Analysis of seismic sequences by using the method of visibility graph

Telesca, Luciano; Lovallo, Michele

doi:10.1209/0295-5075/97/50002

Cited by 104 publications

(61 citation statements)

References 13 publications

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“…However, the generalization and reliability of the outcomes of this relatively new approach remain an open question. Within this framework the so-called visibility graph (VG) method maps time series into networks or graphs, which converts dynamical properties of time series into topological properties of networks, and can identify possible precursory signatures (Telesca et al, 2012(Telesca et al, , 2015.…”

Section: E Daskalaki Et Al: Foreshocks and Short-term Hazard Assessmentioning

confidence: 99%

Foreshocks and short-term hazard assessment of large earthquakes using complex networks: the case of the 2009 L'Aquila earthquake

Daskalaki

Spiliotis

Siettos

et al. 2016

Nonlin. Processes Geophys.

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Abstract. The monitoring of statistical network properties could be useful for the short-term hazard assessment of the occurrence of mainshocks in the presence of foreshocks. Using successive connections between events acquired from the earthquake catalog of the Istituto Nazionale di Geofisica e Vulcanologia (INGV) for the case of the L'Aquila (Italy) mainshock (M w = 6.3) of 6 April 2009, we provide evidence that network measures, both global (average clustering coefficient, small-world index) and local (betweenness centrality) ones, could potentially be exploited for forecasting purposes both in time and space. Our results reveal statistically significant increases in the topological measures and a nucleation of the betweenness centrality around the location of the epicenter about 2 months before the mainshock. The results of the analysis are robust even when considering either large or off-centered the main event space windows.

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Section: E Daskalaki Et Al: Foreshocks and Short-term Hazard Assessmentioning

confidence: 99%

Foreshocks and short-term hazard assessment of large earthquakes using complex networks: the case of the 2009 L'Aquila earthquake

Daskalaki

Spiliotis

Siettos

et al. 2016

Nonlin. Processes Geophys.

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“…The NVG method has the advantage of providing potential further insight into the temporal organization of sequences, by exploring the emerging network structures in a quantitative manner. The NVG has been used to explore organizational features in complex time series from different systems ranging from chaotic signals [23], heartbeat variability [9] and economics to seismology [24,25].…”

Section: Introductionmentioning

confidence: 99%

Word-Length Correlations and Memory in Large Texts: A Visibility Network Analysis

Guzmán‐Vargas

Obregón-Quintana

Aguilar-Velázquez

et al. 2015

Entropy

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We study the correlation properties of word lengths in large texts from 30 ebooks in the English language from the Gutenberg Project (www.gutenberg.org) using the natural visibility graph method (NVG). NVG converts a time series into a graph and then analyzes its graph properties. First, the original sequence of words is transformed into a sequence of values containing the length of each word, and then, it is integrated. Next, we apply the NVG to the integrated word-length series and construct the network. We show that the degree distribution of that network follows a power law, P (k) ∼ k −γ , with two regimes, which are characterized by the exponents γ s ≈ 1.7 (at short degree scales) and γ l ≈ 1.3 (at large degree scales). This suggests that word lengths are much more strongly correlated at large distances between words than at short distances between words. That finding is also supported by the detrended fluctuation analysis (DFA) and recurrence time distribution. These results provideEntropy 2015, 177799 new information about the universal characteristics of the structure of written texts beyond that given by word frequencies.

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“…As part of the effort of developing a mathematically sound visibility graph theory of dynamical systems, in recent years the performance of the visibility method has been tested and found to be consistently capable in different circumstances, including the description of chaotic, fractal-stochastic, dissipative processes [18,19]. The method has also been successfully applied in the characterization of real-world time series in different fields such as physiology and geophysics to cite some [20][21][22][23]. In every case the network counterpart of each particular kind of dynamics has been determined with precision, positioning the visibility algorithm as a well-defined method to analyze the dynamics of complex systems using graph-theoretical tools.…”

Section: Introductionmentioning

confidence: 99%

Horizontal visibility graphs generated by type-I intermittency

et al. 2013

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The type-I intermittency route to (or out of) chaos is investigated within the horizontal visibility (HV) graph theory. For that purpose, we address the trajectories generated by unimodal maps close to an inverse tangent bifurcation and construct their associated HV graphs. We show how the alternation of laminar episodes and chaotic bursts imprints a fingerprint in the resulting graph structure. Accordingly, we derive a phenomenological theory that predicts quantitative values for several network parameters. In particular, we predict that the characteristic power-law scaling of the mean length of laminar trend sizes is fully inherited by the variance of the graph degree distribution, in good agreement with the numerics. We also report numerical evidence on how the characteristic power-law scaling of the Lyapunov exponent as a function of the distance to the tangent bifurcation is inherited in the graph by an analogous scaling of block entropy functionals defined on the graph. Furthermore, we are able to recast the full set of HV graphs generated by intermittent dynamics into a renormalization-group framework, where the fixed points of its graph-theoretical renormalization-group flow account for the different types of dynamics. We also establish that the nontrivial fixed point of this flow coincides with the tangency condition and that the corresponding invariant graph exhibits extremal entropic properties.

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Analysis of seismic sequences by using the method of visibility graph

Cited by 104 publications

References 13 publications

Foreshocks and short-term hazard assessment of large earthquakes using complex networks: the case of the 2009 L'Aquila earthquake

Foreshocks and short-term hazard assessment of large earthquakes using complex networks: the case of the 2009 L'Aquila earthquake

Word-Length Correlations and Memory in Large Texts: A Visibility Network Analysis

Horizontal visibility graphs generated by type-I intermittency

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