Static stress triggering explains the empirical aftershock distance decay

Hainzl, Sebastian; Moradpour, Javad; Davidsen, Jörn

doi:10.1002/2014gl061975

Cited by 26 publications

(26 citation statements)

References 28 publications

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“…A generic attribute in all these cases is that one event can trigger or somehow induce another one to occur -or possibly numerous further events. One of the most prominent examples of such event-event triggering are aftershocks [32,33,34,35,36,37,13]. Aftershock sequences are characterized by timevarying (local) event rates, which are often empirically found to approximately followacross a wide range of scales and systems from friction and fracture to socio-economic systems [35,38,39,40,41,7,9,10,16,27,28,29,30,31] -the Omori-Utsu (OU) relation,…”

Section: Event-event Triggering and Aftershocksmentioning

confidence: 99%

Are triggering rates of labquakes universal? Inferring triggering rates from incomplete information

Ardanuy

Davidsen

2017

Eur. Phys. J. Spec. Top.

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The acoustic emission activity associated with recent rock fracture experiments under different conditions has indicated that some features of event-event triggering are independent of the details of the experiment and the materials used and are often even indistinguishable from tectonic earthquakes. While the event-event triggering rates or aftershock rates behave pretty much identical for all rock fracture experiments at short times, this is not the case for later times. Here, we discuss how these differences can be a consequence of the aftershock identification method used and show that the true aftershock rates might have two distinct regimes. Specifically, tests on a modified Epidemic Type Aftershock Sequence model show that the model rates cannot be correctly inferred at late times based on temporal information only if the activity rates or the branching ratio are high. We also discuss both the effect of the two distinct regimes in the aftershock rates and the effect of the background rate on the inter-event time distribution. Our findings should be applicable for inferring event-event triggering rates for many other types of triggering and branching processes as well.

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Section: Event-event Triggering and Aftershocksmentioning

confidence: 99%

Are triggering rates of labquakes universal? Inferring triggering rates from incomplete information

Ardanuy

Davidsen

2017

Eur. Phys. J. Spec. Top.

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“…For this purpose, we calculate for all earthquakes in the catalogue, the fraction w of aftershocks which is expected to occur in the study region by means of the empirical probability density distribution recently derived for California seismicity , which has been also found to be in agreement with static stress triggering . Although the spatial distribution function has so far been fitted only to California data, Hainzl et al (2014) showed in their electronic material that the distribution is not strongly dependent on the focal mechanism. Thus we use it for all empirical data.…”

Section: Sequence Selectionmentioning

confidence: 99%

Testing alternative temporal aftershock decay functions in an ETAS framework

Hainzl

Christophersen

2017

Geophysical Journal International

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S U M M A R YEarthquake clustering can be well described by the Epidemic Type Aftershock Sequence model (ETAS), where each earthquake potentially triggers its own aftershocks. The temporal decay of aftershocks is most commonly modelled with a power law, the so-called Omori-Utsu law. However, new results suggest that alternative decay functions may be more appropriate. One recent study found that a version of the ETAS model fitted the data better when the OmoriUtsu law was truncated in time. A finite triggering time is consistent with the rate-state model that expects an exponential roll-off after a finite time following the initial power law decay. Another recent study compared a power law, pure exponential and stretched exponential and found that the stretched exponential described the overall decay of aftershocks best. Our aim is to find the best temporal aftershock decay function within the ETAS model framework. We investigate six decay functions; three power laws and three exponential decays. The power laws are an unlimited Omori-Utsu law, a sharply truncated Omori-Utsu law, and an exponential roll-off consistent with the rate-state friction model. The exponential decay functions are the pure exponential, stretched exponential and a modified stretched exponential. We fit model parameters for each decay function to 326 individual earthquake sequences from four regional and one global earthquake catalogue. The three models that fit most of the sequences the best are the truncated Omori-Utsu law (32 per cent of sequences), the power law based on the rate-state friction model (26 per cent) and the unlimited Omori-Utsu law (23 per cent). When the parameters are not fitted individually but the median model parameters are used for each function, the modified stretched exponential function fits most (28 per cent) sequences the best, followed by the unlimited Omori-Utsu law (22 per cent) and the stretched exponential (18 per cent). However, the majority of sequences (53 per cent) is still best fit by a power law. Out of all the tested decay functions, the one based on the rate-state friction model is the only one that performs in a majority of cases better than the Omori-Utsu law for fixed parameters. This suggests that it could be a potential candidate to replace the unlimited Omori-Utsu law in ETAS-model-based earthquake forecasts.Key words: Earthquake hazards; Earthquake interaction, forecasting, and prediction; Statistical seismology. I N T RO D U C T I O NAftershocks occur after almost all large shallow earthquakes and can cause further damages as for example in the Canterbury sequence, New Zealand (Bannister & Gledhill 2012). Although aftershocks are most abundant shortly after the mainshock, they can continue to occur with decaying rate for months and years. Therefore, the specific functional form of the temporal decay is of crucial importance for time-varying seismic hazard assessments.The decay of aftershocks is most commonly modelled by the Omori-Utsu law, a power law, which can present some challenges in p...

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“…Note that this empirical distribution is found to be in agreement with static stress triggering . Although the spatial distribution function has so far been fitted only to California data, Hainzl et al (2014) showed in their electronic material that the distribution is not strongly dependent on the focal mechanism. Thus we use eq.…”

Section: Cluster Selectionmentioning

confidence: 99%

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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Static stress triggering explains the empirical aftershock distance decay

Cited by 26 publications

References 28 publications

Are triggering rates of labquakes universal? Inferring triggering rates from incomplete information

Are triggering rates of labquakes universal? Inferring triggering rates from incomplete information

Testing alternative temporal aftershock decay functions in an ETAS framework

Statistical estimation of the duration of aftershock sequences

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