Universality in solar flares, magnetic storms, earthquakes and pre-seismic electromagnetic emissions by means of nonextensivity

The field of study of complex systems holds that the dynamics of complex systems are founded on universal principles that may used to describe disparate problems ranging from particle physics to economies of societies. A corollary is that transferring ideas and results from investigators in hitherto disparate areas will cross-fertilize and lead to important new results. In this contribution we investigate a universal behavior, if any, in solar flares, magnetic storms, earthquakes and pre-seismic electromagnetic (EM) emissions. A common characteristic in the dynamics of the above-mentioned four phenomena is that the energy release is basically fragmentary, the events being composed of elementary building blocks. By analogy with earthquakes, magnitude of the magnetic storms, solar flares and pre-seismic electromagnetic emissions can be appropriately defined. The key-question we can ask in the frame of complexity is whether the magnitude distribution of earthquakes, magnetic storms, solar flares and pre-fracture EM emissions obeys to the same law. A central property of the magnetic storm, solar flare, and earthquake preparation process is the possible occurrence of coherent large-scale collective with a very rich structure resulting from the repeated nonlinear interactions among its constituents. Consequently, the non-extensive statistical mechanics is an appropriate arena to investigate universality, if any, in magnetic storm, solar flare, earthquake and pre-failure electromagnetic emission occurrence. A model for earthquake dynamics consisting of two rough profiles interacting via fragments filling the gap has been recently introduced by Solotongo-Costa and Posadas [2004]. An energy distribution function, which gives the Gutenberg-Richter law as a particular case, is analytically deduced. Therefore, the primary question we can ask in the frame of complexity is whether the aforementioned equation not only successfully describes the magnitude distribution of earthquakes in various seismic regions but magnetic storms, solar flares and pre-seismic EM emissions rooted in activation of a single fault, as well. A subsequent question is whether this equation successfully describes the magnitude distribution in all the cases under study with similar nonextensive entropic parameter q. We show that both two key-questions accept positive answer. It is worth mentioning that the estimated for the q-nonextensive parameters is in full agreement with the upper limit q < 2 obtained from several independent studies involving the Tsallis nonextensive framework.