Crack to pulse transition and magnitude statistics during earthquake cycles on a self-similar rough fault

Abstract

Faults in nature demonstrate fluctuations from planarity at most length scales that are relevant for earthquake dynamics. These fluctuations may influence all stages of the seismic cycle; earthquake nucleation, propagation, arrest, and inter-seismic behavior. Here I show quasi-dynamic plane-strain simulations of earthquake cycles on a self-similar and finite 10 km long rough fault with amplitude-to-wavelength ratio α=0.01. The minimum roughness wavelength, λmin, and nucleation length scales are well resolved and much smaller than the fault length. Stress relaxation and fault loading is implemented using a variation of the backslip approach, which allows for efficient simulations of multiple cycles without stresses becoming unrealistically large. I explore varying λmin for the same stochastically generated realization of a rough fractal fault. Decreasing λmin causes the minimum and maximum earthquakes sizes to decrease. Thus the fault seismicity is characterized by smaller and more numerous earthquakes, on the other hand, increasing the λmin results in fewer and larger events. However, in all cases, the inferred b-value is constant and the same as for a reference no-roughness simulation (α=0). I identify a new mechanism for generating pulse-like ruptures. Seismic events are initially crack-like, but at a critical length scale, they continue to propagate as pulses, locking in an approximately fixed amount of slip. I investigate this transition using simple arguments and derive a characteristic pulse length, Lc=λmin/(4π4α2) and slip distance, δc based on roughness drag. I hypothesize that the ratio λmin/α2 can be roughly estimated from kinematic rupture models. Furthermore, I suggest that when the fault size is much larger than Lc, then most space-time characteristics of slip differ between a rough fault and a corresponding planar fault.