Abstract
The natural time analysis of all the measured SES activities showed that they are characterized by very strong memory and their normalized power spectra ?(ω) versus ω fall on a universal curve having ?1(= _χ2_ – _χ_2) value equal to 0.070. This curve coincides with the one obtained on theoretical grounds when assuming that SES are governed by critical dynamics. Upon shuffling the events (pulses) randomly, the memory is destroyed and the ?1 value becomes equal to that ?u(= 1/12 ≈ 0.083) of a “uniform” distribution. This shows that the self-similarity solely stems from long range temporal correlations. Concerning the distinction of SES activities from similar looking “artificial” (man-made) noises, we find the following. Modern techniques of Statistical Physics, e.g., detrended fluctuation analysis (DFA), multifractal DFA, wavelet transform, when applied to the original time series cannot achieve such a distinction, but when they are applied in natural time a clear distinction emerges. For example, for the SES activities the DFA exponent in natural time is close to unity, i.e., a ≈ 1, while for “artificial” noises it is markedly smaller, i.e., a < 0.85. Also the entropy S in natural time can achieve such a distinction: For SES activities both S and S– (where S– stands for the entropy in natural time under time reversal) are smaller than the entropy Su ≈ 0.0966 of the “uniform” distribution, which is not the case for the “artificial” noises where S is larger than (or equal to) Su and S– may either be smaller or larger than Su. Upon “shuffling” the events (pulses) randomly, both values of S and S– in the SES activities turn out to be equal to Su, which conforms with the aforementioned conclusion that in SES activities the self-similarity originates solely from long range temporal correlations. Finally, when investigating the dependence of the fluctuations Δχl of the average value of natural time under time reversal versus the window length l, we can also achieve a distinction between SES activities and “artificial” noises. In particular, when studying the log-log plot of Δχl versus l, the former give ascending curves, in contrast to the latter that result in descending curves.
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Varotsos, P.A., Sarlis, N.V., Skordas, E.S. (2011). Natural Time Analysis of Seismic Electric Signals. In: Natural Time Analysis: The New View of Time. Springer Praxis Books(). Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-16449-1_4
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