Computer simulations of statistical models of earthquakes

The frequency-size distribution of earthquake fault systems in nature has been observed to exhibit Gutenberg-Richter (power-law) scaling. Computer simulations of earthquake fault models have been performed to understand the mechanisms for this and other observed behavior. Understanding driven dissipative systems is also important in physics and related areas.; A simple model that contains the essential physics of earthquake faults is the Burridge-Knopoff spring-block model, which incorporates inertia and a velocity-weakening friction force. To save computer time, the Burridge-Knopoff model has been simplified by neglecting inertia and assuming a moving block is overdamped. These cellular automata models show scaling behavior, but only for long-range stress transfer.; I generalized the original nearest-neighbor Burridge-Knopoff model to incorporate a variable interaction range and did simulations to see whether the long-range Burridge-Knopoff model exhibits behavior similar to the long-range cellular automata models. I found that the Burridge-Knopoff model exhibits richer behavior than the cellular automata models, depending on the range R of the stress transfer and the friction parameter alpha, which controls how quickly the friction force deceases with increasing velocity.; My main result is that there exists two scaling regimes with qualitatively different behavior. One regime is for alpha ≲ 1 and R ≫ 1 and is associated with an equilibrium spinodal critical point, consistent with the long-range cellular automata models. The other regime corresponds to alpha ≳ 1 and R = 1 and might be associated with another critical point. This latter interpretation has been given by previous workers, but the nature of the critical point needs more study.; I also simulated the long-range Olami-Feder-Christensen cellular automata model. In the mean-field limit, the scaling of the distribution of the number of block in an event can be understood by spinodal nucleation theory. Scaling events correspond to fluctuations, failed nucleation events, and arrested nucleation events near the metastable free energy minimum related to the spinodal. Breakout events close to the system size do not scale and drive the system out of equilibrium from which the system decays back to equilibrium.; I found that all events begin with a low density object with the dominant growth at the surface. At late times there is much filling-in for the arrested nucleation and breakout events. I also found a possible way to predict breakout events by studying the difference between the average of the stress profile and the background stress.