Long-term memory in earthquakes and the distribution of interoccurrence times

We study seismic records in regimes of stationary seismic activity in Northern and Southern California. Our analysis suggests that the earthquakes are long-term power law correlated with a correlation exponent γ close to 0.4. We show explicitly that the long-term correlations can explain both the fluctuations of magnitudes and interoccurrence times (between events above a certain magnitude M) and, without any fit parameter, the scaling form of the distribution function of the interoccurrence times in the seismic records, recently obtained by Corral (Phys. Rev. Lett., 92 (2004) 108501).