Persistence and Quiescence of Seismicity on Fault Systems

We study the statistics of simulated earthquakes in a quasistatic model of two parallel heterogeneous faults within a slowly driven elastic tectonic plate. The probability that one fault remains dormant while the other is active for a time $\Delta t$ following the previous activity shift is proportional to $\Delta t^{-(1+x)}$, a result that is robust in the presence of annealed noise and strength weakening. A mean field theory accounts for the observed dependence of the persistence exponent $x$ as a function of heterogeneity and distance between faults. These results continue to hold if the number of competing faults is increased.