We investigate Mach wave coherence for kinematic supershear ruptures with spatially heterogeneous source parameters, embedded in 3-D scattering media. We assess Mach wave coherence considering: (1) source heterogeneities in terms of variations in slip, rise time and rupture speed; (2) small-scale heterogeneities in Earth structure, parametrized from combinations of three correlation lengths and two standard deviations (assuming von Karman power spectral density with fixed Hurst exponent); and (3) joint effects of source and medium heterogeneities. Ground-motion simulations are conducted using a generalized finite-difference method, choosing a parametrization such that the highest resolved frequency is ∼5 Hz.

We discover that Mach wave coherence is slightly diminished at near-fault distances (<10 km) due to spatially variable slip and rise time; beyond this distance the Mach wave coherence is more strongly reduced by wavefield scattering due to small-scale heterogeneities in Earth structure. Based on our numerical simulations and theoretical considerations we demonstrate that the standard deviation of medium heterogeneities controls the wavefield scattering, rather than the correlation length. In addition, we find that peak ground accelerations in the case of combined source and medium heterogeneities are consistent with empirical ground-motion prediction equations for all distances, suggesting that in nature ground-shaking amplitudes for supershear ruptures may not be elevated due to complexities in the rupture process and seismic wave scattering.