Evidence of non-extensive statistical physics of the lithospheric instability approaching the 2004 Sumatran-Andaman and 2011 Honshu mega-earthquakes

In the present study, we demonstrate in the frame of non-extensive statistical physics, significant deviations of the global seismic activity from a quasi-stationary regime before Sumatra-Andaman and Honshu mega-earthquakes suggesting the existence of a global scale intermediate-term non-extensive tectonic premonitory of impending mega-earthquake processes in the lithosphere. Using non-extensive statistical mechanics we describe the frequency-moment, the inter-event time and distance distributions, interpreting Sumatran's (2004) and Honshu (2011) earthquakes influence on these. At a phenomenological level, we find that global seismicity is described by non-extensive statistical mechanics (NESM) and that the seismic moment and the earthquake inter-event time distributions reflect a sub-extensive system, where long-range interactions are important. Using the cross-over formulation of NESM leads us to the conclusion that the seismic moment distribution of moderate events yields thermodynamic q-values of q(M) = 1.6 which seem to be constant for the duration of the Sumatra and Honshu earthquake preparation, while r(M) (which describes the seismic moment distribution of great events) varies from 1 to 1.5 as we approach the mega events, The inter-event time and inter-event distance distributions, with q(tau) = 1.5, and q(D) = 0.3, respectively support the conclusion of non-extensive "spatio-temporal duality", suggesting that global shallow moderate seismicity (with 5.5<Mw<M-c = 7.5) is described in a unique way by the q-value triplet (q(M),q(tau),q(D)) = (1.6, 1.5, 0.3), independently from the influence of seismic mega events, while the preparatory process is described by the variation of r(M), which has a value r(M) = 1, consistent with an exponential roll-off years before the Sumatra event. A deviation occurred after 1993 or later when the frequency-moment distribution of the global seismic activity at shallow depths appears as a general straightening, suggesting a deviation of r-parameter from r = 1 to a value r approximate to 1.4-1.5 evidently due to the apparent rise of the rate of strong earthquakes. (c) 2013 Elsevier B.V. All rights reserved.