Scale-free distributions of waiting times for earthquakes

We investigate through detailed statistical analyses the dynamics of earthquakes with epicenters in Romania, Japan, California (USA), and Italy, and show that the distribution of waiting times, defined here akin to econophysics, as to implicitly include information about the magnitude of earthquakes, is very similar to the scale-free distributions observed in hydrodynamic turbulence and stock market dynamics. Our results show that the shape of the observed distributions depends on the size of the magnitude threshold δ, with a cut-off at small waiting times, and is sensitive with respect to the sign of the aforementioned threshold. In the case of earthquakes originating in Romania we also show that the distributions of waiting times for depths have the same power-law behaviour. Moreover, we show that the distributions of released daily energies calculated for Romania and California (USA) have a prominent scale-free nature, which reinforce the idea that seismic zones can be seen as critical systems.