Entropy analysis of substitutive sequences revisited

Karamanos, Konstantinos

doi:10.1088/0305-4470/34/43/309

Cited by 28 publications

(46 citation statements)

References 14 publications

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“…Gliding is the reading of the symbolic sequence using a moving frame. It has been suggested that, at least in some cases, the entropy analysis by lumping is much more sensitive than classical entropy analysis (gliding) (Karamanos, 2000(Karamanos, , 2001.…”

Section: Fundamentals Of Symbolic Dynamicsmentioning

confidence: 99%

Unfolding the procedure of characterizing recorded ultra low frequency, kHZ and MHz electromagetic anomalies prior to the L'Aquila earthquake as pre-seismic ones – Part 1

Eftaxias

Athanasopoulou

Balasis

et al. 2009

Nat. Hazards Earth Syst. Sci.

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Abstract. Ultra low frequency, kHz and MHz electromagnetic (EM) anomalies were recorded prior to the L'Aquila catastrophic earthquake that occurred on 6 April 2009. The main aims of this paper are threefold: (i) suggest a procedure for the designation of detected EM anomalies as seismogenic ones. We do not expect to be able to provide a succinct and solid definition of a pre-seismic EM emission. Instead, we aim, through a multidisciplinary analysis, to provide the elements of a definition. (ii) Link the detected MHz and kHz EM anomalies with equivalent last stages of the earthquake preparation process. (iii) Put forward physically meaningful arguments for quantifying the time to global failure and the identification of distinguishing features beyond which the evolution towards global failure becomes irreversible. We emphasize that we try to specify not only whether a single EM anomaly is pre-seismic in itself, but also whether a combination of kHz, MHz, and ULF EM anomalies can be characterized as pre-seismic. The entire procedure unfolds in two consecutive parts. Here in Part 1 we focus on the detected kHz EM anomaly, which play a crucial role in our approach to these challenges. We try to discriminate clearly this anomaly from background noise. For this purpose, we analyze the data successively in terms of various concepts of entropy and information theory including, Shannon n-block entropy, conditional entropy, entropy of the Correspondence to: K. Eftaxias (ceftax@phys.uoa.gr) source, Kolmogorov-Sinai entropy, T -entropy, approximate entropy, fractal spectral analysis, R/S analysis and detrended fluctuation analysis. We argue that this analysis reliably distinguishes the candidate kHz EM precursor from the noise: the launch of anomalies from the normal state is combined by a simultaneous appearance of a significantly higher level of organization, and persistency. This finding indicates that the process in which the anomalies are rooted is governed by a positive feedback mechanism. This mechanism induces a non-equilibrium process, i.e., a catastrophic event. This conclusion is supported by the fact that the two crucial signatures included in the kHz EM precursor are also hidden in other quite different, complex catastrophic events as predicted by the theory of complex systems. However, our view is that such an analysis by itself cannot establish a kHz EM anomaly as a precursor. It likely offers necessary but not sufficient criteria in order to recognize an anomaly as preseismic. In Part 2 we aim to provide sufficient criteria: the fracture process is characterized by fundamental universally valid scaling relationships which should be reflected in a real fracto-electromagnetic activity. Moreover, we aim to answer the following two key questions: (i) How can we link an individual EM precursor with a distinctive stage of the EQ preparation process; and (ii) How can we identify precursory symptoms in EM observations that indicate that the occurrence of the EQ is unavoidable.

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Section: Fundamentals Of Symbolic Dynamicsmentioning

confidence: 99%

Unfolding the procedure of characterizing recorded ultra low frequency, kHZ and MHz electromagetic anomalies prior to the L'Aquila earthquake as pre-seismic ones – Part 1

Eftaxias

Athanasopoulou

Balasis

et al. 2009

Nat. Hazards Earth Syst. Sci.

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“…The MHz EM signals were continuously monitored by a telemetric network, which consists of 12 stations [36]. determination of the beginning of an earthquake sequence is still constrained [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][29][30][31][32][33][34]. As per [12] one ought to expect that the preliminary procedures of earthquakes have different aspects, which might be witnessed before the final rupture at land, geochemical, hydrological and natural scales [12].…”

Section: Introductionmentioning

confidence: 99%

“…While each of these phenomena has been observed prior to certain earthquakes, such observations have been random in nature [1,35]. Finally, it is essential to note that ultralow (ULF), low (LF), high (HF) and very high frequency (VHF) EM irregularities have been observed over periods extending from a couple of days to a couple of hours preceding destructive land earthquakes or strong and shallow undersea earthquakes [11][12][13][14][15][16][17][18][19][20][21][22][23][25][26][27][29][30][31][32][33][34]. This paper concentrates on significant, short-term disturbances of natural EM radiation in the MHz frequency range.…”

Section: Introductionmentioning

confidence: 99%

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

Nikolopoulos¹,

Cantzos²

2016

J Earth Sci Clim Change

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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.

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“…Symbolic dynamics provide a rigorous way of looking at "real" dynamics. First, a symbolic analysis [4,22,23,26,28,[102][103][104] of experimental data is attempted, in terms of Shannon n-block entropy, Shannon n-block entropy per letter, conditional entropy, entropy of the source and T-entropy. It is well-known that Shannon entropy works best in dealing with systems composed of subsystems, which can access all the available phase space and which are either independent or interact via short-range forces.…”

Section: Hf-emissions 321khz Bandmentioning

confidence: 99%

Electromagnetic Pre-earthquake Precursors: Mechanisms, Data and Models-A Review

D¹

2015

J Earth Sci Clim Change

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Entropy analysis of substitutive sequences revisited

Cited by 28 publications

References 14 publications

Unfolding the procedure of characterizing recorded ultra low frequency, kHZ and MHz electromagetic anomalies prior to the L'Aquila earthquake as pre-seismic ones – Part 1

Unfolding the procedure of characterizing recorded ultra low frequency, kHZ and MHz electromagetic anomalies prior to the L'Aquila earthquake as pre-seismic ones – Part 1

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

Electromagnetic Pre-earthquake Precursors: Mechanisms, Data and Models-A Review

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