Transition matrix analysis of earthquake magnitude sequences

Estimation of complexity is a fascinating research topic in nonlinear signal and system analysis. Information theoretic functionals can be used to identify and quantify general relationships among variables; these relationships can be considered as the fingerprints of complexity. Up to now, the complexity of seismic sequences has been mostly related to the concept of self-similarity, suggesting that the earthquake dynamics can be interpreted as due to many components interacting over a wide range of time or space scales. This paper deals with a new idea of complexity of seismicity, focusing, in particular, on the transition probability between magnitudes. Using the Transition Matrix Method, a set of complexity parameters can be defined for earthquakes. Furthermore, the relationships among these parameters and those characterizing the earthquake magnitude dynamics have been analyzed in simulated and observational seismic sequences.