17:15 〜 19:15
[SSS12-P19] 非定常化された時空間ETASモデル
キーワード：ETASモデル、非定常性、ベイズ推定、平滑化拘束、ABIC
The (original) epidemic-type aftershock sequence (ETAS) model developed by Ogata [1988] is widely used for the analysis of the temporal occurrence pattern of earthquakes. Then, Ogata [1998] extended this model to the space-time version. The background seismicity in the space-time ETAS model has spatial variability, whereas it does not have temporal variability. This study incorporates the temporal change for the background seismicity into the space-time ETAS model.
For simplicity, the background seismicity is assumed to be a product of the temporal and spatial variations such as μΤ(t)μs(x, y). Then, similar to Kumazawa and Ogata [2014], which introduced the time-varying background seismicity into the original ETAS model (i.e., the non-stationary ETAS model), μΤ(t) is represented by a piecewise linear function [e.g., Powell, 1981; Iwata, 2008] of which breaking points were taken at the occurrence times of each of the earthquakes. Then, using a Bayesian approach with a smoothness constraint, μΤ(t) was estimated; the strength of the smoothness constraint was optimized through the maximization of a marginal likelihood.
As a demonstration, the developed non-stationary space-time ETAS model was applied to the swarm-like activity that occurred in the aftershock sequence of the 2018 Hokkaido Eastern Iburi earthquake since the beginning of October 2018. The spatial variation μs(x, y) was obtained by the kernel density estimation, and then μΤ(t) was estimated with the aforementioned framework. As a result of the analysis, the estimated μΤ(t) shows a temporal decay. The ABIC (Akaike's Bayesian Information Criterion) value of the non-stationary space-time ETAS model is 3.28 smaller than that of the stationary (i.e., constant μΤ(t)) space-time ETAS model, suggesting that the temporal decay in the background seismicity is significant.
References
- Iwata, 2008, Geophys. J. Int., doi:10.1111/j.1365-246X.2008.03864.x
- Kumazawa and Ogata, 2014, Ann. Appl. Stat., doi:10.1214/14-AOAS759
- Ogata, 1988, J. Amer. Stat. Assoc., doi:10.1080/01621459.1988.10478560
- Ogata, 1998, Ann. Inst. Stat. Math., doi:10.1023/A:1003403601725
- Powell, 1981, Approximation Theory and Methods, Cambridge Univ. Press
For simplicity, the background seismicity is assumed to be a product of the temporal and spatial variations such as μΤ(t)μs(x, y). Then, similar to Kumazawa and Ogata [2014], which introduced the time-varying background seismicity into the original ETAS model (i.e., the non-stationary ETAS model), μΤ(t) is represented by a piecewise linear function [e.g., Powell, 1981; Iwata, 2008] of which breaking points were taken at the occurrence times of each of the earthquakes. Then, using a Bayesian approach with a smoothness constraint, μΤ(t) was estimated; the strength of the smoothness constraint was optimized through the maximization of a marginal likelihood.
As a demonstration, the developed non-stationary space-time ETAS model was applied to the swarm-like activity that occurred in the aftershock sequence of the 2018 Hokkaido Eastern Iburi earthquake since the beginning of October 2018. The spatial variation μs(x, y) was obtained by the kernel density estimation, and then μΤ(t) was estimated with the aforementioned framework. As a result of the analysis, the estimated μΤ(t) shows a temporal decay. The ABIC (Akaike's Bayesian Information Criterion) value of the non-stationary space-time ETAS model is 3.28 smaller than that of the stationary (i.e., constant μΤ(t)) space-time ETAS model, suggesting that the temporal decay in the background seismicity is significant.
References
- Iwata, 2008, Geophys. J. Int., doi:10.1111/j.1365-246X.2008.03864.x
- Kumazawa and Ogata, 2014, Ann. Appl. Stat., doi:10.1214/14-AOAS759
- Ogata, 1988, J. Amer. Stat. Assoc., doi:10.1080/01621459.1988.10478560
- Ogata, 1998, Ann. Inst. Stat. Math., doi:10.1023/A:1003403601725
- Powell, 1981, Approximation Theory and Methods, Cambridge Univ. Press