Micro-scale, mid-scale, and macro-scale in global seismicity identified by empirical mode decomposition and their multifractal characteristics

Abstract

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. 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. 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. 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/fα 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. 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. 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.

On the Statistical Significance of the Variability Minima of the Order Parameter of Seismicity by Means of Event Coincidence Analysis

“…In this section, we present the results of ECA for the interrelation between the strong (target) EQs and the order parameter fluctuation minima β min that have been found in the regional studies of Japan [59], Eastern Mediterranean [62], and in the global seismicity [60,61], see Figure 1. For these reasons, the time-series of target EQs will serve as event time-series A and the time-series of β min as event time-series B, whereas the unit of time for ∆T and τ is one day.…”

“…The time evolution of β W is followed by sliding the window of W consecutive EQs, event by event, through the EQ catalog and assigning to its value the occurrence time of the EQ which follows the last EQ of the window studied in the EQ catalog. The fluctuations of the order parameter of seismicity as quantified by β W have been studied in various seismically active regions, like Japan [30,31,59] or Eastern Mediterranean [62], and in the global seismicity as well [60,61]. These studies have revealed that before strong EQs β W s exhibit characteristic minima labeled β min and were focused, so far, on a small number of the stronger EQs in each geographic region (see Tables 1-5…”

“…The aforementioned regional studies of the variability of the order parameter κ 1 of seismicity have been also generalized to global seismicity by analyzing in natural time the Global Centroid Moment Tensor Catalog [77,78] of the period 1 January 1976 to 1 October 2014 [60,61]. Two different target EQ magnitude thresholds M thres have been used, i.e., M thres = 8.5 and M thres = 8.4, and for the latter threshold the method has been also applied when using the mid-scale time-series of seismicity [79] (cf.…”

“…Sarlis et al [60] and later Sarlis et al [61] extended the methodology for the identification of β min to predict smaller EQs, i.e., the ones with M ≥ 8.4. This led to the results shown in Table 4.…”

“…the latter may be considered as critical phenomena [11,[47][48][49][50][51][52][53][54][55]. The study of the fluctuations of κ 1 before strong EQs revealed the existence of characteristic precursory minima [56,57] that have been determined when studying either the regional or the global seismicity [30,[58][59][60][61][62]. It is the scope of the present work to employ the very recent tool of ECA for the investigation of the statistical significance of such minima.…”