Magnitude correlations in the Olami-Feder-Christensen model

An important issue for earthquake prediction is the dependence of the earthquake magnitude from past seismicity. Recently, clustering in magnitude has been evidenced: earth- quakes occur with higher probability close in time, space, and magnitude to previous events. An open question is if this magnitude correlations can be found in simple models for earthquakes. Here we show that the Olami-Feder-Christensen model generates synthetic catalogs which exhibit cor- relations between occurrence times and magnitudes of subsequent events similar to those observed in experimental catalogs. These correlations are observed only in the range of parameters where the magnitude distribution of synthetic catalogs agrees with the experimental one. The similarity of the functional form of magnitude correlations with experimental data and their dependence on temporal distances confirm that correlations found in real catalogs cannot be attributed to spurious effects related to magnitude incompleteness.