Symbolic Dynamics and Entropy Analysis of Feigenbaum Limit Sets

Karamanos, Konstantinos; Nicolis, Grégoire

doi:10.1016/s0960-0779(98)00095-2

Cited by 49 publications

(64 citation statements)

References 22 publications

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“…Symbolic time series analysis is a useful tool for modelling and characterization of nonlinear dynamical systems (Voss et al, 1996). It provides a rigorous way of looking at "real" dynamics with finite precision (Hao, 1989(Hao, , 1991Kitchens, 1998;Karamanos and Nicolis, 1999). Briefly, it is a way of coarsegraining or simplifying the description.…”

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.

View full text Add to dashboard Cite

show abstract

“…It provides a rigorous way of looking at "real" dynamics with finite precision [8,9]. Briefly, it is a way of coarse-graining or simplifying the description.…”

Section: Symbolic Dynamicsmentioning

confidence: 99%

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

Balasis

Donner

Potirakis

et al. 2013

Entropy

103

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This review provides a summary of methods originated in (non-equilibrium) statistical mechanics and information theory, which have recently found successful applications to quantitatively studying complexity in various components of the complex Entropy 2013, 15 4845 system Earth. Specifically, we discuss two classes of methods: (i) entropies of different kinds (e.g., on the one hand classical Shannon and Rényi entropies, as well as non-extensive Tsallis entropy based on symbolic dynamics techniques and, on the other hand, approximate entropy, sample entropy and fuzzy entropy); and (ii) measures of statistical interdependence and causality (e.g., mutual information and generalizations thereof, transfer entropy, momentary information transfer). We review a number of applications and case studies utilizing the above-mentioned methodological approaches for studying contemporary problems in some exemplary fields of the Earth sciences, highlighting the potentials of different techniques.

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“…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%

“…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%

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 and Entropy Analysis of Feigenbaum Limit Sets

Cited by 49 publications

References 22 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

Statistical Mechanics and Information-Theoretic Perspectives on Complexity in the Earth System

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

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