## 3 Samples and Methods
### Multivariate Statistical Analysis
#### 3.2.2 Principal Component Analysis (PCA)  
Principal component analysis (PCA) is another powerful multivariate statistical technique used to extract the linear relationships of the original variables. By transforming the original variables into their linear combinations (principal component, PC), dimensionality reduction is achieved while retaining important information. Varimax rotation was applied to enhance the interpretability of principal components (PCs) by maximizing the variance of their loadings. This was achieved by reducing the number of both high and low coefficients, thereby increasing the contrast between them [69; 70]. When the original variables are transformed linearly by varimax rotation, the obtained PCs after dimensionality reduction can effectively preserve the features of the original variables, among which those with the largest proportion of variance have the strongest ability to reflect the original variables [17; 18; 71]. In the PCA results, the original data matrix was decomposed into two  
\begin{table}
\begin{tabular}{c c c c c c c c c c c c c c c c c c c} \hline \hline  & **No.** & **Well** & **Formation** & **R1\({}^{*}\)** & **R2** & **R3** & **R4\({}^{*}\)** & **R5\({}^{*}\)** & **R6\({}^{*}\)** & **R7\({}^{*}\)** & **R8\({}^{*}\)** & **R9\({}^{*}\)** & **R10** & **R11** & **R22** & **R13** & **R14** & **R15** & **R16** & **R17** \\ \hline
1 & Source-1 & VN-2 & 1,2-2 & 0.22 & 0.11 & 0.68 & 0.32 & 1.87 & 0.66 & 0.32 & 0.36 & 0.26 & 0.12 & 0.46 & 0.43 & / & / & / & / \\
2 & Source-2 & VN-2 & 1,2-2 & 0.17 & 0.14 & 0.69 & 0.25 & 4.89 & 0.50 & 0.12 & 0.22 & 0.38 & 0.21 & 0.24 & 0.47 & 0.46 & 0.26 & 0.59 & 0.84 & 1.22 \\
3 & Source-3 & VN-4 & 1,3-7 & 0.27 & 0.08 & 0.46 & 1.87 & 0.29 & 0.25 & 0.48 & 0.48 & 0.45 & 0.24 & 0.39 & 0.45 & 0.47 & 0.20 & 0.56 & 0.97 & 1.78 \\
5 & Source-5 & VN-2 & 1,3-7 & 0.23 & 0.20 & 0.56 & 0.41 & 1.87 & 0.29 & 0.30 & 0.31 & 0.59 & 0.48 & 0.26 & 0.52 & 0.38 & 0.49 & 0.27 & 1.01 & 0.57 & 1.17 \\
6 & Source-5 & VN-2 & 1,3-7 & 0.33 & 0.29 & 0.26 & 0.56 & 0.41 & 2.90 & 0.30 & 0.43 & 0.48 & 0.26 & 0.52 & 0.38 & 0.49 & 0.34 & 1.32 & 1.30 & 1.10 \\
7 & Source-7 & VN-2 & 1,3-7 & 0.38 & 0.26 & 0.46 & 0.62 & 0.55 & 0.43 & 0.25 & 1.05 & 0.51 & 0.25 & 0.89 & 0.45 & 0.47 & 0.34 & 1.32 & 1.30 & 1.10 \\
8 & QU-1 & VN-2 & 1,3-7 & 0.27 & 0.27 & 0.46 & 0.58 & 2.04 & 0.21 & 0.09 & 0.69 & 0.41 & 0.17 & 0.51 & 0.48 & / & / & / & / & / \\
9 & QU-2 & VN-2 & 1,3-7 & 0.30 & 0.16 & 0.54 & 0.54 & 1.94 & 0.21 & 0.10 & 1.27 & 0.56 & 0.27 & 0.59 & 0.53 & / & / & / & / & / \\
10 & QU-3 & VN-2 & 1,3-7 & 0.33 & 0.20 & 0.47 & 0.70 & 1.88 & 0.24 & 0.41 & 1.05 & 0.51 & 0.19 & 0.62 & 0.45 & / & / & / & / & / \\
11 & QU-4 & DQ-4 & 0.43 & 0.17 & 0.39 & 1.10 & 1.04 & 0.10 & 0.07 & 1.73 & 0.73 & 0.21 & 0.50 & 0.43 & / & / & / & / & / & / \\
12 & Cu-5 & DQ-1 & 1,4-4 & 0.43 & 0.20 & 0.37 & 1.16 & 2.62 & 0.23 & 0.08 & 1.57 & 0.61 & 0.19 & 0.59 & 0.48 & / & / & / & / & / & / \\
13 & Indication-1 & VN-2 & 1,3-7 & 0.23 & 0.18 & 0.59 & 0.38 & 0.63 & 0.33 & 0.12 & 1.21 & 0.55 & 0.15 & 0.67 & 0.39 & 0.64 & 0.27 & 1.38 & 0.88 & 0.16 \\
14 & Indication-2 & VN-4 & 1,3-7 & 0.24 & 0.18 & 0.58 & 0.41 & 0.41 & 0.27 & 0.12 components: the score matrix, which represents the projections of the data onto the PCs, and the loading matrix, which indicates the contribution of each original variable to the principal components. The data in Table 2 were used for PCA analysis.