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

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Elias Rafn Heimisson 


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 $\alpha = 0.01$. The minimum roughness wavelength, $\lambda_{min}$, 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 $\lambda_{min}$ for the same stochastically generated realization of a rough fractal fault. Decreasing $\lambda_{min}$ 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 $\lambda_{min}$ 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 ($\alpha = 0$). 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, $L_c = {\lambda_{min}}/({4 \pi^4 \alpha^2})$ and slip distance, $\delta_c$ based on roughness drag. I hypothesize that the ratio $\lambda_{min}/\alpha^2$ can be roughly estimated from kinematic rupture models. Furthermore, I suggest that when the fault size is much larger than $L_c$, then most space-time characteristics of slip differ between a rough fault and a corresponding planar fault.



Earth Sciences, Engineering, Geophysics and Seismology, Mechanical Engineering, Physical Sciences and Mathematics, Tectonics and Structure, Tribology


earthquake, rate-and-state friction, Earthquake cycle simulations, Earthquake ruptures, Earthquake statistics, Pulses, Rough faults


Published: 2019-10-08 08:05

Last Updated: 2020-03-09 18:51

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CC BY Attribution 4.0 International

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