Similar power laws for foreshock and aftershock sequences in a spring-block model for earthquakes

We introduce a crust relaxation process in a continuous cellular automaton version of the Burridge and Knopoff [1967] model. The most important model parameters are the level of conservation and the ratio of the crust relaxat ion time to the tectonic reloading time. In correspondence with the origina l spring-block model, the modified model displays a robust power law distri bution of event sizes. The principal new result obtained with our model is the spatiotemporal clustering of events exhibiting several characteristics of earthquakes in nature. Large events are followed by aftershock sequences obeying the Omori [1894] law and preceded by localized foreshocks, which a re initiated after a time period of seismic quiescence. While we observe a considerable variability of precursory seismicity, we find that the rate of foreshocks increases on average, according to a power law with an exponent q, which is in good agreement with the exponent p of the Omori law. In con trast to other events, the distribution of foreshock sizes is characterized by a significantly smaller Richter B value. Our model reproduces simultane ously the empirically observed values of the power law exponents, the Richt er B, p and q, and their variability.