A CELLULAR-AUTOMATA, SLIDER-BLOCK MODEL FOR EARTHQUAKES .2. DEMONSTRATION OF SELF-ORGANIZED CRITICALITY FOR A 2-D SYSTEM

It has been suggested that distributed seismicity is an example of self-organized criticality. If this is the case, the Earth's crust in an active tectonic zone is in a near-critical state and faults can interact over large distances. Observed seismicity and earthquake statistics are consequences of the dynamical interaction of seismic faulting over a wide range of scales. We address this problem by considering a two-dimensional array of slider blocks with static/dynamic friction. The two-dimensional system is treated as a cellular automaton such that only one slider block is allowed to slip at a given time and interacts only with its nearest neighbours through connecting springs. Because of this treatment, the amount of slip for each failed block can be obtained analytically, and the system is deterministic with no stochastic inputs or spatial heterogeneities. In many cases, the slip of one block induces the slip of adjacent blocks. The size of an event is specified by the number of blocks that participate in the event. The number of small events with a specified size has a power-law dependence on the size with a power close to -1.36. The distributions of normalized recurrence times for most events are close to a Poisson process, and gradually deviate towards periodicity for large events. The recurrence time statistics are generally insensitive to parameter variations. Large events may occur at stress levels considerably lower than the failure strength of an individual block, and the stress drops associated with large events are generally small. This may provide an explanation for observed low stress levels in tectonically active areas.