# Sensitivity Analysis of Numerical Coherency Model for Rock Sites
## 5 Conclusions  
This study aimed to analyze the parameters influencing plane-wave coherency at rock sites through a sensitivity analysis based on numerical simulations and to evaluate the reliability of the numerical analysis method by comparing it with empirical coherency functions. The numerical model utilized a 2D Gaussian random field to account for spatial variability. Seismic wave propagation was simulated using the finite element analysis code OpenSees3.3.0.  
The sensitivity analysis of four parameters (number of simulations, CV, CL\({}_{h}\), and analysis depth) indicated that 150 simulations are sufficient for stable coherency analysis. The results showed that plane-wave coherency decreases as the CV increases, while the CL\({}_{h}\) has a minimal impact. The effect of analysis depth was negligible beyond 100 m. However, since \(V_{s}\) and CV profiles can vary by site, the sensitivity analysis of the analysis depth is recommended when developing numerical coherency functions.  
The comparison with the existing empirical coherency function confirmed the reliability of the numerical analysis method. This demonstrates the potential for developing site-specific coherency functions from numerical simulations, which can be widely used for SSI analyses of critical structures, including nuclear power plants and basements linked to tall buildings. The simulation of spatial variable ground motion will help to reduce seismic demand overestimations using uniform motion time histories.  
However, several limitations remain. The numerical coherency function requires further validation against empirical results using spatial variability parameters derived from rigorous site investigations. Further studies to enhance the accuracy of the numerically  
\begin{table}
\begin{tabular}{c c c c c} \hline  & **25 m** & **50 m** & **100 m** & **150 m** \\ \hline R\({}^{2}\) value [-] & 0.993 & 0.985 & 0.986 & 0.992 \\ \hline \end{tabular}
\end{table}
Table 2: R\({}^{2}\) values according to separation distance.  
Figure 9: Comparison between numerical-based curve and empirical curve for Pinyon Flat site.  
derived coherency model are warranted, including the utilization of machine learning. The use of probabilistic methods is also recommended to quantify the inherent uncertainty in the coherency estimation.  
Conceptualization, D.P.; methodology, D.L.; software, D.L., Y.L., H.-S.K. and J.-S.P.; formal analysis, D.L., Y.L., H.-S.K. and J.-S.P.; data curation, D.L., Y.L., H.-S.K. and J.-S.P.; writing--original draft preparation, D.L.; writing--review and editing, D.P. and D.L.; supervision, D.P.; funding acquisition, D.P. All authors have read and agreed to the published version of the manuscript.  
This research is funded by National Research Foundation of Korea (NRF) grant funded by the Korean government (MSIT) (No. 2022R1A2C3003245) and Korea Hydro & Nuclear Power Co. Ltd. (No. L24S015000).  
Not applicable.  
The original contributions presented in this study are included in the article. Further inquiries can be directed to the corresponding author.  
Authors [PERSON], [PERSON] and [PERSON] were employed by the company Korea Hydro & Nuclear Power Co., Ltd. The remaining authors declare that the research was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest. The sponsors had no role in the design, execution, interpretation, or writing of the study.