Following Hergarten and Neugebauer [Phys. Rev. Lett. 88, 238501, 2002] who discovered aftershocks and foreshocks in the Olami-Feder-Christensen (OFC) discrete block-spring earthquake model, we investigate to what degree the simple toppling mechanism of this model is sufficient to account for the clustering of real seismicity in time and space. We find that synthetic catalogs generated by the OFC model share many properties of real seismicity at a qualitative level; Omori's law (aftershocks) and inverse Omori's law (foreshocks), increase of the number of aftershocks and of the aftershock zone size with the mainshock magnitude. There are, however, significant quantitative differences. The number of aftershocks per mainshock in the OFC model is smaller than in real seismicity, especially for large mainshocks. We find that foreshocks in the OFC catalogs can be in large part described by a simple model of triggered seismicity, such as the epidemic-type aftershock sequence (ETAS) model. But the, properties of foreshocks in the OFC model depend on the mainshock magnitude, in qualitative agreement with the critical earthquake model and in disagreement with real seismicity and with the ETAS model.
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