Dependence of earthquake recurrence times and independence of magnitudes on seismicity history

The fulfillment of a scaling law for earthquake recurrence–time distributions is a clear indication of the importance of correlations in the structure of seismicity. In order to characterize these correlations we measure conditional recurrence–time and magnitude distributions for worldwide seismicity as well as for Southern California during stationary periods. Disregarding the spatial structure, we conclude that the relevant correlations in seismicity are those of the recurrence time with previous recurrence times and magnitudes; in the latter case, the conditional distribution verifies a scaling relation depending on the difference between the magnitudes of the two events defining the recurrence time. In contrast, with our present resolution, magnitude seems to be independent on the history contained in the seismic catalogs (except perhaps for Southern California for very short time scales, less than about 30 min for the magnitude ranges analyzed).