A non‐stationary epidemic type aftershock sequence model for seismicity prior to the December 26, 2004 <i>M</i> 9.1 Sumatra‐Andaman Islands mega‐earthquake

Bansal, A. R.; Ogata, Yosihiko

doi:10.1002/jgrb.50068

Cited by 32 publications

(17 citation statements)

References 52 publications

(71 reference statements)

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“…If AIC 12 is smaller, the two-stage ETAS model with the change point T 0 fits better than the ETAS model applied to the whole interval. The quantity q monotonically depends on sample size (number of earthquakes in the whole period [S, T ]) when searching for the maximum likelihood estimate of the change point [Ogata (1992[Ogata ( , 1999, Kumazawa, Ogata and Toda (2010), Bansal and Ogata (2013)]. This penalty term q, as well as an increased number of estimated parameters, imposes a hurdle for a change point to be significant, and it is usually rejected when the one-stage ETAS model fits sufficiently well.…”

Section: Theoretical Cumulative Intensity Function and Time Transformmentioning

confidence: 99%

Nonstationary ETAS models for nonstandard earthquakes

Kumazawa¹,

Ogata²

2014

Ann. Appl. Stat.

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The conditional intensity function of a point process is a useful tool for generating probability forecasts of earthquakes. The epidemic-type aftershock sequence (ETAS) model is defined by a conditional intensity function, and the corresponding point process is equivalent to a branching process, assuming that an earthquake generates a cluster of offspring earthquakes (triggered earthquakes or so-called aftershocks). Further, the size of the first-generation cluster depends on the magnitude of the triggering (parent) earthquake. The ETAS model provides a good fit to standard earthquake occurrences. However, there are nonstandard earthquake series that appear under transient stress changes caused by aseismic forces such as volcanic magma or fluid intrusions. These events trigger transient nonstandard earthquake swarms, and they are poorly fitted by the stationary ETAS model. In this study, we examine nonstationary extensions of the ETAS model that cover nonstandard cases. These models allow the parameters to be time-dependent and can be estimated by the empirical Bayes method. The best model is selected among the competing models to provide the inversion solutions of nonstationary changes. To address issues of the uniqueness and robustness of the inversion procedure, this method is demonstrated on an inland swarm activity induced by the 2011 Tohoku-Oki, Japan earthquake of magnitude 9.0.Comment: Published in at http://dx.doi.org/10.1214/14-AOAS759 the Annals of Applied Statistics (http://www.imstat.org/aoas/) by the Institute of Mathematical Statistics (http://www.imstat.org

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Section: Theoretical Cumulative Intensity Function and Time Transformmentioning

confidence: 99%

Nonstationary ETAS models for nonstandard earthquakes

Kumazawa¹,

Ogata²

2014

Ann. Appl. Stat.

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“…Some evidence for strain accumulation has been suggested based on a single measurement of Global Positioning System (GPS) velocity (Paul et al, 2001) and the available earthquake data from the global catalog (Nuannin et al, 2005;Bansal and Ogata, 2013). Here, we present the evidence of strain accumulation in the Andaman region from GPS and tide gauge measurements made prior to the 2004 Sumatra-Andaman earthquake.…”

Section: Introductionmentioning

confidence: 92%

“…In addition, the b value decreased significantly in the earthquake nucleation zone in the Sumatra and in the North Andaman region (Nuannin et al, 2005) in the two years preceding the 2004 earthquake. Bansal and Ogata (2013) identified a general increase in background seismicity rate, which commenced in July 2000 in the epicentral region. GPS Measurements Prior to the 2004 Earthquake GPS measurements in the Sumatra region began in 1991 (Prawirodirdjo et al, 1997;Bock et al, 2003).…”

Section: Introductionmentioning

confidence: 96%

Evidence of Strain Accumulation in the Andaman Region for the Giant 2004 Sumatra Andaman Earthquake

Catherine

Gahalaut

Srinivas

et al. 2013

Bulletin of the Seismological Society of America

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We report results of Global Positioning System (GPS) and tide gauge data from the Andaman region that pertain to the period before the 26 December 2004 Sumatra-Andaman earthquake (M w 9.2). In the preceding 40 years, seismicity in the frontal arc region was generally very low, implying locking of the main thrust zone. The campaign mode GPS data support strain accumulation in the region, corresponding to a slip deficit rate of about 3 cm=year. However, the tide-gauge data of the preceding three years from the earthquake indicate land subsidence at a rate of about 3:3 cm=year, whereas uplift was expected in the period prior to the earthquake, as the region experienced coseismic subsidence during the earthquake.

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“…With this criterion, the model with a smaller value of the AIC is expected to perform better prediction. The difference in the AIC values, ΔAIC, between the two competing models is useful, because exp{− ΔAIC/2} can be interpreted as the relative probability of how the model with the smaller AIC value is superior to the other, see the selected papers of Akaike (Parzen et al 1998 or maximize the likelihood (e.g., Bansal and Ogata 2013) with respect to the change-point candidate parameter T 0 , which can be called the MLE of the change-point with respect to the time.…”

Section: Statistical Models To Monitor Aftershock Sequencesmentioning

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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A non‐stationary epidemic type aftershock sequence model for seismicity prior to the December 26, 2004 M 9.1 Sumatra‐Andaman Islands mega‐earthquake

Cited by 32 publications

References 52 publications

Nonstationary ETAS models for nonstandard earthquakes

Nonstationary ETAS models for nonstandard earthquakes

Evidence of Strain Accumulation in the Andaman Region for the Giant 2004 Sumatra Andaman Earthquake

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

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