[S09] AM-1

[S09-10] A hypocentral version of the spherical space-time ETAS model

*Yongbo Li¹, Jiancang Zhuang², Shi Chen¹ (1. Institute of Geophysics, China Earthquake Administration, 2. The Institute of Statistical Mathematics, Research Organization of Information and Systems)

Abstract: Earthquake events are often characterized by certain statistical patterns in both time and space, particularly concerning major earthquakes and their subsequent aftershocks. Omori (1894) was the first to introduce an empirical formula for describing the number of aftershocks that occur over a period following the main shock. Ogata (1988; 1998) further advanced this field by proposing the Epidemic-Type Aftershock Sequence (ETAS) model, which treats earthquake events as point processes. Subsequent refinements of the ETAS model were carried out by Zhuang et al. (2002; 2004); Zhuang (2005); Ogata and Zhuang (2006). Guo et al. (2015) introduced a beta distribution to simulate the depth characteristics of triggered events and proposed the 3D ETAS model. Through stochastic reconstruction, Guo, Zhuang et al. (2015) illustrated that the 3D-ETAS model exhibits superior performance compared to the 2D ETAS model. However, both the 2D-ETAS and 3D-ETAS models utilize Euclidean distance based on spherical coordinates to model the spatial probability density function of triggered events. This modeling approach might not be suitable for high-latitude areas or extensive regional studies. To tackle this issue, Xiong and Zhuang (2023) have advanced the spatial probability function by incorporating the great circle distance.
In this study, we merge the 3D ETAS model with the SETAS model, giving rise to the 3D-SETAS model. Based on the new model, we evaluated the global background seismic occurrence rates at different depths. We also validated our model using stochastic reconstruction techniques. The outcomes of stochastic depth reconstruction are presented in Figure (1). When compared to the SETAS model, the new model exhibits a stronger alignment between calculated outcomes and theoretical values.
Reference:
Brummelen, G. V., (2013). Heavenly Mathematics: The Forgotten Art of Spherical Trigonometry, Princeton University Press.
Guo, Y., Zhuang, J. & Zhou, S., 2015. A hypocentral version of the space–time ETAS model, Geophysical Journal International, 203(1), 366-372.doi: 10.1093/gji/ggv319.
Ogata, Y., 1988. Statistical Models for Earthquake Occurrences and Residual Analysis for Point Processes, Journal of the American Statistical Association, 83(401).doi: 10.1080/01621459.1988.10478560.
Ogata, Y., 1998. Space-Time Point-Process Models for Earthquake Occurrences, Annals of the Institute of Statistical Mathematics, 50(2), 379-402.doi: 10.1023/a:1003403601725.
Ogata, Y. & Zhuang, J., 2006. Space–time ETAS models and an improved extension, Tectonophysics, 413(1-2), 13-23.doi: 10.1016/j.tecto.2005.10.016.
Omori, F., 1894. On the Aftershocks of Earthquakes, Journal of the College of Science, 7, 111-120.
Xiong, Z. & Zhuang, J., 2023. SETAS: A Spherical Version of the Space–Time ETAS Model, Seismological Research Letters.doi: 10.1785/0220220198.
Zhuang, J., 2005. A study on the background and clustering seismicity in the Taiwan region by using point process models, Journal of Geophysical Research, 110(B5).doi: 10.1029/2004jb003157.
Zhuang, J., Ogata, Y. & Vere-Jones, D., 2002. Stochastic Declustering of Space-Time Earthquake Occurrences, Journal of the American Statistical Association, 97(458), 369-380.doi: 10.1198/016214502760046925.
Zhuang, J., Ogata, Y. & Vere-Jones, D., 2004. Analyzing earthquake clustering features by using stochastic reconstruction, Journal of Geophysical Research: Solid Earth, 109(B5).doi: 10.1029/2003jb002879.