Criticality in earthquakes. Good or bad for prediction?

Through the analysis of the correlation functions in simulations of an earthquake model, the critical properties of the system are studied. Simulations are performed in a more realistic modification of the Olami–Feder–Christensen model of earthquakes and result in uncorrelated avalanches distributed following a power-law with weak signs of foreshocks and aftershocks. The spatial autocorrelation function of the system and other structural variables are computed in every step of the simulation. The spatial autocorrelation between points separated from each other by a constant distance equal to 1/4 and 1/8 of the linear size of the system shows large variations, temporally correlated with the time series of avalanche size; i.e., spatial correlation values are in average very high before a large earthquake, very small after a large earthquake and they evolve between these two states. However, the temporal average of the spatial autocorrelation over the whole simulation shows values close to zero, result that is in contradiction with the idea that the correlation length is of the same order as the linear size of the system (diverging in an infinite system), which is the main signature of a critical scenario. By averaging the autocorrelation in smaller time windows, the critical properties of temporal states can be used as an indication of upcoming catastrophic events. The structural variables are also correlated with the occurrence of large avalanches, suggesting the possibility of monitoring these variables in order to achieve prediction.