Omori law for foreshocks and aftershocks in a realistic earthquake model

Abstract

We study a physical model for earthquakes which extends the standard spring-block model. It is able to quantitatively describe the observations which detect differences between the statistics of foreshocks and aftershocks and the properties of main shocks. The model uses two layers to provide an intrinsic mechanism for stress relaxation and a stochastic equation to describe the contacts of crustal plates which should be treated at the scale of the elastic correlation length of the rocks and therefore result from the combined dynamics of many local contacts. The model parameters are derived from the physical properties of rocks to provide a realistic picture of the mechanisms involved in earthquakes. We show that the Omori law has different exponents for foreshocks and aftershocks, in agreement with observations. Similarly the model detects the differences in the b coefficient of the Gutenberg-Richter law for main shocks, foreshocks and aftershocks. Moreover, the dynamics of the model exhibits various classes of events such as swarm of small earthquakes and major earthquakes extending over a broader fault range, suggesting that it might be the basis for further studies of the phenomena at the contact of crustal plates.