Model for the Distribution of Aftershock Interoccurrence Times

Shcherbakov, R.; Yakovlev, G.; Turcotte, Donald L.; Rundle, John B.

doi:10.1103/physrevlett.95.218501

Cited by 106 publications

(106 citation statements)

References 20 publications

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“…The scaling function exhibits two different regimes. For smaller arguments, it decays as a power law with an exponent ≈0.75 [corresponding to the p value in the OU relation and consistent with the interevent time distribution for small times [57] (not shown)], which is similar to what has been observed in other AE experiments [23,24]. For larger arguments, we find a steeper power-law-like decay with an exponent of about 1.75.…”

Section: Prl 119 068501 (2017) P H Y S I C a L R E V I E W L E T T Esupporting

confidence: 73%

Triggering Processes in Rock Fracture

et al. 2017

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We study triggering processes in triaxial compression experiments under a constant displacement rate on sandstone and granite samples using spatially located acoustic emission events and their focal mechanisms. We present strong evidence that event-event triggering plays an important role in the presence of large-scale or macrocopic imperfections, while such triggering is basically absent if no significant imperfections are present. In the former case, we recover all established empirical relations of aftershock seismicity including the Gutenberg-Richter relation, a modified version of the Omori-Utsu relation and the productivity relation-despite the fact that the activity is dominated by compaction-type events and triggering cascades have a swarmlike topology. For the Gutenberg-Richter relations, we find that the b value is smaller for triggered events compared to background events. Moreover, we show that triggered acoustic emission events have a focal mechanism much more similar to their associated trigger than expected by chance.

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Section: Prl 119 068501 (2017) P H Y S I C a L R E V I E W L E T T Esupporting

confidence: 73%

Triggering Processes in Rock Fracture

et al. 2017

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“…However, ETAS applications are so far based on the assumption of infinite triggering times, which is inconsistent with p ≤ 1 on long timescales, as mentioned above. Previous analysis already indicated that finite aftershock durations can significantly affect the interevent-time distribution (Shcherbakov et al 2005). Here we will show that this inconsistent model assumption can also lead to biased results in ETAS estimation and that applications of the ETAS model with temporally limited aftershock triggering leads to p-value estimates that are more consistent with the rate-and-state friction model.…”

Section: Introductionsupporting

confidence: 55%

Statistical estimation of the duration of aftershock sequences

Hainzl¹,

Christophersen

Rhoades

et al. 2016

Geophys. J. Int.

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S U M M A R YIt is well known that large earthquakes generally trigger aftershock sequences. However, the duration of those sequences is unclear due to the gradual power-law decay with time. The triggering time is assumed to be infinite in the epidemic type aftershock sequence (ETAS) model, a widely used statistical model to describe clustering phenomena in observed earthquake catalogues. This assumption leads to the constraint that the power-law exponent p of the Omori-Utsu decay has to be larger than one to avoid supercritical conditions with accelerating seismic activity on long timescales. In contrast, seismicity models based on rate-and statedependent friction observed in laboratory experiments predict p ≤ 1 and a finite triggering time scaling inversely to the tectonic stressing rate. To investigate this conflict, we analyse an ETAS model with finite triggering times, which allow smaller values of p. We use synthetic earthquake sequences to show that the assumption of infinite triggering times can lead to a significant bias in the maximum likelihood estimates of the ETAS parameters. Furthermore, it is shown that the triggering time can be reasonably estimated using real earthquake catalogue data, although the uncertainties are large. The analysis of real earthquake catalogues indicates mainly finite triggering times in the order of 100 days to 10 years with a weak negative correlation to the background rate, in agreement with expectations of the rate-and state-friction model. The triggering time is not the same as the apparent duration, which is the time period in which aftershocks dominate the seismicity. The apparent duration is shown to be strongly dependent on the mainshock magnitude and the level of background activity. It can be much shorter than the triggering time. Finally, we perform forward simulations to estimate the effective forecasting period, which is the time period following a mainshock, in which ETAS simulations can improve rate estimates after the occurrence of a mainshock. We find that this effective forecasting period is only in the order of 100 days for moderate mainshocks and in the order of a few years for large events, even if the underlying triggering process lasts much longer.

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“…This is in direct analogy to the behavior of our stiff slider-block model. There is also observational evidence that the interoccurrence times between all earthquakes in a region (on many different faults) satisfy Poissonian statistics (Shcherbakov, et al, 2005). This is in direct analogy to the behavior of our soft slider-block model.…”

Section: Discussionmentioning

confidence: 68%

“…These authors fit a Weibull distribution to this data and found that τ =166.1±44.5 years and γ =1.50±0.80. Although the fits of the Weibull distribution were quite good in both these cases, the number of events were not sufficient to establish the validity of the Weibull distribution over alternative distributions (Savage, 1994).…”

Section: Weibull Distributionmentioning

confidence: 99%

“…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. The earthquakes occur randomly but the rate of occurrence is determined by Omori's law for the temporal decay of aftershock activity.…”

Section: Introductionmentioning

confidence: 99%

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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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Model for the Distribution of Aftershock Interoccurrence Times

Cited by 106 publications

References 20 publications

Triggering Processes in Rock Fracture

Triggering Processes in Rock Fracture

Statistical estimation of the duration of aftershock sequences

Recurrence and interoccurrence behavior of self-organized complex phenomena

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