Simulation study of earthquakes based on the two-dimensional Burridge-Knopoff model with long-range interactions

Spatiotemporal correlations of the two-dimensional (2D) spring-block (Burridge-Knopoff) models of earthquakes with the long-range interblock interactions are extensively studied by means of numerical computer simulations. The long-range interaction derived from an elastic theory, which takes account of the effect of the elastic body adjacent to the fault plane, falls off with distance r as 1/r³ . Comparison is made with the properties of the corresponding short-range models studied earlier. Seismic spatiotemporal correlations of the long-range models generally tend to be weaker than those of the short-range models. The magnitude distribution exhibits a “near-critical” behavior, i.e., a power-law-like behavior close to the Gutenberg-Richter law, for a wide parameter range with its B -value, B≃0.55 , insensitive to the model parameters, in sharp contrast to that of the 2D short-range model and those of the 1D short-range and long-range models where such a near-critical behavior is realized only by fine tuning the model parameters. In contrast to the short-range case, the mean stress drop at a seismic event of the long-range model is nearly independent of its magnitude, consistent with the observation. Large events often accompany foreshocks together with a doughnutlike quiescence as their precursors, while they hardly accompany aftershocks with almost negligible seismic correlations observed after the main shock.