## 4 Multilayered Local Zonation of Seismic Site Effects
### Multilayered Local Zonation
Consequently, unification of the multilayered zonation map was conducted based on PCA of the spatially explicit combination of seismic site effect indicators in local geometry. Principal component analysis is a statistical method to convert a number of variables with potentially correlated attributes into a set of variables that capture the variability within the underlying data [68; 69]. The principal components (PCs) are linear combinations of these variables that account for single and common variability. The analysis uses an orthogonal linear transformation to identify an \(N\)-dimensional vector that represents the maximum total variability in a set of \(N\) variables, in which the first PC is the summary of the total variability in the data, in which each variable is transformed to a mean of zero and a variance of one [70]. PCA can therefore be used to highlight multivariate site zonation patterns with respect to statistical and spatial correlations. The application of PCA is as follows: (1) initial component extraction, (2) determination of the PCs in the model, (3) factor loading-based rotation of the matrix for the solution, (4) solution interpretation, (5) factor and generic scoring calculation, and (6) summary of results (Table 3) [70]. To determine the PCs of priority among the three site response parameters (\(V_{S30}\), \(T_{G}\), and \(H\)), three combinations (Table 3) were applied to the PCA. In combinations #1 and #2, two PCs resulted due to the two-dimensional vector. Combination #3 had three PCs. The PCs were ranked according to their importance and associated with the vector for each PC based on how much of the variability in the data they captured [69]. The selection of PCs from the PCAs was based in part on the subjective assessment and component interpretability [71]. In combination #1, PCA determined that almost 97% of the total variation corresponded to \(V_{S30}\) and \(T_{G}\) components. In combination #2, the total variance of the \(V_{S30}\) and \(H\) components was 88% of the overall variation. In combination #3, PCA results accounted for approximately 99% of the total variance. Table 3 also details the loading of each parameter for the retained PCs. PC1 has the highest level of data variance, with 90% of the overall variance. The \(V_{S30}\) was heavily loaded in PC1 for all combinations. However, only 10% of the overall parameters in the combination of PC2 and PC3 because of the higher variance of PC1. The positive loading of PC1 in combination #3 was high with \(V_{S30}\) (0.51), \(T_{G}\) (0.15), and \(H\) (0.38). Accordingly, PC1 can be the strongest representation for seismic site effects. Using the weights of the variability, the loads of the three parameters allowed the identification of 10 spatial site classification (from B to E in Table 1) aspects of site effect, based on the way the parameters co-varied across space. Figure 11 shows that in Daejeon city, there are significant regional variations in site response, although there are very slight differences between the parameter combinations. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Component**} & \multirow{2}{*}{**Initial Eigen Value**} & \multicolumn{3}{c}{**Loading of Parameters**} & \multicolumn{2}{c}{**Percent of**} & \multirow{2}{*}{**Eigen Value**} & \multirow{2}{*}{**Coefficient of Correlations**} \\ \cline{3-3} \cline{5-6}  & & \(V_{S30}\) & & & & \\ \hline \multicolumn{6}{c}{Combination \#1: \(V_{S30}\), \(T_{G}\)} \\ \hline PC1 & 1.34 & 0.51 & 0.05 & - & 87.47 & 0.96 \\ PC2 & 0.19 & 0.25 & \(-\)0.12 & - & 10.53 & 0.61 \\ \hline \multicolumn{6}{c}{Combination \#2: \(V_{S30}\), \(H\)} \\ \hline PC1 & 1.20 & 0.66 & - & 0.38 & 76.17 & 0.94 \\ PC2 & 0.37 & 0.16 & - & 0.75 & 11.83 & 0.11 \\ \hline \multicolumn{6}{c}{Combination \#3: \(V_{S30}\), \(H\), \(T_{G}\)} \\ \hline PC1 & 1.36 & 0.75 & \(-\)0.07 & \(-\)0.16 & 70.95 & 0.94 \\ PC2 & 0.43 & 0.01 & 0.15 & \(-\)0.25 & 22.25 & 0.61 \\ PC3 & 0.13 & 0.25 & \(-\)0.19 & \(-\)0.04 & 6.80 & 0.44 \\ \hline \hline \end{tabular}
\end{table}