Bias in fitting the ETAS model: a case study based on New Zealand seismicity

Harte, David

doi:10.1093/gji/ggs026

Cited by 51 publications

(48 citation statements)

References 22 publications

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“…In the case of the ETAS model, any information on past events would theoretically improve forecasts at all later times if the ETAS parameters were known and the ETAS model were a perfect description of reality. However, even if the ETAS model is correct, the rather large uncertainties in the parameter estimates due to usually small sample sizes will limit the forecasting ability (Harte 2013;Rhoades 2013). In particular, these uncertainties often result in branching ratios larger than 1 which lead to unrealistic forecasts of seismicity escalating with time.…”

Section: E F F E C T I V E F O R E C a S T I N G P E R I O D T Fmentioning

confidence: 99%

“…While the Omori-Utsu decay generally provides a good fit to the data at short times, its applicability to longer times is questionable (Harte 2013). This raises questions about the duration of the sequence.…”

Section: Introductionmentioning

confidence: 99%

“…A necessary condition for stability of forward simulations is that the aftershock sequences decay sufficiently fast, namely with p > 1. Otherwise the total number of aftershocks would become infinite for long times and the total seismicity would escalate with time (Harte 2013;Zhuang et al 2013). However, physics-based aftershock models predict p ≤ 1 for direct aftershocks, which would lead to unstable solutions of the ETAS model.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: E F F E C T I V E F O R E C a S T I N G P E R I O D T Fmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Statistical estimation of the duration of aftershock sequences

Hainzl¹,

Christophersen

Rhoades

et al. 2016

Geophys. J. Int.

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“…The functional form of the Omori-Utsu law poses challenges: For p ≤ 1 it does not integrate and has to be truncated at a finite triggering time T for the expected number of aftershocks to be finite. Even for 1 < p < 1.2, the aftershock activity can continue for thousands if not millions of years according to the parameters fitted to the early part of aftershock decay (Harte 2013). However, we do not have the data available to test the applicability of the Omori-Utsu law for these time periods.…”

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confidence: 94%

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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“…Often, such pre-determination of model parameters may not be feasible because the seismicity is localized (e.g., reservoir associated seismicity) or the model parameters are spatially inhomogeneous. Aside, owing to the strong dependence between µ(t) and other ETAS model parameters (Harte 2013;Marsan et al 2013a), input of erroneous model parameters to the algorithm would result in biased estimates of the background rate. Therefore, a method that can simultaneously estimate both, the model parameters and the background rate, becomes desirable.…”

Section: Introductionmentioning

confidence: 99%

Non-stationary ETAS to model earthquake occurrences affected by episodic aseismic transients

Kattamanchi

Tiwari

Ramesh

2017

Earth Planets Space

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We present a non-stationary epidemic-type aftershock sequence (ETAS) model in which the usual assumption of stationary background rate is relaxed. Such a model could be used for modeling seismic sequences affected by aseismic transients such as fluid/magma intrusion, slow slip earthquakes (SSEs), etc. The non-stationary background rate is expressed as a linear combination of B-splines, and a method is proposed that allows for simultaneous estimation of background rate as well as other ETAS model parameters. We also present an extension to this non-stationary ETAS model where an adaptive roughness penalty function is used and consequently provides better estimates of rapidly varying background rate functions. The performance of the proposed methods is demonstrated on synthetic catalogs and an application to detect earthquake swarms (possibly associated with SSEs) in Hikurangi margin (North Island, New Zealand) is presented.

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Bias in fitting the ETAS model: a case study based on New Zealand seismicity

Cited by 51 publications

References 22 publications

Statistical estimation of the duration of aftershock sequences

Statistical estimation of the duration of aftershock sequences

Testing alternative temporal aftershock decay functions in an ETAS framework

Non-stationary ETAS to model earthquake occurrences affected by episodic aseismic transients

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