Influence of Time and Space Correlations on Earthquake Magnitude

Lippiello, Eugenio; Arcangelis, L. de; Godano, C.

doi:10.1103/physrevlett.100.038501

Cited by 100 publications

(97 citation statements)

References 33 publications

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“…Hence, b ≈ 1 means that the exponent γ is around γ = 1.6-1.7. The above are some of the reasons why the OFC model is considered to be the prime example [106] for a supposedly SOC system for earthquakes, but the question of whether real earthquakes are described or not by SOC models of this type, or whether other kinds of mechanisms, e.g., [107][108][109], need to be involved, still remains unsolved [82,86,100,[110][111][112][113][114].…”

Section: Olami-feder-christensen Earthquake Modelmentioning

confidence: 99%

Entropy in Natural Time and the Associated Complexity Measures

Sarlis

2017

Entropy

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Natural time is a new time domain introduced in 2001. The analysis of time series associated with a complex system in natural time may provide useful information and may reveal properties that are usually hidden when studying the system in conventional time. In this new time domain, an entropy has been defined, and complexity measures based on this entropy, as well as its value under time-reversal have been introduced and found applications in various complex systems. Here, we review these applications in the electric signals that precede rupture, e.g., earthquakes, in the analysis of electrocardiograms, as well as in global atmospheric phenomena, like the El Niño/La Niña Southern Oscillation.

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Section: Olami-feder-christensen Earthquake Modelmentioning

confidence: 99%

Entropy in Natural Time and the Associated Complexity Measures

Sarlis

2017

Entropy

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“…However, since the integral of g(t | m,m ) from 0 to ∞ is 1 for all the values of m and m , the results throughout this article also hold for this model. Lippiello et al [18,35,36] also considered the case of dependence between occurrence times and locations. Without loss of generality, we can omit the spatial component.…”

Section: Lippiello Et Al's Modelmentioning

confidence: 99%

“…Lippiello et al [18,35,36] also proposed an alternative to the ETAS model and studied its properties, including criticality. The conditional intensity of this model is…”

Section: Lippiello Et Al's Modelmentioning

confidence: 99%

Stability of earthquake clustering models: Criticality and branching ratios

2013

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We study the stability conditions of a class of branching processes prominent in the analysis and modeling of seismicity. This class includes the epidemic-type aftershock sequence (ETAS) model as a special case, but more generally comprises models in which the magnitude distribution of direct offspring depends on the magnitude of the progenitor, such as the branching aftershock sequence (BASS) model and another recently proposed branching model based on a dynamic scaling hypothesis. These stability conditions are closely related to the concepts of the criticality parameter and the branching ratio. The criticality parameter summarizes the asymptotic behavior of the population after sufficiently many generations, determined by the maximum eigenvalue of the transition equations. The branching ratio is defined by the proportion of triggered events in all the events. Based on the results for the generalized case, we show that the branching ratio of the ETAS model is identical to its criticality parameter because its magnitude density is separable from the full intensity. More generally, however, these two values differ and thus place separate conditions on model stability. As an illustration of the difference and of the importance of the stability conditions, we employ a version of the BASS model, reformulated to ensure the possibility of stationarity. In addition, we analyze the magnitude distributions of successive generations of the BASS model via analytical and numerical methods, and find that the compound density differs substantially from a Gutenberg-Richter distribution, unless the process is essentially subcritical (branching ratio less than 1) or the magnitude dependence between the parent event and the direct offspring is weak.

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“…The complex stochastic interactions among these subsystems are commonly quantified by calculating the cross-correlations. This method has been applied in systems ranging from nanodevices [5][6][7], atmospheric geophysics [8], and seismology [9][10][11], to finance [12][13][14][15][16][17][18][19][20][21][22][23]. Here we propose a method of estimating the most significant component in explaining long-range cross-correlations.…”

Section: Introductionmentioning

confidence: 99%

Quantifying and modeling long-range cross correlations in multiple time series with applications to world stock indices

et al. 2011

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We propose a modified time lag random matrix theory in order to study time lag crosscorrelations in multiple time series. We apply the method to 48 world indices, one for each of 48 different countries. We find long-range power-law cross-correlations in the absolute values of returns that quantify risk, and find that they decay much more slowly than cross-correlations between the returns. The magnitude of the cross-correlations constitute "bad news" for international investment managers who may believe that risk is reduced by diversifying across countries. We find that when a market shock is transmitted around the world, the risk decays very slowly. We explain these time lag cross-correlations by introducing a global factor model (GFM) in which all index returns fluctuate in response to a single global factor. For each pair of individual time series of returns, the cross-correlations between returns (or magnitudes) can be modeled with the auto-correlations of the global factor returns (or magnitudes). We estimate the global factor using principal component analysis, which minimizes the variance of the residuals after removing the global trend. Using random matrix theory, a significant fraction of the world index cross-correlations can be explained by the global factor, which supports the utility of the GFM. We demonstrate applications of the GFM in forecasting risks at the world level, and in finding uncorrelated individual indices. We find 10 indices are practically uncorrelated with the global factor and with the remainder of the world indices, which is relevant information for world managers in reducing their portfolio risk. Finally, we argue that this general method can be applied to a wide range of phenomena in which time series are measured, ranging from seismology and physiology to atmospheric geophysics.

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Influence of Time and Space Correlations on Earthquake Magnitude

Cited by 100 publications

References 33 publications

Entropy in Natural Time and the Associated Complexity Measures

Entropy in Natural Time and the Associated Complexity Measures

Stability of earthquake clustering models: Criticality and branching ratios

Quantifying and modeling long-range cross correlations in multiple time series with applications to world stock indices

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