10/28/2023 0 Comments Macro vs micro sizeLater studies of this order parameter have shown 18, 42, 43, 44 that its fluctuations β W( κ 1) when studied within excerpts of the EQ catalog comprising W consecutive EQs, they exhibit characteristic minima that almost coincide 17, 45, 46 with the observation of Seismic Electric Signals (SES) activities 47, 48 which are series of low-frequency (≤1 Hz) variations of the electric field of the Earth that appear a few weeks up to six months before EQs in Greece 48, 49, 50, 51, 52, 53 and Japan 36, 54, 55, 56, 57. This order parameter abruptly changes to zero upon the occurrence of a strong EQ (which corresponds to the new phase, the “disordered” phase) while it remains non-zero when no such strong EQ occurs (“ordered” phase) (see also pp. ![]() For the case of seismicity, NTA enabled 41 the introduction of an order parameter labeled κ 1. 40): when a body passes through the phase transition point, we can define a quantity called the order parameter, in such a way that it takes non-zero (positive or negative) values in the unsymmetrical phase and is zero in the symmetrical phase. We recall that according to the definition of this parameter (see p. Taking the view that EQs are critical phenomena, the quantity by which one can identify the approach of a dynamical system to the state of criticality is termed order parameter. Natural time analysis (NTA) has been introduced 35 almost fifteen years ago and enables the identification of novel dynamical features hidden behind the time-series resulting from complex systems 37. In particular, we shall show that the mid-scale is the most appropriate scale to achieve such a purpose by analyzing the seismicity in a new time domain termed natural time 35, 36, 37, 38, 39. Consequently, the following important question arises: If in general the EQ magnitude time-series is a result of the superposition of these three distinct time-series of different spectral content (micro-, mid- and macro-scale), it is of major importance to investigate here which of these three scales is of primary usefulness for EQ prediction. The identification of these three time scales has been based on the different multifractal behaviour observed through multifractal detrended fluctuation analysis (MFDFA) 34 for the corresponding time-series. In an independent study, Fan and Lin 27 analysed the EQ magnitude time-series in Southern California by the empirical mode decomposition (EMD) 29, 30, 31, 32, 33 method and identified the presence of three different time scales: The micro-scale, the mid-scale and the macro-scale. ![]() Here, we focus on the analysis of EQ magnitude time-series for which we have shown 13, 14 that there exist correlations between successive EQs of magnitude 7.0 or larger in a global scale. Seismicity exhibits complexity in many aspects giving rise to correlations between hypocenters, occurrence times, and EQ magnitudes M which have been the subject of several studies 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28. It is shown that when using the mid-scale time-series only, we can obtain results similar to those obtained by the natural time analysis of global seismicity when focusing on the prediction of earthquakes with M ≥ 8.4.Įarthquake (EQ) is a common physical phenomenon that is related with the tectonic structure of the solid Earth crust on which we live and whose prediction 1 is very important for human welfare. The results have been also verified to hold regionally for the earthquakes in Japan and shed light on the significance of the mid-scale of 30 to 300 events in the natural time analysis of global (and regional) seismicity. ![]() Concerning the mid-scale one, in the range of 30 to 300 consecutive events the maximum entropy method power spectra indicates that it exhibits an 1/ f α behaviour with α close to 1/3 which is compatible with the long-range correlations identified by detrended fluctuation analysis during periods of stationary seismicity. Their multifractal detrended fluctuation analysis reveals that the micro-scale time-series exhibits anticorrelated behaviour in contrast to the mid-scale one which is long-range correlated. Using Hurst analysis one can identify three different sums of these IMFs and the trend which exhibit distinct multifractal behaviour and correspond to micro-, mid- and macro-scales. The magnitude time-series of the global seismicity is analyzed by the empirical mode decomposition giving rise to 14 intrinsic mode functions (IMF) and a trend.
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