Estimating the ETAS model from an early aftershock sequence

Omi, Takahiro; Ogata, Yosihiko; Hirata, Yoshito; Aihara, Kazuyuki

doi:10.1002/2013gl058958

Cited by 65 publications

(59 citation statements)

References 22 publications

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“…Omi et al . [, ] model aftershock incompleteness for each individual aftershock sequence, rather than for a whole earthquake catalog, but they only use the temporal ETAS formulation.…”

Section: Introductionmentioning

confidence: 99%

Estimating ETAS: The effects of truncation, missing data, and model assumptions

et al. 2017

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The Epidemic‐Type Aftershock Sequence (ETAS) model is widely used to describe the occurrence of earthquakes in space and time, but there has been little discussion dedicated to the limits of, and influences on, its estimation. Among the possible influences we emphasize in this article the effect of the cutoff magnitude, Mcut, above which parameters are estimated; the finite length of earthquake catalogs; and missing data (e.g., during lively aftershock sequences). We analyze catalogs from Southern California and Italy and find that some parameters vary as a function of Mcut due to changing sample size (which affects, e.g., Omori's c constant) or an intrinsic dependence on Mcut (as Mcut increases, absolute productivity and background rate decrease). We also explore the influence of another form of truncation—the finite catalog length—that can bias estimators of the branching ratio. Being also a function of Omori's p value, the true branching ratio is underestimated by 45% to 5% for 1.05 < p < 1.2. Finite sample size affects the variation of the branching ratio estimates. Moreover, we investigate the effect of missing aftershocks and find that the ETAS productivity parameters (α and K0) and the Omori's c and p values are significantly changed for Mcut < 3.5. We further find that conventional estimation errors for these parameters, inferred from simulations that do not account for aftershock incompleteness, are underestimated by, on average, a factor of 8.

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“…Omi et al . [, ] model aftershock incompleteness for each individual aftershock sequence, rather than for a whole earthquake catalog, but they only use the temporal ETAS formulation.…”

Section: Introductionmentioning

confidence: 99%

Estimating ETAS: The effects of truncation, missing data, and model assumptions

et al. 2017

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“…and Iwata 2008Iwata , 2013Iwata , 2014 and developed methods of making probabilistic earthquake forecasting with missing earthquakes taken into account (e.g., Ogata 2006;Omi et al 2013Omi et al , 2014Omi et al , 2015. A non-Bayesian procedure that corrects such temporally varying incomplete detection of earthquakes can be found in Marsan and Enescu (2012), where they assumed that the b-value is constant and that the occurrence rate of earthquakes follows the Omori-Utsu formula or the ETAS model.…”

Section: Introductionmentioning

confidence: 99%

Data completeness of the Kumamoto earthquake sequence in the JMA catalog and its influence on the estimation of the ETAS parameters

Zhuang

Ogata

Wang

2017

Earth Planets Space

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This study investigates the missing data problem in the Japan Meteorological Agency catalog of the Kumamoto aftershock sequence, which occurred since April 15, 2016, in Japan. Based on the assumption that earthquake magnitudes are independent of their occurrence times, we replenish the short-term missing data of small earthquakes by using a bi-scale transformation and study their influence on the maximum likelihood estimate (MLE) of the epidemic-type aftershock sequences (ETAS) parameters by comparing the analysis results from the original and the replenished datasets. The results show that the MLEs of the ETAS parameters vary when this model is fitted to the recorded catalog with different cutoff magnitudes, while those MLEs remain stable for the replenished dataset. Further analysis shows that the seismicity becomes quiescent after the occurrence of the second major shock, which can be regarded as a precursory phenomenon of the occurrence of the subsequent M J 7.3 mainshock. This relative quiescence is demonstrated more clearly by the analysis of the replenished dataset.

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“…If the detection rates of aftershocks regarding magnitudes are same throughout the target period, we can make use of a homogeneous dataset under a smaller threshold magnitude instead of the dataset of completely detected threshold magnitudes to allow less-uncertain inference and prediction Katsura 1993, 2006). It is also desirable to recover information on missing aftershocks using modeling of detection rates, particularly in the early stage of aftershocks (Omi et al 2013(Omi et al , 2014a.…”

Section: Seismicity Quiescence and Empirical Medium-term Forecastingmentioning

confidence: 99%

Statistical monitoring of aftershock sequences: a case study of the 2015 Mw7.8 Gorkha, Nepal, earthquake

Ogata

Tsuruoka

2016

Earth Planets Space

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Early forecasting of aftershocks has become realistic and practical because of real-time detection of hypocenters. This study illustrates a statistical procedure for monitoring aftershock sequences to detect anomalies to increase the probability gain of a significantly large aftershock or even an earthquake larger than the main shock. In particular, a significant lowering (relative quiescence) in aftershock activity below the level predicted by the Omori-Utsu formula or the epidemic-type aftershock sequence model is sometimes followed by a large earthquake in a neighboring region. As an example, we detected significant lowering relative to the modeled rate after approximately 1.7 days after the main shock in the aftershock sequence of the Mw7.8 Gorkha, Nepal, earthquake of April 25, 2015. The relative quiescence lasted until the May 12, 2015, M7.3 Kodari earthquake that occurred at the eastern end of the primary aftershock zone. Space-time plots including the transformed time can indicate the local places where aftershock activity lowers (the seismicity shadow). Thus, the relative quiescence can be hypothesized to be related to stress shadowing caused by probable slow slips. In addition, the aftershock productivity of the M7.3 Kodari earthquake is approximately twice as large as that of the M7.8 main shock.

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Estimating the ETAS model from an early aftershock sequence

Cited by 65 publications

References 22 publications

Estimating ETAS: The effects of truncation, missing data, and model assumptions

Estimating ETAS: The effects of truncation, missing data, and model assumptions

Data completeness of the Kumamoto earthquake sequence in the JMA catalog and its influence on the estimation of the ETAS parameters

Statistical monitoring of aftershock sequences: a case study of the 2015 Mw7.8 Gorkha, Nepal, earthquake

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