Dynamical model of an earthquake fault with localization

We consider the one-dimensional dynamical Burridge-Knopoff stick-slip model for an earthquake fault with spatially inhomogeneous friction. The model is self-organizing under the externally imposed constraint of a spatial irregularity of strength which is designed to simulate residual damage to the system due to earlier earthquakes. The dissipation due to seismic wave radiation is adjusted so that the system is asymptotic to elasticity at all wavelengths. The model yields a self-organizing, spatially localized sequence of seismic events constrained by the spatial fluctuations. Repetitive, localized patterns of seismicity are erratically interrupted due to dynamical breaching of friction barriers. The model simulates an earthquake phenomenology that includes (1) the usual Gutenberg-Richter power-law energy-rate distribution at low energies with a rolloff at large energies, (2) spatial localization of large events on parts of a fault system and small events in the other parts of the system, (3) an ability to radiate seismic energy to distances far from the fault, and (4) a set of fractures whose lengths are never equal to the dimensions of the lattice or that intersect a free edge.