous initial shear stress fields. In the 3-D homogeneous case, rupture fronts are curved owing to interactions with the free surface and the finite fault width; however, this curvature does not greatly diminish the coherence of Mach fronts relative to cases in which the rupture front is constrained to be straight, as studied by Dunham and Bhat (2008a). Introducing heterogeneity in the initial shear stress distribution causes ruptures to propagate at speeds that locally fluctuate above and below the shear wave speed. Calculations of the Fourier amplitude spectra (FAS) of ground velocity time histories corroborate the kinematic results of Bizzarri and Spudich (2008a): (1) The ground motion of a supershear rupture is richer in high frequency with respect to a subshear one. (2) When a Mach pulse is present, its high frequency content overwhelms that arising from stress heterogeneity. Present numerical experiments indicate that a Mach pulse causes approximately an omega(-1.7) high frequency falloff in the FAS of ground displacement. Moreover, within the context of the employed representation of heterogeneities and over the range of parameter space that is accessible with current computational resources, our simulations suggest that while heterogeneities reduce peak ground velocity and diminish the coherence of the Mach fronts, ground motion at stations experiencing Mach pulses should be richer in high frequencies compared to stations without Mach pulses. In contrast to the foregoing theoretical results, we find no average elevation of 5%-damped absolute response spectral accelerations (SA) in the period band 0.05-0.4 s observed at stations that presumably experienced Mach pulses during the 1979 Imperial Valley, 1999 Kocaeli, and 2002 Denali Fault earthquakes compared to SA observed at non-Mach pulse stations in the same earthquakes. A 20% amplification of short period SA is seen only at a few of the Imperial Valley stations closest to the fault. This lack of elevated SA suggests that either Mach pulses in real earthquakes are even more incoherent that in our simulations or that Mach pulses are vulnerable to attenuation through nonlinear soil response. In any case, this result might imply that current engineering models of high frequency earthquake ground motions do not need to be modified by more than 20% close to the fault to account for Mach pulses, provided that the existing data are adequately representative of ground motions from supershear earthquakes.