Nonextensive Statistical Mechanics

7.1 Physics 247Fig. 7.32 Dependence of the correlation function on the natural time ninsidethe Omori regimefollowing a specific event taken from the California catalag. Aging is visible. For further detailssee [541].Fig. 7.33 Dependence of the correlation function on the natural time n outside the Omori regimefollowing a specific event taken from the California catalag. No aging is visible. For further detailssee [541].regime. Whenever aging is observed, data collapse can be obtained (see Fig. 7.34)through rescaling, more specifically by using as abscissa n/f (n W ) instead of n,where f (n W ) = an γ W+ 1, a and γ being fitting parameters. The connection withq-statistics comes from the fact that the type of dependence that we observe inFig. 7.34 appears to be of the q-exponential form. Let us address this point now. Thiscorrelation function has been calculated [380] for a simple mean-field model calledthe coherent noise model (Newman model): the results can be seen in Figs. 7.35,7.36, and 7.37. Another model for earthquakes has been discussed as well [381], theOlami–Feder–Christensen models. The results for the Newman and the OFC models−0.7 n/n1.05W−0.6 n/n1.05Ware respectively C(n + n W , n W ) = e2.98 and C(n + n W , n W ) = e2.9 :seeFig. 7.38. Summarizing, both earthquake models that have been considered yieldvirtually the same result, namely that the rescaled correlation function is of theq-exponential form with q ≃ 2.98.