Seismic cycles and the evolution of stress correlation in cellular automaton models of finite fault networks

A cellular automaton is used to study the relation between the structure of a regional fault network and the temporal and spatial patterns of regional seismicity. Automata in which the cell sizes form discrete fractal hierarc hies are compared with those having a uniform cell size. Conservative model s in which all the stress is transferred at each step of a cascade are comp ared with nonconservative ("lossy") models in which a specified fraction of the stress energy is lost from each step. Particular attention is given to the behavior of the system as it is driven toward the critical state by un iform external loading. All automata exhibit a scaling region at times clos e to the critical stale in which the events become larger and energy releas e increases as a power-law of the time to the critical state. For the hiera rchical fractal automata, this power-law behavior is often modulated by flu ctuations that are periodic in the logarithm of the time to criticality. Th ese fluctuations are enhanced in the nonconservative models, but are not ro bust. The degree to which they develop appears to depend on the particular distribution of stresses in the larger cells which varies from cycle to cyc le. Once the critical state is reached, seismicity in the uniform conservat ive automaton remains random in time, space, and magnitude. Large events do nor significantly perturb the stress distribution in the system. However, large events in the nonconservative uniform automaton and in the fractal sy stems produce large stress perturbations that move the system our of the cr itical state. The result is a seismic cycle in which a large event is follo wed by a shadow period of quiescence and then a new approach back toward th e critical state. This seismic cycle does not depend on the fractal structu re, but is a direct consequence of large-scale heterogeneity of these syste ms in which the size of the largest cell (or the size of the largest noncon servative event) is a significant fraction of the size of the network. In e ssence, seismic cycles in these models are boundary effects. The largest ev ents tend to cluster in time and the rate of small events remains relativel y constant throughout a cycle in agreement with observed seismicity.