ETAS (the epidemic-type aftershock sequence model)

The ETAS modeling can be used in order to identify the background as well as the triggered component of seismicity.

seismicity patternsstatistical modelingstress triggeringfluid flowsearthquake swarmearthquake modeling

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Contributor(s)

Initial contribute: 2019-06-24

Authorship

:  
Institute of Geo Sciences, University of Potsdam, Potsdam, Germany
:  
hainzl@geo.uni-potsdam.de
:  
Institute of Statistical Mathematics, Tokyo, Japan
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Application-focused categoriesNatural-perspectiveSolid-earth regions

Detailed Description

English {{currentDetailLanguage}} English
Quoted from: Sebastian Hainzl and Yosihiko Ogata, 2005. Detecting fluid signals in seismicity data through statistical earthquake modeling. Journal of Geophysical Research Solid Earth. https://doi.org/10.1029/2004JB003247 
 
The estimation of the five parameters (λ00, α, ) of the ETAS model (equation (3)) is carried out by the maximum likelihood method. The log likelihood with respect to the occurrence times of the earthquakes is given by
equation image
where and define the starting and the ending time of the activity [Ogata , 1993].

[23] Model selection, particularly the determination of the number of parameters, is carried out using the Akaike information criterion (AIC) [Akaike , 1974Parzen et al. , 1998]. The statistic AIC = −2 MLL + 2is computed for each of the models fit to the same data, where MLL is the maximum log likelihood value with respect to the parameters, and k is the total number of fitted parameters. In comparing models with different numbers of parameters, addition of the quantity 2roughly compensates for the additional flexibility which the extra parameters provide. The model with the lower AIC value is taken as giving the better choice for forward prediction purposes. Insofar as it depends on the likelihood ratio, the AIC can also be used as a rough guide for testing the model. In testing a model with parameters against a null hypothesis with just parameters, we take a difference of 2 in AIC values as a rough estimate of significance at the 5% level. An alternative to the Akaike information criterion is the modified version of Schwarz's information criterion, BIC = MLL − 0.5ln(/2π), where is the number of events [Main et al. , 1999]. In this case, the best model has the largest BIC value. The BIC criterion has been shown to be superior in the case of larger data sets [Koehler and Murphree , 1988].

--Please refer to "Detecting fluid signals in seismicity data through statistical earthquake modeling"

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Sebastian Hainzl, Yosihiko Ogata (2019). ETAS (the epidemic-type aftershock sequence model), Model Item, OpenGMS, https://geomodeling.njnu.edu.cn/modelItem/994a5b22-e7d3-4e10-9e79-9690aa1ad7f8
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Contributor(s)

Initial contribute : 2019-06-24

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Authorship

:  
Institute of Geo Sciences, University of Potsdam, Potsdam, Germany
:  
hainzl@geo.uni-potsdam.de
:  
Institute of Statistical Mathematics, Tokyo, Japan
Is authorship not correct? Feed back

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