9:15 AM - 9:30 AM
[SSS08-02] The ETAS model can explain both foreshock and the Båth Law
Keywords:ETAS model, stochastic reconstruction, asymptotics, forecast
Earthquake clustering is a well-known phenomenon, which is associated with foreshocks, aftershock sequences, and earthquake swarms. Among research into earthquake clusters, the foreshock phenomenon has long been of interest, for the reason of its potential usefulness in predicting damaging earthquakes. Another well-known empirical law among research into earthquake clusters is the Båth law, which asserts that the magnitude difference of the mainshock and the largest aftershock has a median of 1.2. This law is useful for evaluating the possible loss caused by aftershocks.
Since both the foreshock and the Båth law use the largest event within a given earthquake cluster (i.e. the mainshock) as the reference, they cannot be clearly specified until the ending of the clusters. It is under argument whether they are independent principal features of earthquake clustering or whether they can be derived by other simpler, known laws related to seismicity.
On the other hand, the Epidemic Type Aftershock Sequence (ETAS) model, which was originally designed for describing the mainshock-and-aftershock sequence (Ogata, 1988, 1998), in which mainshocks, aftershocks, and foreshocks have no difference in terms of their behaviors related to triggering further events, has been widely used by researchers as a new standard baseline for testing hypotheses associated with earthquake clustering (e.g. Zhuang et al. 2004). The rigorous mathematical formulation of this model makes it possible to theoretically evaluate to what degree the ETAS model can explain the foreshock observations and the Båth law.
This talk discusses to what degree the ETAS model can explain the foreshock phenomenon and the Båth law. Based on the ETAS model, which is a branching model with two empirical exponential laws, the positive exponential law for the expected number of earthquakes that an earthquake can trigger, and the well-known Gutenberg-Richter law (negative exponential distribution) for earthquake magnitude, this study shows that the magnitude distribution of the largest descendant from a given event determines the foreshock probabilities and deduces the Båth law from the asymptotic form of this magnitude distribution, both of which are close to the values of actual seismicity data. I also comment on the recent results obtained in previous research.
Main references
Ogata, Y. (1988), Statistical models for earthquake occurrences and residual analysis for point processes, Journal of the American Statistical Association, 83(401), 9–27.
Ogata, Y. (1998), Space-time point-process models for earthquake occurrences, Annals of the Institute of Statistical Mathematics, 50(2), 379–402.
Zhuang, J., Y. Ogata, and D. Vere-Jones (2004), Analyzing earthquake clustering features by using stochastic reconstruction, Journal of Geophysical Research, 109(3), B05301
Zhuang, J., A. Christophersen, M. K. Savage, D. Vere-Jones, Y. Ogata, and D. D. Jackson (2008), Differences between spontaneous and triggered earthquakes: Their influences on foreshock probabilities, Journal Geophysical Research, 113(B12), doi:10.1029/2008JB005579.
Zhuang J. (2021). Explaining foreshock and the Båth law using a generic earthquake clustering model. In Statistical Methods and modelling of seismogenesis, N. Limnios, E. Papadimitriou, G. Tsaklidis. Iste.
Since both the foreshock and the Båth law use the largest event within a given earthquake cluster (i.e. the mainshock) as the reference, they cannot be clearly specified until the ending of the clusters. It is under argument whether they are independent principal features of earthquake clustering or whether they can be derived by other simpler, known laws related to seismicity.
On the other hand, the Epidemic Type Aftershock Sequence (ETAS) model, which was originally designed for describing the mainshock-and-aftershock sequence (Ogata, 1988, 1998), in which mainshocks, aftershocks, and foreshocks have no difference in terms of their behaviors related to triggering further events, has been widely used by researchers as a new standard baseline for testing hypotheses associated with earthquake clustering (e.g. Zhuang et al. 2004). The rigorous mathematical formulation of this model makes it possible to theoretically evaluate to what degree the ETAS model can explain the foreshock observations and the Båth law.
This talk discusses to what degree the ETAS model can explain the foreshock phenomenon and the Båth law. Based on the ETAS model, which is a branching model with two empirical exponential laws, the positive exponential law for the expected number of earthquakes that an earthquake can trigger, and the well-known Gutenberg-Richter law (negative exponential distribution) for earthquake magnitude, this study shows that the magnitude distribution of the largest descendant from a given event determines the foreshock probabilities and deduces the Båth law from the asymptotic form of this magnitude distribution, both of which are close to the values of actual seismicity data. I also comment on the recent results obtained in previous research.
Main references
Ogata, Y. (1988), Statistical models for earthquake occurrences and residual analysis for point processes, Journal of the American Statistical Association, 83(401), 9–27.
Ogata, Y. (1998), Space-time point-process models for earthquake occurrences, Annals of the Institute of Statistical Mathematics, 50(2), 379–402.
Zhuang, J., Y. Ogata, and D. Vere-Jones (2004), Analyzing earthquake clustering features by using stochastic reconstruction, Journal of Geophysical Research, 109(3), B05301
Zhuang, J., A. Christophersen, M. K. Savage, D. Vere-Jones, Y. Ogata, and D. D. Jackson (2008), Differences between spontaneous and triggered earthquakes: Their influences on foreshock probabilities, Journal Geophysical Research, 113(B12), doi:10.1029/2008JB005579.
Zhuang J. (2021). Explaining foreshock and the Båth law using a generic earthquake clustering model. In Statistical Methods and modelling of seismogenesis, N. Limnios, E. Papadimitriou, G. Tsaklidis. Iste.