Earthquakes: Recurrence and Interoccurrence Times

Abaimov, Sergey G.; Turcotte, Donald L.; Shcherbakov, R.; Rundle, John B.; Yakovlev, G.; Goltz, Christian; Newman, William I.

doi:10.1007/s00024-008-0331-y

Cited by 51 publications

(38 citation statements)

References 56 publications

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“…It was shown that the time-interval distribution of the system-wide events obeys the Weibull distribution [16,20]. This enables us to the conjecture that the Weibull distribution is induced from the enhancement of the average event size,S.…”

Section: E the Onset Mechanism Of The Weibull Distributionmentioning

confidence: 95%

The Weibull–log Weibull transition of the interoccurrence time statistics in the two-dimensional Burridge–Knopoff Earthquake model

Hasumi¹,

Akimoto²,

Aizawa³

2009

Physica A: Statistical Mechanics and its Applications

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In analyzing synthetic earthquake catalogs created by a two-dimensional Burridge-Knopoff model, we have found that a probability distribution of the interoccurrence times, the time intervals between successive events, can be described clearly by the superposition of the Weibull distribution and the log-Weibull distribution. In addition, the interoccurrence time statistics depend on frictional properties and stiffness of a fault and exhibit the Weibull -log Weibull transition, which states that the distribution function changes from the log-Weibull regime to the Weibull regime when the threshold of magnitude is increased. We reinforce a new insight into this model; the model can be recognized as a mechanical model providing a framework of the Weibull -log Weibull transition.

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Section: E the Onset Mechanism Of The Weibull Distributionmentioning

confidence: 95%

The Weibull–log Weibull transition of the interoccurrence time statistics in the two-dimensional Burridge–Knopoff Earthquake model

Hasumi¹,

Akimoto²,

Aizawa³

2009

Physica A: Statistical Mechanics and its Applications

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“…Each of the three object areas in the three seismic zones have three scenarios, which are categorized by the average recurrence interval with Ms ≥ 6.5, Ms ≥ 7.0, and Ms ≥ 7.5 in every seismic zone. Moreover, References [51,52] defined recurrence interval as the mean value of the time intervals between each historical earthquake event for a given region with a magnitude more than a specified value. However, as the magnitude increases, it becomes more apparent that the seismic data are not complete enough, by which the length of the return period cannot be correctly reflected.…”

Section: Definition Of Scenarios and Recurrence Intervalsmentioning

confidence: 99%

Using RISKPLAN for Earthquake Risk Assessment in Sichuan Province, China

Yan

Seeland

2019

Sustainability

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Sichuan Province of China is a prominent population and economic growth center as well as an earthquake-stricken region. A sound understanding of the seismic risk that Sichuan Province is facing is useful to raise risk awareness, achieve disaster risk reduction (DRR), and guarantee sustainable socio-economic development. Earthquake risk assessment is the first step in these efforts. This study strives to demonstrate the feasibility of applying an integrated earthquake risk assessment in Sichuan Province of China using RISKPLAN, a risk evaluation tool of natural hazards developed by the Swiss Federal Office for the Environment (FOEN). The time and location of seismic events in Sichuan were incorporated into three scenarios and calculated with respect to expected losses under different assumed conditions of earthquake occurrence, such as the recurrence interval and magnitude. Furthermore, cost-effectiveness calculations were made regarding the various possible scenarios to assess the ratio of expected losses and the required financial means for prevention and mitigation measures against the effects of seismic activities in Sichuan. Our results show that when the magnitude of the seismic event is greater than expected, reduction and mitigation investments for a possible earthquake risk will be all the more rewarding.

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“…Several studies of earthquake catalogues and simulations show that the Weibull distribution is a good match for the empirical return intervals distribution [25][26][27][28][29][30][31][32][33][34]. In addition to statistical analysis, arguments supporting the Weibull distribution are based on Extreme Value Theory [35], numerical simulations of slider-block models [32], and growth-decay mod-els governed by the geometric Langevin equation [6]. The Weibull distribution is also used to model the fracture strength of brittle and quasibrittle engineered materials [36][37][38] and geologic media [39].…”

Section: A Earthquake Return Intervalsmentioning

confidence: 99%

Finite-size effects on return interval distributions for weakest-link-scaling systems

2014

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The Weibull distribution is a commonly used model for the strength of brittle materials and earthquake return intervals. Deviations from Weibull scaling, however, have been observed in earthquake return intervals and the fracture strength of quasibrittle materials. We investigate weakest-link scaling in finite-size systems and deviations of empirical return interval distributions from the Weibull distribution function. Our analysis employs the ansatz that the survival probability function of a system with complex interactions among its units can be expressed as the product of the survival probability functions for an ensemble of representative volume elements (RVEs). We show that if the system comprises a finite number of RVEs, it obeys the κ-Weibull distribution. The upper tail of the κ-Weibull distribution declines as a power law in contrast with Weibull scaling. The hazard rate function of the κ-Weibull distribution decreases linearly after a waiting time τ(c) ∝ n(1/m), where m is the Weibull modulus and n is the system size in terms of representative volume elements. We conduct statistical analysis of experimental data and simulations which show that the κ Weibull provides competitive fits to the return interval distributions of seismic data and of avalanches in a fiber bundle model. In conclusion, using theoretical and statistical analysis of real and simulated data, we demonstrate that the κ-Weibull distribution is a useful model for extreme-event return intervals in finite-size systems.

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Earthquakes: Recurrence and Interoccurrence Times

Cited by 51 publications

References 56 publications

The Weibull–log Weibull transition of the interoccurrence time statistics in the two-dimensional Burridge–Knopoff Earthquake model

The Weibull–log Weibull transition of the interoccurrence time statistics in the two-dimensional Burridge–Knopoff Earthquake model

Using RISKPLAN for Earthquake Risk Assessment in Sichuan Province, China

Finite-size effects on return interval distributions for weakest-link-scaling systems

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