Statistical analysis of a model for earthquake faults with long-range stress transfer

We present both theoretical and numerical analysis of a cellular automaton version of a slider-block model for earthquake faults that includes long-range stress transfer. Theoretically we develop a coarse-grained description in the mean-field (infinite range) limit and discuss the relevance of the meta-stable state, limit of stability (spinodal) and nucleation to the phenomenology of the model. We also simulate the model and confirm the relevance of the theory for systems with long, but finite range, interactions. Results of particular interest include the existence of Gutenberg-Richter like scaling consistent with that found on real earthquake fault systems, the association of large events with nucleation near the spinodal, the existence of more than one scaling regime, and the result that such systems can be described, in the mean-field limit, with techniques appropriate to systems in equilibrium.