Local distributions and rate fluctuations in a unified scaling law for earthquakes

A recently proposed unified scaling law for interoccurrence times of earthquakes is analyzed, both theoretically and with data from Southern California. We decompose the corresponding probability density into local-instantaneous distributions, which scale with the rate of earthquake occurrence. The fluctuations of the rate, characterizing the nonstationarity of the process, show a double power-law distribution and are fundamental to determine the overall behavior, described by a double power law as well.