Spatiotemporal properties of Sub-Rayleigh and supershear rupture velocity fields: Theory and experiments
Résumé
Fundamental spatiotemporal field properties and particle velocity waveform signatures of sub-Rayleigh and supershear ruptures were experimentally investigated through a series of laboratory earthquake experiments. We appeal to dynamic rupture theory to extract and highlight previously unnoticed aspects and results, which are of direct relevance to our new experiments. Kinematic relationships derived from both singular and non-singular solutions are applied to analyze and interpret various features observed in these experiments. A strong correspondence is demonstrated between particle velocity records obtained in lab experiments and synthetic particle velocity waveform profiles derived from theory. Predicted temporal profiles, sense of particle motion, and amplitude decay properties of sub-Rayleigh and supershear particle velocity waveforms are experimentally verified. In a particular set of supershear rupture experiments, the fault-normal (FN) and fault-parallel (FP) velocity waveforms were simultaneously recorded at fixed, off-fault field points as a shear Mach front swept these locations. Particle velocity records collected over a broad range of stable supershear rupture speeds validate the predicted scaling relationship δ u˙1 s / δ u˙2s =√{Vr2/Cs2-1} =βs, between the FP (δu1s˙) and the FN (δ u2s ˙) velocity jumps propagated by a shear Mach front. Additional experimental findings include detailed rupture speed measurements of sub-Rayleigh and supershear ruptures and the observation of a supershear daughter crack with vanishing shear Mach front. Previously unappreciated scaling relations between particle velocity field components, attributed to dilatational and shear waves, are also developed and experimentally verified. In particular, the FP velocity jump δu1s ˙ (x1 ,x2) propagated by the shear Mach front, and the sliding speed δu˙1(x1 ,0+), measured at a field point positioned extremely close to the frictional fault plane, are shown to obey a speed-dependent scaling relationship given by δ u˙1 s / δ u˙1 + = 1 - 2 Cs2 Vr2, which was gleaned from a non-singular, steady state velocity field solution.