Are seismic waiting time distributions universal?

Davidsen, Jörn; Goltz, Christian

doi:10.1029/2004gl020892

Cited by 112 publications

(89 citation statements)

References 21 publications

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“…This defines a correlated behavior for earthquakes separated by short time intervals, while for larger time intervals earthquakes are independent. In later studies the universal behavior in the interevent time distribution has been questioned (Davidsen and Goltz, 2004; The corresponding q-logarithmic distributions ln q (P (> τ )) for the entire dataset (circles) and for M ≥ M c (crosses), exhibiting correlation coefficients ρ = −0.9842 and ρ = −0.9952, respectively. The straight line is the q-exponential distribution.…”

Section: G Michas Et Al: Non-extensivity In Earthquake Sequencesmentioning

confidence: 99%

Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece)

Michas

Vallianatos

Sammonds

2013

Nonlin. Processes Geophys.

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Abstract. In the present work the statistical properties of the earthquake activity in a highly seismic region, the West Corinth rift (Central Greece), are being studied by means of generalized statistical physics. By using a dataset that covers the period 2001-2008, we investigate the earthquake energy distribution and the distribution of the time intervals (interevent times) between the successive events. As has been reported previously, these distributions exhibit complex statistical properties and fractality. By using detrended fluctuation analysis (DFA), a well-established method for detection of long-range correlations in non-stationary signals, it is shown that long-range correlations are also present in the earthquake activity. The existence of these properties motivates us to use non-extensive statistical physics (NESP) to investigate the statistical properties of the frequencymagnitude and the interevent time distributions, along with other well-known relations in seismology, such as the gamma distribution for interevent times. The results of the analysis indicate that the statistical properties of the earthquake activity can be successfully reproduced by means of NESP and that the earthquake activity at the West Corinth rift is correlated at all-time scales.

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Section: G Michas Et Al: Non-extensivity In Earthquake Sequencesmentioning

confidence: 99%

Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece)

Michas

Vallianatos

Sammonds

2013

Nonlin. Processes Geophys.

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“…Based on studies of all earthquakes in southern California during a prescribed time interval, Bak et al (2002) obtained a universal scaling for the statistical distribution of interoccurrence times. Subsequently, other studies of this type have been carried out (Carbone, et al, 2005;Corral, 2003Corral, , 2004aCorral, , b, 2005aDavidsen and Goltz, 2004;Lindman, et al, 2005;Livina, et al, 2005a, b). Shcherbakov et al (2005) showed that this observed behavior for aftershocks can be explained by a non-homogeneous Poisson process.…”

Section: Introductionmentioning

confidence: 98%

Recurrence and interoccurrence behavior of self-organized complex phenomena

Abaimov

Turcotte

Shcherbakov

et al. 2007

Nonlin. Processes Geophys.

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Abstract. The sandpile, forest-fire and slider-block models are said to exhibit self-organized criticality. Associated natural phenomena include landslides, wildfires, and earthquakes. In all cases the frequency-size distributions are well approximated by power laws (fractals). Another important aspect of both the models and natural phenomena is the statistics of interval times. These statistics are particularly important for earthquakes. For earthquakes it is important to make a distinction between interoccurrence and recurrence times. Interoccurrence times are the interval times between earthquakes on all faults in a region whereas recurrence times are interval times between earthquakes on a single fault or fault segment. In many, but not all cases, interoccurrence time statistics are exponential (Poissonian) and the events occur randomly. However, the distribution of recurrence times are often Weibull to a good approximation. In this paper we study the interval statistics of slip events using a slider-block model. The behavior of this model is sensitive to the stiffness α of the system, α=k C /k L where k C is the spring constant of the connector springs and k L is the spring constant of the loader plate springs. For a soft system (small α) there are no system-wide events and interoccurrence time statistics of the larger events are Poissonian. For a stiff system (large α), system-wide events dominate the energy dissipation and the statistics of the recurrence times between these system-wide events satisfy the Weibull distribution to a good approximation. We argue that this applicability of the Weibull distribution is due to the power-law (scale invariant) behavior of the hazard function, i.e. the probability that the next event will occur at a time t 0 after the last event has a power-law dependence on t 0 . The Weibull distribution is the only distribution that has a scale invariant hazard function. We further show that the onset of system-wide events is a well defined critical point. We find that the number of system-wide events N SWE Correspondence to: S. G. Abaimov (abaimov@geology.ucdavis.edu) satisfies the scaling relation N SWE ∝ (α−α C ) δ where α C is the critical value of the stiffness. The system-wide events represent a new phase for the slider-block system.

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“…The parameter d is thus an important one in statements concerning the universality of the left/right tails in the waiting time distribution (see Davidsen and Goltz, 2004;Corral, 2003).…”

Section: Scaling Of T(l×l): An Empirical Approachmentioning

confidence: 99%

“…When (17) has a power-law singularity at zero. The exponent of this power asymptotic is not universal (see an opposite opinion in (Davidsen and Goltz, 2004)). The statistical difficulties inherent in the analysis of small/large deviations and the potential dependence of the answer on the order of the limiting processes in t and L constitute the main sources of contradictory assertions as to the tails of the distribution of ) ( p L t .…”

Section: The Distribution Of T(l×l) For Small Valuesmentioning

confidence: 99%

Seismic Interevent Time: A Spatial Scaling and Multifractality

Molchan

Kronrod

2007

Pure appl. geophys.

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(TK).The optimal scaling problem for the time t(L×L) between two successive events in a seismogenic cell of size L is considered. The quantity t(L×L) is defined for a random cell of a grid covering a seismic region G. We solve that problem in terms of a multifractal characteristic of epicenters in G known as the tau-function or generalized fractal dimensions; the solution depends on the type of cell randomization. Our theoretical deductions are corroborated by California seismicity with magnitude M ≥ 2. In other words, the population of waiting time distributions for L = 10-100 km provides positive information on the multifractal nature of seismicity, which impedes the population to be converted into a unified law by scaling. This study is a follow-up of our analysis of power/unified laws for seismicity (see PAGEOPH 162 (2005), 1135 and GJI 162 (2005, 899). Introduction

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Are seismic waiting time distributions universal?

Cited by 112 publications

References 21 publications

Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece)

Non-extensivity and long-range correlations in the earthquake activity at the West Corinth rift (Greece)

Recurrence and interoccurrence behavior of self-organized complex phenomena

Seismic Interevent Time: A Spatial Scaling and Multifractality

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