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 ratedependent
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 (Tcycle) 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 Tcycle 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 Tcycle 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.