Non-Linear Analysis of Point Processes Seismic Sequences in Guerrero, Mexico: Characterization of Earthquakes and Fractal Properties

Márquez, Elsa Leticia Flores; Valverde-Esparza, Sharon M.

doi:10.5772/29173

Cited by 2 publications

(9 citation statements)

References 59 publications

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“…This would translate into intermittency in the time series. Recent studies (Flandrin et al, 2004(Flandrin et al, , 2005Gledhill, 2003;Huang, 2004, 2009) support the idea of carrying out noise-added analyses with the EMD. The noiseadded analyses involves multiple realizations of added noises to the time series in question, leading to the ensemble EMD (EEMD), as proposed by Huang (2004, 2009).…”

Section: Ensemble Empirical Mode Decomposition As Applied To State-tomentioning

confidence: 97%

“…Quantifying the earthquake sequencing in terms of its fractal properties was done by means of the Fano factor and the Allan factor (Allan, 1966;Barnes and Allan, 1966;Teich, 1993, 1995;Thurner et al, 1997;Telesca et al, 2001Telesca et al, , 2009Telesca et al, , 2011Flores-Marquez and Valverde-Esparza, 2012;Serinaldi and Kilsby, 2013). Since the fractal properties of the time series studied here has never been investigated, we calculate the Fano factor and the Allan factor for the purpose of quantitative analysis.…”

Section: S Cavers and K Vasudevan: Earthquake Sequencing: Analysmentioning

confidence: 99%

“…The correlation in the process {N k (τ )} is the correlation in the underlying point process Teich, 1993, 1995;Thurner et al, 1997;Telesca, 2005;Telesca et al, 2001Telesca et al, , 2009Telesca et al, , 2011) have accessed such a representation of the point-processes to underscore the existence or non-existence of fractality in them. They have two calculable measures, Fano factor (FF) and Allan factor (AF), to quantify the fractality of the process Teich, 1993, 1995;Thurner et al, 1997;Telesca, 2005;Telesca et al, 2001Telesca et al, , 2009Telesca et al, , 2011Flores-Marquez and Valverde-Esparza, 2012). The Fano factor is a measure of correlation over different timescales (Thurner et al, 1997).…”

Section: Evaluation Of Fractality In a State-to-state Transition Freqmentioning

confidence: 99%

“…Telesca et al (2009Telesca et al ( , 2011henceforth, referred to as Telesca's approach) and Flores-Marquez and Valverde-Esparza (2012) have shown the power-law exponent for the AF to be 0 < α < 1. In this paper, we examine both the results of Telesca's approach to the initial catalogue of the data used and of the new representation of the point process with a Markov chain model.…”

Section: Evaluation Of Fractality In a State-to-state Transition Freqmentioning

confidence: 99%

“…Thurner et al (1997) pointed out that the sequence of counts, generated by recording the number of events in successive counting time-windows of certain length, contained information about the point process depicted by the set of event times. This idea was further tested in understanding the dynamics of earthquake sequencing (Telesca et al, 2009(Telesca et al, , 2011Flores-Marquez and Valverde-Esparza, 2012), and in particular, the fractal behaviour of the sequence of counts. We know that this idea was initially restricted to the sequence of counts for varying windows of interval times.…”

Section: Evaluation Of Fractality In a State-to-state Transition Freqmentioning

confidence: 99%

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Brief Communication: Earthquake sequencing: analysis of time series constructed from the Markov chain model

Cavers

Vasudevan

2015

Nonlin. Processes Geophys.

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Abstract. Directed graph representation of a Markov chain model to study global earthquake sequencing leads to a time series of state-to-state transition probabilities that includes the spatio-temporally linked recurrent events in the recordbreaking sense. A state refers to a configuration comprised of zones with either the occurrence or non-occurrence of an earthquake in each zone in a pre-determined time interval. Since the time series is derived from non-linear and nonstationary earthquake sequencing, we use known analysis methods to glean new information. We apply decomposition procedures such as ensemble empirical mode decomposition (EEMD) to study the state-to-state fluctuations in each of the intrinsic mode functions. We subject the intrinsic mode functions, derived from the time series using the EEMD, to a detailed analysis to draw information content of the time series. Also, we investigate the influence of random noise on the data-driven state-to-state transition probabilities. We consider a second aspect of earthquake sequencing that is closely tied to its time-correlative behaviour. Here, we extend the Fano factor and Allan factor analysis to the time series of state-to-state transition frequencies of a Markov chain. Our results support not only the usefulness of the intrinsic mode functions in understanding the time series but also the presence of power-law behaviour exemplified by the Fano factor and the Allan factor.

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Section: Ensemble Empirical Mode Decomposition As Applied To State-tomentioning

confidence: 97%

Section: S Cavers and K Vasudevan: Earthquake Sequencing: Analysmentioning

confidence: 99%

Section: Evaluation Of Fractality In a State-to-state Transition Freqmentioning

confidence: 99%

Section: Evaluation Of Fractality In a State-to-state Transition Freqmentioning

confidence: 99%

Section: Evaluation Of Fractality In a State-to-state Transition Freqmentioning

confidence: 99%

See 3 more Smart Citations

Brief Communication: Earthquake sequencing: analysis of time series constructed from the Markov chain model

Cavers

Vasudevan

2015

Nonlin. Processes Geophys.

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Insight into earthquake sequencing: analysis and interpretation of time-series constructed from the directed graph of the Markov chain model

Cavers¹,

Vasudevan²

2015

Preprint

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Abstract. Directed graph representation of a Markov chain model to study global earthquake sequencing leads to a time-series of state-to-state transition probabilities that includes the spatio-temporally linked recurrent events in the record-breaking sense. A state refers to a configuration comprised of zones with either the occurrence or non-occurrence of an earthquake in each zone in a pre-determined time interval. Since the time-series is derived from non-linear and non-stationary earthquake sequencing, we use known analysis methods to glean new information. We apply decomposition procedures such as ensemble empirical mode decomposition (EEMD) to study the state-to-state fluctuations in each of the intrinsic mode functions. We subject the intrinsic mode functions, the orthogonal basis set derived from the time-series using the EEMD, to a detailed analysis to draw information-content of the time-series. Also, we investigate the influence of random-noise on the data-driven state-to-state transition probabilities. We consider a second aspect of earthquake sequencing that is closely tied to its time-correlative behavior. Here, we extend the Fano factor and Allan factor analysis to the time-series of state-to state transition frequencies of a Markov chain. Our results support not only the usefulness the intrinsic mode functions in understanding the time-series but also the presence of power-law behaviour exemplified by the Fano factor and the Allan factor.

show abstract

Non-Linear Analysis of Point Processes Seismic Sequences in Guerrero, Mexico: Characterization of Earthquakes and Fractal Properties

Cited by 2 publications

References 59 publications

Brief Communication: Earthquake sequencing: analysis of time series constructed from the Markov chain model

Brief Communication: Earthquake sequencing: analysis of time series constructed from the Markov chain model

Insight into earthquake sequencing: analysis and interpretation of time-series constructed from the directed graph of the Markov chain model

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