Describing Seismic Pattern Dynamics by Means of Ising Cellular Automata

This chapter is dedicated to the description and testing of a new method of obtaining Probabilistic Activation Maps of seismic activity. This method is based upon two major concepts: Cellular Automata (CA) and Information Theory. The proposed method can be used in other fields, as long as the spatially extended system is described in terms of a Cellular Automata with two available states, +1 and −1, as in the Ising case described here. The crucial point is to obtain the rules of an Ising Cellular Automata that maps one pattern into its future state by means of an entropic principle. We have already applied this technique to the seismicity in two regions: Greece and the Iberian Peninsula. In this chapter, we study other regions to test if the observed behavior holds in general. For this purpose, we will discuss the results for California, Turkey and Western Canada. The Cellular Automaton rules obtained from the correponding catalogs are found to be well described by an Ising scheme. When these rules are applied to the most recent pattern, we obtain a Probabilistic Activation Map, where the probability of surpassing a certain energy (equivalent to a certain magnitude) in the next interval of time is represented, which is a useful information for seismic hazard assessment.