Traces of Long-Memory in Pre-Seismic MHz Electromagnetic Time Series-Part 1: Investigation Through the R/S Analysis and Time-Evolving Spectral Fractals

Abstract

This paper reports characteristic pre seismic electromagnetic disturbances in the MHz range detected prior to seven significant earthquakes of M L ≥ 5.0 which occurred in Greece between 2009 and 2015. The whole data set was investigated through Rescaled Range (R/S) analysis and wavelet based spectral fractal analysis. The long-memory trends hidden in the analysed signals were investigated via the Hurst exponent (H). The R/S method indicated that in the majority of the segments of the investigated signals, the H -exponents were in the range 0.7-0.9. Several exponents were above 0.9. This is associated with persistency. In several segments, the Hurst exponent exhibited small variance. Noteworthy fluctuations were also found. In many cases the H -time fluctuations were independent of the time evolution of the associated electromagnetic signals. The spectral fractal method, being more suited for this purpose, highlighted the characteristic signals' epochs, governed by long-lasting fractal organisation. The calculated Hurst exponents in the characteristic long-lasting fractal epochs were associated with medium anti-persistent behaviour or with continuous switching between anti-persistency and persistency. The H -exponents of the random fractal organised segments were mainly persistent. From the data presented in this paper, it is deduced that the R/S method provides additional information on the estimation of the Hurst exponent when combined with the spectral fractal method. Both techniques should be employed in sequential steps to enhance the precursory value of the results.

Fractal Analysis of Pre-Seismic Electromagnetic and Radon Precursors: A Systematic Approach

“…The complex long-term connections between space and time before earthquakes are concealed in traces in earthquake hazard systems [11,16,17,43,44,[55][56][57][58]. The pre-seismic traces may unfold with fractal methods [3,6,8,9,11,14,16,17,43,44,52,[55][56][57][58]61,84].…”

“…The pre-seismic traces may unfold with fractal methods [3,6,8,9,11,14,16,17,43,44,52,[55][56][57][58]61,84]. These seismic systems evolve naturally into self-organised critical (SOC) states with fractal organisation in space and time [4].…”

“…These trends can be traced effectively through the identification of temporal power-laws in the power spectral density (PSD) of the associated time series, accounting that the PSD is one of the prevailing measures for that purpose [4,5,8,14,84]. Importantly, when the time-series exhibit noteworthy time-periods of high b -exponent power-laws, they are considered as well-established temporal fractals, which for the cases of the seismical critical systems, are associated with the spatial fractal evolution of the earth's crust during rupture [3,4,6,8,[9][10][11]14,[16][17][18]43,44,52,[55][56][57][58]61,84]. In this sense, Figure 3 presents three example cases with the above characteristics, namely time-series containing fractal epochs associated with temporal PSD power-laws close to critical points and associated with long-memory dynamics.…”

“…In comparison, this paper includes nine great earthquakes with M L ≥ 6.0 and the remaining twenty seven events with 5.0 ≤ M L < 6.0 . It should be noted though, that this paper includes also the re-analysis of some earthquake raw data published in other papers of the reporting team [16,27,43,44,[55][56][57][58], however, under a different view and with new approach. It can be, thus, supported, that either from the view of great earthquakes ( M L ≥ 6.0 ) or the perspective of the number of the analysed events (37), this research includes a significant amount of seismic data.…”

Insights on the Global Climatic Changes and their Discernible Impacts

“…Nikolopoulos et al [1] derived critical information from significant earthquakes data spanning 2009-2015 with few noteworthy seismic events at shallow depths. Their findings state that the analyses of the rescaled range (R/S) and the wavelet-based spectral fractal should be employed in sequence to enhance the precursory value of results.…”