Tsallis and Levy statistics in the preparation of an earthquake

Abstract

Abstract. Precursory fracture induced electromagnetic (EM) emissions, rooted in opening cracks and ranging from MHz to kHz, with the MHz appearing earlier, are produced and detected both at laboratory and geophysical scale. Recently, we have proposed the following two epochs/stages model of EQ generation: (i) The final kHz part is triggered by the fracture of high strength and large asperities that are distributed along the activated fault and sustain the system. (ii) The initial MHz part is thought to be due to the fracture of highly heterogeneous system that surrounds the family of asperities. Interestingly, the MHz EM time-series can be described in analogy with a thermal second order phase transition. Herein we focus on the MHz pre-seismic activity, and especially on the naturally arising question: what is the physical mechanism that organizes the heterogeneous system in its critical state? Combining ideas of Levy and Tsallis statistics and criticality with features hidden in the precursory MHz time-series we argue that a Levy walk type mechanism can organize the heterogeneous system to criticality. Based on a numerically produced truncated Levy walk, we propose a way to estimate in the stage of critical fluctuations: (i) the associated Levy index-a, which describes quantitatively the underlying Levy dynamics, and (ii) the range of values where the nonextesitive Tsallis index q is restricted. We also show that the kHz EM activity could not be described by a truncated Levy mechanism. This result further indicates an abrupt sweep of the population of asperities that sustain the system.

Unfolding the procedure of characterizing recorded ultra low frequency, kHZ and MHz electromagnetic anomalies prior to the L'Aquila earthquake as pre-seismic ones - Part 2

“…The Chinese (Qian et al, 1994) and Greek (Eftaxias, et Contoyiannis et al, 2005;Contoyiannis and Eftaxias, 2008) experience can be summarized in the following points: the frequency band of the detected EM anomalies is quite wide; anomalies are detected earlier in the electric field than in the magnetic field.…”

“…Clear MHz-kHz EM anomalies have been detected over periods ranging from a few days to a few hours before shallows land-based (or near coastline) EQs with magnitude 6 or larger since the installation of the station. Recent results indicate that the observed precursors contain characteristic pre-fracture features (Eftaxias et al, 2002(Eftaxias et al, , 2004(Eftaxias et al, , 2007bKapiris et al, 2004a, b;Contoyiannis et al, 2005Contoyiannis et al, , 2008Karamanos et al, 2006;Kalimeri et al, 2008;Papadimitriou et al, 2008).…”

“…Especially, such a fracture process is characterized by anti-persistency, and can be described in analogy with a thermal continuous second order phase transition. These two crucial footprints should be mirrored on the associated MHz EM precursor (Kapiris et al, 2004a, Contoyiannis et al, 2005Contoyiannis and Eftaxias, 2008).…”

Nonextensive Dynamics of Drifting Sea Ice

“…Apparently, the occurrence of natural hazards depends on the actual state of the given system. It appears that it is for this reason �rst attempts to estimate in numerical parameters the role of nonequilibrium state were made in seismology [5,6,16].…”

Recent seismic activity at Cephalonia (Greece): a study through candidate electromagnetic precursors in terms of non-linear dynamics

“…Contoyiannis et al, 2004aContoyiannis et al, , 2005Contoyiannis et al, , 2010Contoyiannis and Eftaxias, 2008;Potirakis et al, 2015). More details on the application of MCF can be found in several published articles (e.g.…”