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Statistical model for standard seismicity and detection of anomalies by residual analysis
Yosihiko Ogata
- Vol. 57, Iss: 2, pp 348-363
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TLDR
In this paper, a statistical point-process model is derived to describe the standard activity of earthquake occurrences by assuming that general seismicity is given by the superposition of aftershock sequences.Abstract:
A statistical point-process model is derived to describe the standard activity of earthquake occurrences by assuming that general seismicity is given by the superposition of aftershock sequences. The parameters are estimated ty the maximum likelihood method. Using the estimated model, the “residual point process” of the data is defined and used to find the anomalies which are included in the data set but not captured in the considered model for the standard seismicity. For instance, seismic quiescences can be measured quantitatively by using the residual process. Some examples are provided to illustrate such analyses. Furthermore, a time series of the magnitudes on the residual point process is considered, to investigate its dependence either on the time or on the history of the seismicity. By assuming the exponential distribution at each time and modelling of the b- value , we can examine such dependences and estimate them. Two practical examples are shown.read more
Citations
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Journal ArticleDOI
The Centenary of the Omori Formula for a Decay Law of Aftershock Activity
TL;DR: In this article, the problem of fitting the modified Omori formula and related point process models to observational data is discussed mainly, and the problems of fitting these formulae to the observational data are discussed mainly.
Journal ArticleDOI
Space-Time Point-Process Models for Earthquake Occurrences
TL;DR: Several space-time statistical models are constructed based on both classical empirical studies of clustering and some more speculative hypotheses, and the goodness-of-fit of the models, as measured by AIC values, is discussed for two high quality data sets, in different tectonic regions as mentioned in this paper.
Journal ArticleDOI
Seismicity Analysis through Point-process Modeling: A Review
TL;DR: In this paper, the occurrence times of earthquakes can be considered to be a point process, and suitable modeling of the conditional intensity function is useful for the investigation of various statistical features of seismic activity.
Journal ArticleDOI
Space–time ETAS models and an improved extension
Yosihiko Ogata,Jiancang Zhuang +1 more
TL;DR: In this article, the epidemic type aftershock sequence (ETAS) model was proposed and an extended version of the best fitted space-time point-process models for earthquake occurrences was suggested.
Journal ArticleDOI
Detection of precursory relative quiescence before great earthquakes through a statistical model
TL;DR: The Epidemic Type Aftershock-Sequences (ETAS) model as discussed by the authors was proposed to identify patterns in an earthquake sequence in an area, using occurrence time and magnitude data.
References
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TL;DR: In this article, a new estimate minimum information theoretical criterion estimate (MAICE) is introduced for the purpose of statistical identification, which is free from the ambiguities inherent in the application of conventional hypothesis testing procedure.
Journal ArticleDOI
Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes
TL;DR: Several classes of stochastic models for the origin times and magnitudes of earthquakes are discussed and the utility of seismic quiescence for the prediction of a major earthquake is investigated.
Journal ArticleDOI
The Centenary of the Omori Formula for a Decay Law of Aftershock Activity
TL;DR: In this article, the problem of fitting the modified Omori formula and related point process models to observational data is discussed mainly, and the problems of fitting these formulae to the observational data are discussed mainly.
Journal ArticleDOI
Space-Time Point-Process Models for Earthquake Occurrences
TL;DR: Several space-time statistical models are constructed based on both classical empirical studies of clustering and some more speculative hypotheses, and the goodness-of-fit of the models, as measured by AIC values, is discussed for two high quality data sets, in different tectonic regions as mentioned in this paper.
Journal ArticleDOI
Seismicity Analysis through Point-process Modeling: A Review
TL;DR: In this paper, the occurrence times of earthquakes can be considered to be a point process, and suitable modeling of the conditional intensity function is useful for the investigation of various statistical features of seismic activity.