What criticality in cellular automata models of earthquakes?

Six different 2-D prototype cellular automata models are developed to analyse the main variants of the massless automata proposed so far to reproduce earthquake physics. The analysis aims at identifying the existence of features common to these models, if any. The different model variants were studied with regard to: (1) initial grid configuration, homogeneous or random heterogenous; (2) loading function, random or uniform; (3) local dissipation; (4) local redistribution. As a first general result, it is found that the model exhibit critically over a very restricted range of spatial scales, much smaller than that imposed by the geometrical dimensions of the grid alone. The latter, in contrast, governs the initial transient dynamics, which exhibits much larger events. As a second general result, the foreshocks are found to increase systematically in both rate of occurrence and size prior to main shocks, with a simultaneous progressive deficit of small events. This, in turn, implies an increase in correlation length and a 'precursor' decrease in the b-value. As a third general result, the presence of foreshocks in cellular automata and the difficulties in detecting them in real earthquakes still only give a limited applicability of the present cellular automata models to the real world. As a final general result, periodic recurrence of main shocks is found only for locally dissipative models.