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Recurrence Time Distributions of Large Earthquakes in a Stochastic Model for Coupled Fault Systems: The Role of Fault Interaction

¹ Institute of Physics and Institute of Mathematics
University of Potsdam
Am Neuen Palais 10, 14469 Potsdam, Germany
gert.zoeller{at}uni-potsdam.de
 (G.Z.)
² GeoForschungsZentrum Potsdam
Telegrafenberg, 14773 Potsdam, Germany
hainzl{at}gfz-potsdam.de
 (S.H.)

We study the effect of fault interaction on the recurrence time distribution of large earthquakes on the same fault. A single isolated fault is modeled by a Brownian relaxation oscillator leading to a Brownian passage-time distribution for the recurrence intervals. Interaction between different faults is imposed in terms of stress increase and decrease resulting in three possible ways: the occurrence of an earthquake is advanced or delayed, or the earthquake is triggered instantaneously. The results indicate the existence of two regimes: for weakly coupled faults, the recurrence time distribution of earthquakes on one fault follows mostly the Brownian passage-time distribution. For a strongly coupled system, the faults are synchronized and the effect of instantaneous triggering becomes dominant: the recurrence time distribution follows a Gamma or a Weibull distribution. The transition from weak to strong coupling is abrupt and behaves like a phase transition. It occurs when the stress transfer equals the average stress deficit. The results are interpreted in terms of a phase diagram. This diagram includes a regime, where the distribution of recurrence times is similar to a numerical model for California. We claim that the emergence of the Gamma and the Weibull distribution can be considered as an effect of fault interaction.