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 qM = 1.6 which seem to be constant for the duration of the Sumatra and Honshu earthquake preparation, while rM (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 qτ = 1.5, and qD = 0.3, respectively support the conclusion of non-extensive “spatio-temporal duality”, suggesting that global shallow moderate seismicity (with 5.5 < Mw < Mc = 7.5) is described in a unique way by the q-value triplet (qM,qτ,qD) = (1.6, 1.5, 0.3), independently from the influence of seismic mega events, while the preparatory process is described by the variation of rM, which has a value rM = 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 ≈ 1.4–1.5 evidently due to the apparent rise of the rate of strong earthquakes.

► Application of non-extensive statistical physics (NESP) to global seismicity.
► Global seismic moment and inter-event time distributions reflect a sub-extensivity.
► The inter-event time, and distance distributions of global seismicity support non-extensive spatio-temporal duality.