What can physical source models tell us about the recurrence time of earthquakes?

Earthquake prediction, no matter what the timescale, has been and continues to be a contentious subject and it is indubitably a prominent challenge for modern seismology and earthquake physics. Indeed, few natural events can have the catastrophic consequences of earthquakes (earthquakes today accounts for about 60 % of natural fatalities). A physical description of earthquake represents an amenable approach to the prediction, but it suffers of some limitations, basically due to the notorious ignorance about the initial state of a given fault and about the physical law controlling its traction evolution. Independently on those intrinsic, epistemic limitations, the concept of the earthquake recurrence, based upon the idea of the cyclic (or characteristic) earthquake, has been often invoked to describe (and thus to predict) subsequent instability events on a seismogenic structure. In this paper, by using the simplest analog fault model, the one–degree–of–freedom mass–spring system, we quantitatively show that the concepts of the recurrence time and the earthquake cycle have limitations (even not meaningless). We will discuss in a compendious synopsis all the possible physical mechanisms which can dramatically affect the recurrence time. Our conclusions emphasize again that the competing mechanisms potentially occurring during faulting, even in the simplest and idealized condition of an isolated fault, can significantly complicate the regular cyclicity of earthquakes predicted by the analog fault system. These conclusions can contribute to the debate about the role of the physical modelling of earthquakes in the contest of seismic hazard assessment.