Numerical friction experiments of heterogeneous fault with controlling shear stress by means of earthquake sequence simulations: Preliminary results on the relation between cm-scale and km-scale friction laws
Abstract:The scale effect of the friction law is crucial in connecting field observations, laboratory experiments, and natural fault behaviors. Here we present our recent study towards understanding of the scale effect of the friction law.
The fault friction law is usually studied in laboratory experiments for cm-scale specimens, and one of the prominent problems is its direct applicability to the large-scale behavior. Small repeating earthquakes (repeaters) may be a realization of heterogeneous frictional property on faults, which were modeled by rate-weakening patches embedded in a rate-strengthening fault [e.g., Chen and Lapusta, 2009]. After the 2011 Tohoku-oki earthquake, so many repeaters were found in the Tohoku subduction zone [e.g., Kato and Igarashi, 2012]. But it is quite difficult to numerically resolve them in a large-scale simulation of the whole subduction zone, which is demanded for potential disaster mitigation. Then, it is important to investigate a spatiotemporally coarse-grained friction law of a fault region including unstable inclusions. We hypothesized that each point on a fault obeys the cm-scale friction law (the rate-state friction law in the aging law formulation) with sub-mm state evolution distance L, and assumed a rate-weakening circular patch (80 m diameter) which generates repeating events. We set 256 m periodicity along the fault, and conducted dynamic earthquake sequence simulations [e.g., Liu and Lapusta, 2009] by driving the system by far field stress τ0. We did not prescribe the long term slip rate by setting a region of constant slip rate as is done in previous studies. Those simulations can be seen as numerical friction experiments with controlling the shear stress and observing the slip rate.
The macroscopic steady-state can be explained by a logarithmic law, with the frictional resistance slightly smaller and the rate-dependency slightly more rate-strengthening than the spatial average. The transient behavior on a step in τ0 can be explained by the aging law with significantly longer L and smaller a- and b-values. The optimum parameters are different for different amount of the stress step, indicating that the macroscopic friction law takes a different form from the aging law. Effects of high velocity weakening efficient within the rate-weakening patch has been also investigated.