1. Jiancang Zhuang zhuangjc@ism.ac.jp Inst. Statist. Math. Detecting spatial variations of earthquake clustering parameters via maximum weighted likelihood estimates

2. Motivations 1.Seismicity clusters differ from place to place. It is important to quantify such difference, for a better understanding of the connection between seismicity and tectonic environment and for better probability forecasts of earthquakes for different types of seismicity. 2.Fitting the space-time ETAS model for a small region with a few events makes the estimation and forecasts unstable. 3.Realization of weighted likelihood models is simple and straightforward.

3. Kernel Estimates Location-dependent Density /rate estimation Location-dependent model parameters of point process

4. Space-Time Epidemic Type Aftershock Sequence (ETAS) model  Seismicity rate = "background" + “Triggered seismicity":  Time distribution: the Omori-Utsu law  Spatial location distribution of children:  productivity: mean number of children

5. Likelihood and weighted likelihood

6. Comparing to Ogata's Bayesian method with a smoothness prior Ogata’s HIST ETAS modelWeighted likelihood Parameters estimation The parameters for each location must be estimated simultaneously. The parameters for each location can be estimated independently. Programming for parallel computation Not so easy.Easy. Triggering parameters Source location dependent.Target location dependent. Selection of Smoothness Objective selection of smoothnessSubjectively selection of kernel functions

7. Parameters should be all dual-way dependent on both the source and the target locations. To reduce the complexity of model implementation, since the events in an earthquake sequence are quite close in space, such differences could be neglected when investigating seismicity in a much larger scale. target dependent source dependent

8. Dataset 1 -- Japan JMA (Japan Meteorological Agency) catalog Longitude: 121 ◦ ∼ 155 ◦ E, Latitude: 21 ◦ ∼ 48 ◦ N, Depth: 0 ∼ 100 km, Time: 1 Jan 1965 to 31 Dec 2009 Magnitude: M J ≥4.0 19,019 events

10. Background rate: event/(day∙deg 2 )

11. A

13. Volcanic line

14. Dataset 2 - Italy ITAG catalog (INGV) Longitude: 8 ◦ ∼ 18 ◦ E, Latitude: 35 ◦ ∼ 48 ◦ N, Depth: 0 ∼ 70 km, Time: 17 Apr 2005 to 28 May 2014 Magnitude: M ≥ 2.6 5,627 events

15. (Billi et al, 2007, Geosphere) Tectonic settings and seismicity

17. A Clustering Parameters

18. I II III IV IIIIIIIV AH H L HH HHLL Subregions of clustering features H: high value L: low value

19. Conclusions 1.Results from fitting both the Japan and Italy regions show how the clustering characteristics of seismicity vary in space and their connections to the tectonic environments. 2.The weighted likelihood estimator can be used to obtain stable estimates of spatial changes of the ETAS parameters. 3.With complicated seismicity in both regions, the ETAS model with weighted likelihood estimates is potentially powerful for improving earthquake forecast from using a constant ETAS model.