Burridge–Knopoff model and self-similarity

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 possess self-similarity. We present an extension of the BK model, based on the introduction of nonlinear terms for the inter-block springs of the BK model, which results in the self-similarity of earth crust elastic properties being accounted for directly. Phase space analysis of the model reveals the behavior of a system of randomly kicked coupled oscillators. The nonlinear stiffness terms cause synchronization of the collective motion and produce stronger seismic events.