# ETAS Space-Time Modeling of Chile Triggered Seismicity Using Covariates: Some Preliminary Results
## 7 Conclusions  
In this paper, we present an application of the ETAS model with covariates to describe the Chilean seismicity, also using GPS information of the observed data. In particular, the triggered seismicity in Chile is analyzed distinguishing between the North and the South of the country, since the different behavior of the seismicity along the coast of Chile. According to the analyzed areas, different results are obtained, accounting for the main relevant covariates related to the depth of events and some GPS measurements, corresponding to  
Figure 9: Transformed residuals obtained from the model with four covariates (black line) and one covariate (green line), for the Northern area (**left** panel) and the Southern Area (**right** panel). The red line is the theoretical one.  
\begin{table}
\begin{tabular}{l c c} \hline
**Parameter** & **Estimate** & **Std. Error** \\ \hline Mt1D & \(-0.1050\) & \(0.0273\) \\ Mt5D & \(0.2030\) & \(0.0129\) \\ \hline \end{tabular}
\end{table}
Table 5: _Cont._the Earth movement observed until the time of main events. It represents an innovative method, improving the assessment of seismic events in space and time, considering a contagion model within a regression-like framework accounting for external covariates.  
Moreover, the introduction of covariates to the classical ETAS model seems to improve the description of the Chilean seismicity, explaining better the overall variability of the studied phenomenon and leading to a decrease in the unpredictable variability. Indeed, in the seismic context, the proposed approach can provide more general formalism for the earthquake occurrence in space and time, such that the effect on the future activity does not depend only on the closeness of the previous events but also on specific characteristics of the main event, such as magnitude, as usual, and further information, such as geological features or some GPS-related data.  
The reported results confirm the need for a more flexible model for describing the complexity of the spatio-temporal aftershock activity. Moreover, introducing external information is an innovative and promising perspective of study that could be also relevant for studying different phenomena with epidemic features.  
The proposed approach could still be improved and would require more investigation, both in terms of inference and diagnostic results (e.g., accounting for directional effect for a more realistic analysis). Additionally, the proposed model could be used for predicting future events in space and time such as in [14,38].  
Data curation, O.N. and A.G.; Formal analysis, M.C., O.N. and A.G.; Funding acquisition, O.N.; Investigation, M.C., O.N., G.A., N.D. and A.G.; Methodology, M.C. and A.G.; Project administration, O.N.; Writing--original draft, M.C.; Writing--review and editing, O.N., G.A. and N.D. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the Fondecyt National grant number 1201478.  
Not applicable.  
The used Chilean seismic data are provided by the Chilean National Seismological Center of the University of Chile, [[http://sismologia.cl](http://sismologia.cl)]([http://sismologia.cl](http://sismologia.cl)) (accessed on 20 August 2021).  
The authors declare no conflict of interest.