Burridge-Knopoff model and self-similarity

The seismic processes are well known to be self-similar in both spatial and temporal behavior. At the same time, the Burridge-Knopoff (BK) model of earthquake fault dynamics, one of the basic models of theoretical seismicity, does not posses self-similarity. In this article an extension of BK model, which directly accounts for the self-similarity of earth crust elastic properties by introducing nonlinear terms for inter-block springs of BK model, is presented. The phase space analysis of the model have shown it to behave like a system of coupled randomly kicked oscillators. The nonlinear stiffness terms cause the synchronization of collective motion and produce stronger seismic events.