Lévy and Gauss statistics in the preparation of an earthquake

In course of the preparation of a strong earthquake (EQ), the fracture of the highly heterogeneous system surrounding the fault has been suggested to follow the theory of critical phenomena and continuous phase transitions. Among the variety of electromagnetic phenomena which have been reported to be observed prior to a strong EQ, the ground-observed fracture-induced electromagnetic emissions (EME) in the MHz band have repeatedly been reported to present intermittency-induced criticality, while it has been suggested that reflect the specific stage of EQ preparation. Moreover, based on the analysis of pre-EQ MHz EME time series, it has been suggested that the underlying cracking procedure is organized to criticality by means of the Lévy flight mechanism. In an attempt to gain a deeper understanding to the involved EQ preparation processes and the organization to critical state, we study here the pre-EQ MHz EME presenting critical characteristics in terms of the mechanism of Lévy flight and its possible engagement with Gaussian stochastic processes. We suggest that if the analysis of the MHz EME time series according to the method of critical fluctuations indicates critical characteristics with a power law exponent, p2, value in the range 1.5,2, then a strong EQ should not be expected to follow. This is because such a result indicates a slow transition from the Lévy to the Gaussian process, cutting-off the long scales due to the Gaussian mechanism. This prevents the organization of the critical state to be completed according to the Lévy flight scenario and the spreading of the correlations all over the focal area. The above hypothesis is corroborated by a number of MHz EME time series analyses.