Earthquake recurrence as a record breaking process

Davidsen, Jörn; Grassberger, Peter; Paczuski, Maya

doi:10.1029/2006gl026122

Cited by 56 publications

(62 citation statements)

References 18 publications

(23 reference statements)

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“…Davidsen et al (2008) incorporated the spatial information in the criteria for identifying the recurrence of a particular event. When applied to seismicity, they observed scaling laws for both the spatial and temporal separation distances between recurrences (Davidsen et al, 2006). Baiesi and Paczuski (2004) included the magnitude information via the Gutenberg-Richter law in creating a spacetime window for aftershock collection, revealing a scale-free network of correlated earthquakes.…”

Section: Introductionmentioning

confidence: 99%

Observing spatio-temporal clustering and separation using interevent distributions of regional earthquakes

Batac

Kantz

2014

Nonlin. Processes Geophys.

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Abstract. Past studies that attempted to quantify the spatiotemporal organization of seismicity have defined the conditions by which an event and those that follow it can be related in space and/or time. In this work, we use the simplest measures of spatio-temporal separation: the interevent distances R and interevent times T between pairs of successive events. We observe that after a characteristic value R * , the distributions of R begin to follow that of a randomly shuffled sequence, suggesting that events separated by R > R * are more likely to be uncorrelated events generated independent of one another. Interestingly, the conditional T distributions for short-distance (long-distance) events, R ≤ R * (R > R * ), peak at correspondingly short (long) T values, signifying the spatio-temporal clustering (separation) of correlated (independent) events. By considering different threshold magnitudes within a range that ensures substantial catalogue completeness, invariant quantities related to the spatial and temporal spacing of correlated events and the rate of generation of independent events emerge naturally.

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Section: Introductionmentioning

confidence: 99%

Observing spatio-temporal clustering and separation using interevent distributions of regional earthquakes

Batac

Kantz

2014

Nonlin. Processes Geophys.

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“…The complex network-based analysis provides a new approach for nonlinear time series analysis and offers a complementary view to the traditional recurrence quantification analysis (RQA). It has been demonstrated that complex network measures can be usefully applied to: classify nonlinear dynamics of complex systems [6][7][8]; describe causal signatures in seismic activity [9][10][11]; and interpret the geometric properties of an underlying system [4], among many other applications.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Systems Induced on Networks Constructed from Time Series

Hou

Small

Lao

2015

Entropy

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Several methods exist to construct complex networks from time series. In general, these methods claim to construct complex networks that preserve certain properties of the underlying dynamical system, and hence, they mark new ways of accessing quantitative indicators based on that dynamics. In this paper, we test this assertion by developing an algorithm to realize dynamical systems from these complex networks in such a way that trajectories of these dynamical systems produce time series that preserve certain statistical properties of the original time series (and hence, also the underlying true dynamical system). Trajectories from these networks are constructed from only the information in the network and are shown to be statistically equivalent to the original time series. In the context of this algorithm, we are able to demonstrate that the so-called adaptive k-nearest neighbour algorithm for generating networks out-performs methods based on -ball recurrence plots. For such networks, and with a suitable choice of parameter values, which we provide, the time series generated by this method function as a new kind of nonlinear surrogate generation algorithm. With this approach, we are able to test whether the simulation dynamics built from a complex network capture the underlying structure of the original system; whether the complex network is an adequate model of the dynamics.

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“…Complex networks are increasingly being used to study geophysical systems (Baiesi and Paczuski, 2004;Davidsen et al, 2006Davidsen et al, , 2008Peixoto and Davidsen, 2008;Peixoto et al, 2010;Gu et al, 2013;Zaliapin and Ben-Zion, 2013;Zanardo et al, 2013;Dodds and Rothman, 2000;Mantilla et al, 2006;Feng and Dijkstra, 2014;Bassett et al, 2012). Climate dynamics in particular have been an object of much attention where dynamical networks (also called functional or interaction networks) have been used to study phenomena such as: long-range correlation in the atmosphere known as teleconnections Kawale et al, 2011); climate models (Donges et al, 2009a, b); El Niño Southern Oscillation (Yamasaki et al, 2008;Martin et al, 2013); with more analyses continuously being carried out (Steinhaeuser et al, 2012;Ebert-Uphoff and Deng, 2012;Deza et al, 2013).…”

Section: Introductionmentioning

confidence: 99%

Estimating time delays for constructing dynamical networks

Martin

Davidsen

2014

Nonlin. Processes Geophys.

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Abstract. Dynamical networks -networks inferred from multivariate time series -have been widely applied to climate data and beyond, resulting in new insights into the underlying dynamics. However, these inferred networks can suffer from biases that need to be accounted for to properly interpret the results. Here, we report on a previously unrecognized bias in the estimate of time delays between nodes in dynamical networks inferred from cross-correlations, a method often used. This bias results in the maximum correlation occurring disproportionately often at large time lags. This is of particular concern in dynamical networks where the large number of possible links necessitates finding the correct time lag in an automated way. We show that this bias can arise due to the similarity of the estimator to a random walk, and are able to map them to each other explicitly for some cases. For the random walk there is an analytical solution for the bias that is closely related to the famous Lévy arcsine distribution, which provides an upper bound in many other cases. Finally, we show that estimating the cross-correlation in frequency space effectively eliminates this bias. Reanalysing large lag links (from a climate network) with this method results in a distribution peaked near zero instead, as well as additional peaks at the originally assigned lag. Links that are reassigned smaller time lags tend to have a smaller distance between them, which indicates that the new time delays are physically reasonable.

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Earthquake recurrence as a record breaking process

Cited by 56 publications

References 18 publications

Observing spatio-temporal clustering and separation using interevent distributions of regional earthquakes

Observing spatio-temporal clustering and separation using interevent distributions of regional earthquakes

Dynamical Systems Induced on Networks Constructed from Time Series

Estimating time delays for constructing dynamical networks

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