Mean-field studies of a slider-block model with noise

We have studied a simple model of earthquake faults based on the cellular automaton version of the slider-block model. The model is represented by the two-dimensional array of massless blocks connected by springs to its neighbors and the loader plate. Stress is introduced to the system by moving the loader plate with infinitesimally low velocity and stress is dissipated by the toppling sites. The residual value of the toppled site is a random variable with prescribed noise amplitude. The model described is one of the variants of the Rundle-Jackson-Brown (RJB) model. We conduct systematic studies of noise dependence of our model in mean and near mean-field. In mean-field every site interacts with all other sites of the grid, that is the system has infinite range of interaction, while in the near mean-field case the range of interaction is large but final. Theoretical and numerical results presented here show that the distribution of avalanches in this model exhibits strong deviations from the expected simple power law distribution. The value of the noise parameter effectively restricts the evolution of the system in the phase-space, controlling the transition from exact periodic to totally chaotic behavior. Exact, scaling and numerical results are shown and possible relations to real earthquakes are discussed.