On-off intermittency in mean-field earthquake model

Earthquake occurrence is characterized by clustering of events leading to a complex time organization. A recent model, that introduces a memory effect within a Self-Organized Criticality (SOC) approach, was able to reproduce the statistical features in time and energy of seismic catalogs. We present a mean-field solution of this model which provides a quadratic equation similar to the logistic map for the event probability. By introducing a triggering threshold, we generate a sequence of events with a statistical organization depending on the control parameter a. If a is generated by the SOC with memory model, one finds oil-off intermittency features, in good agreement with experimental analysis of the California catalog. Conversely, if a is randomly chosen, the typical Poisson-like behaviour is observed. This result supports the idea that the on-off intermittent behaviour, experimentally observed, is related to a mechanism of event triggering driven by the history of seismic events.