Statistical Features of Earthquake Temporal Occurrence

The physics of an earthquake is a subject with many unknowns. It is true that we have a good understanding of the propagation of seismic waves through the Earth and that given a large set of seismographic records we are able to reconstruct a posteriori the history of the fault rupture (the origin of the waves). However, when we consider the physical processes which lead to the initiation of a rupture with a subsequent slip and its growth through a fault system to give rise to an earthquake, then our knowledge is really limited. Not only the friction law and the rupture evolution rules are largely unknown, but the role of many other processes such as plasticity, fluid migration, chemical reactions, etc., and the couplings between them, remain unclear [1, 2]. On the other hand, one may wonder about the physics of many earthquakes. How do the collective properties of the set defined by all earthquakes in a given region, or better, in the whole world, emerge from the physics of individual earthquakes? How does seismicity, which is the structure formed by all earthquakes, depend on its elementary constituents –the earthquakes? And which are these properties? Which kind of dynamical process does seismicity constitute? It may be that these collective properties are largely independent on the physics of the individual earthquakes, in the same way that many of the properties of a gas or a solid do not depend on the constitution of its elementary units –the atoms (for a broad range of temperatures it doesn't matter if we have atoms, with its complicated quantum structure, or microscopic marbles). It is natural then to consider that the physics of many earthquakes has to be studied with a different approach than the physics of one earthquake, and in this sense we can consider the use of statistical physics not only appropriate but necessary to understand the collective properties of earthquakes. Here, we provide a summary of recent work on the statistics of the temporal properties of seismicity, considering the phenomenon as a whole and with the goal of looking for general laws. We show the fulfillment of a scaling law for recurrence-time distributions, which becomes universal for stationary seismicity and for aftershock sequences which are transformed into stationary