Foreshocks and b Value: Bridging Macroscopic Observations to Source Mechanical Considerations

Spring-block models, such as the Olami-Feder-Christensen (OFC) model, were introduced several years ago to describe earthquake dynamics in the context of self-organized criticality. With the aim to address the dependency of the seismicity style on source’s material properties, we present an analytical enrichment of a 2D OFC model. We conclude with an analytical expression which introduces, through an appropriate constitutive equation, an effective dissipation parameter a eff related analytically not only with the elastic properties of the fault plane, but also with stochastic structural heterogeneities and structural processes of the source through a gradient coefficient. Moreover, within the proposed formulation, the low b values experimentally observed in foreshock sequences can be modeled by a process of material softening in the seismogenic volume. To check our analytical findings, a cellular automaton was built-up whereas simulation results have verified the model’s predictions for the evolution of b in macroscopic records.