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 selforganized criticality. With the aim to address the dependency of the seismicity style on sources material properties we present an analytical enrichment of a 2D OFC model. We concluded with an analytical expression which introduces, through an appropriate constitutive equation, an effective dissipation parameter a 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 build-up whereas simulation results have verified models predictions for the evolution of b in macroscopic records. 
Markos Avlonitis and Gerasimos Papadopoulos
physics.geo-ph