A Moore's cellular automaton model to get probabilistic seismic hazard maps for different magnitude releases: A case study for Greece

Cellular automata are simple mathematical idealizations of natural systems and they supply useful models for many investigations in natural science. Examples include sandpile models, forest fire models, and slider block models used in seismology. In the present paper, they have been used for establishing temporal relations between the energy releases of the seismic events that occurred in neighboring parts of the crust. The catalogue is divided into time intervals, and the region is divided into cells which are declared active or inactive by means of a threshold energy release criterion. Thus, a pattern of active and inactive cells which evolves over time is determined. A stochastic cellular automaton is constructed starting with these patterns, in order to simulate their spatio-temporal evolution, by supposing a Moore's neighborhood interaction between the cells. The best model is chosen by maximizing the mutual information between the past and the future states. Finally, a Probabilistic Seismic Hazard Map is given for the different energy releases considered. The method has been applied to the Greece catalogue from 1900 to 1999. The Probabilistic Seismic Hazard Maps for energies corresponding to m = 4 and m = 5 are close to the real seismicity after the data in that area, and they correspond to a background seismicity in the whole area. This background seismicity seems to cover the whole area in periods of around 25-50 years. The optimum cell size is in agreement with other studies; for m > 6 the optimum area increases according to the threshold of clear spatial resolution, and the active cells are not so clustered. The results are coherent with other hazard studies in the zone and with the seismicity recorded after the data set, as well as provide an interaction model which points out the large scale nature of the earthquake occurrence.