Earthquake size-frequency statistics in a forest-fire model of individual faults

The earthquake size-frequency distribution of individual seismic faults commonly differs from the Gutenberg-Richter law of regional seismicity by the presence of an excess of large earthquakes. Here we present a cellular automaton of the forest-fire model type that is able to reproduce several size-frequency distributions depending on the number and location of asperities on the fault plane. The model describes a fault plane as a two-dimensional array of cells where each cell can be either a normal site or a trigger site. Earthquakes start on trigger sites. Asperities appear as the dual entities of the trigger sites. We study the effect that the number and distribution of asperities (the dual of the set of trigger sites), the earthquake rate, and the aspect ratio of the fault have on the size-frequency distribution. Size-frequency distributions have been grouped into subcritical, critical, and supercritical, and the relationship between the model parameters and these three kinds of distributions is presented in the form of phase maps for each of the five asperity types tested. We also study the connection between the model parameters and the aperiodicity of the large earthquakes. For this purpose the concept of aperiodicity spectrum is introduced. The aperiodicity in the recurrence of the large earthquakes in a fault shows an interesting variability that can be potentially useful for prediction purposes.