Examples of the electric field recordings in normalized units, i.e., by subtracting the mean value and dividing by the standard deviation . The following SES activities are depicted: (a) the one recorded on 18 April 1995 at Ioannina station; (b) the long duration SES activity recorded from 27 December 2010 to 30 December 2009 at Lamia station. (c) is an excerpt of (b) showing that, after long periods of quiescence, the electric field exhibits measurable excursions (transient pulses).
(a) Example of a surrogate time-series (in normalized units as in Fig. 1) obtained by removing segments of length from the signal of Fig. 1(a) with 50% data loss (i.e., ). (b) The natural time representation of (a). The values obtained from the analysis of (b) in natural time are , , , and .
The dependence of the DFA measure vs the scale in natural time: we increase the percentage of data loss by removing segments of length samples from the signal of Fig. 1(a). The black (plus) symbols correspond to no data loss , the red (crosses) to 30% data loss , the green (asterisks) to 50% data loss , and the blue (squares) to 70% data loss . Except for the case , the data have been shifted vertically for the sake of clarity. The slopes of the corresponding straight lines that fit the data lead to , 0.94, 0.88, and 0.84 from top to bottom, respectively. They correspond to the average values of obtained from 5000 surrogate time-series that were generated with the method of surrogate by Ma et al. (Ref. 72) (see the text).
The probabilities (a) , (b) , and (c) to recognize the signal of Fig. 1(a) as true SES activity when considering various percentages of data loss , 0.3, 0.5, 0.7, and 0.8 as a function of the length of the contiguous samples removed. The removal of large segments leads to better results when using DFA in natural time (a), whereas the opposite holds when using the conditions of Eqs. (6) and (7) for , , and (b). The optimum selection (c) for the identification of a signal as SES activity consists of a proper combination of the aforementioned procedures in (a) and (b), see the text. The values presented have been obtained from 5000 surrogate time-series (for a given value of and ), and hence they have a plausible error of 1.4% .
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