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 relaxation time to the tectonic reloading time. In correspondence with the original spring-block model, the modified model displays a robust power law distribution 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 are 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 contrast to other events, the distribution of foreshock sizes is characterized by a significantly smaller Richter B value. Our model reproduces simultaneously the empirically observed values of the power law exponents, the Richter B, p and q, and their variability.