Realistic spatial and temporal earthquake distributions in a modified Olami-Feder-Christensen model

The Olami-Feder-Christensen model describes a limiting case of an elastic surface that slides on top of a substrate and is one of the simplest models that display some features observed in actual seismicity patterns. However, temporal and spatial correlations of real earthquakes are not correctly described by this model in its original form. I propose and study a modified version of the model, which includes a mechanism of structural relaxation. With this modification, realistic features of seismicity emerge, which are not obtained with the original version, mainly: aftershocks that cluster spatially around the slip surface of the main shock and follow the Omori law, and averaged frictional properties similar to those observed in rock friction, in particular the velocity-weakening effect. In addition, a Gutenberg-Richter law for the decaying of number of earthquakes with magnitude is obtained, with a decaying exponent within the range of experimentally observed values. Contrary to the original version of the model, a realistic value of the exponent appears without the necessity to fine tune any parameter.