Linking the Recurrence Time of Earthquakes to Source Parameters: A Dream or a Real Possibility?

By using a single-degree-of-freedom spring-slider analog fault model, we generate a synthetic catalog of nearly 500 different seismic sequences. We explore the parameter space by assuming different values of constitutive parameters and tectonic environment. We also consider three different versions of the rate-dependent and state-dependent friction laws the Dieterich-Ruina (DR), the Ruina-Dieterich (RD) and the Chester-Higgs (CH) models], and different approximations of the behavior of the friction at high sliding speeds, as well as the radiation damping effects. Our results indicate that for all the considered models, the recurrence time (T _cycle) exhibits an inverse proportionality on the loading rate; a linear, positive dependence on the effective normal stress; and a linear, negative dependence on the characteristic distance controlling the state variable evolution. These results confirm and generalize previous studies. Remarkably, we found here that the coefficients of proportionality strongly depend on the adopted friction model, on the high speed behavior and on the reference set of parameters. Notably, we also found that the positive proportionality between T _cycle and the difference b – a, confirmed for DR and RD laws, does not hold in general for the CH law. Overall, we conclude that even in the simplest (and idealized) case of characteristic earthquakes considered here, in which the limiting cycle is reached by the system, and even in the framework of a very simplified fault model, the possibility to a priori predict, through an universal analytical relation, the inter-event time of an impending earthquake still remains only a dream. On the other hand, a numerical prediction of T _cycle would require the exact knowledge of the rheological model (and its parameters at all times over the entire life of the fault) and the actual state of the fault, which indeed are often unknown.