Attenuation of radiated ground motion and stresses from three-dimensional supershear ruptures

Radiating shear and Rayleigh waves from supershear ruptures form Mach waves that transmit large-amplitude ground motion and stresses to locations far from the fault. We simulate bilateral ruptures on a finite-width vertical strike-slip fault (of width W and half-length L with L >> W) breaking the surface of an elastic half-space, and focus on the wavefield out to distances comparable to L. At distances much smaller than W, two-dimensional plane-strain slip-pulse models (i.e., models in which the lateral extent of the slip zone is unbounded) accurately predict the subsurface wavefield. Amplitudes in the shear Mach wedge of those models are undiminished with distance from the fault. When viewed from distances far greater than W, rupture is accurately modeled as a moving point source that produces a shear Mach cone and, on the free surface, Rayleigh-wave Mach fronts. Geometrical spreading of the shear Mach cone occurs radially and amplitudes there decrease with the inverse square-root of distance. The transition between these two asymptotic limits occurs at distances comparable to W. Similar considerations suggest that Rayleigh Mach waves suffer no attenuation in the ideally elastic medium studied here. The rate at which fault strength weakens at the rupture front exerts a strong influence on the off-fault fields only in the immediate vicinity of the fault (for both sub-Rayleigh and supershear ruptures) and at the Mach fronts of supershear ruptures. More rapid weakening generates larger amplitudes at the Mach fronts.