## 5 Results and Discussions
### Results of Compositional Data Analysis
#### 5.3.2 Results of the BL Method  
Theoretically, data that are closer to the boundary line should be more similar (since the data comes from the same geological unit). Therefore, data close to the boundary line should be selected as much as possible. However, it is also important to consider the statistical validity of the data. Too few data points may not adequately represent the true distribution characteristics, while too many data points may deviate from the similar background. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Element** & **Region** & **Min** & **25\%** & **50\%** & **75\%** & **Max** & **StdDev** & **Mean** & **Kurt** & **Skew** \\ \hline \multirow{2}{*}{Ag} & North & \(-5.21\) & \(-4.01\) & \(-3.86\) & \(-3.68\) & \(-0.24\) & \(0.35\) & \(-3.83\) & \(12.86\) & \(1.79\) \\  & South & \(-6.28\) & \(-4  
Figure 10: _Cont._  
To address this, the southern and northern boundary lines were selected with distances ranging from 500 to 5000 meters, incrementing by 500 meters. The percentiles for different boundary ranges in the northern and southern regions were calculated, and the differences  
Figure 10: Geochemical maps of each element after CR (**a–l**) corresponding to the 12 elements. in percentiles were measured using a difference metric (D-value) and displayed in a line chart to assess the degree of difference in percentiles for different boundary ranges (Figure 11). From Figure 11, it can be seen that at a 1000 m distance, the data difference between the northern and southern regions is the smallest, meaning the similarity is highest. Therefore, the data within this range is selected as the parameter for BL. In the boundary-based leveling process, a certain area needs to be designated as the \"standard area\", and the data from other areas are then leveled based on this \"standard area\" using the fitting function determined by the percentiles. Since the data for each map sheet follow sampling specifications, any area can be randomly selected as the \"standard area\". In this study, the southern region was chosen as the standard area because its larger sample size helps effectively reduce errors caused by insufficient samples or data fluctuations, thus improving the reliability of the leveling results. Therefore, the southern region's data is used to adjust the northern region's data. The leveling parameters are derived from the percentiles of the data within the 1000 m boundary range, and the fitting information can be seen in Table 7 and Figure 12. It is clearly evident that the element Ag requires the most leveling; theoretically, the distribution curve near the boundary line should be close to X = Y, but it deviates significantly, which is worth noting. Additionally, the R\({}^{2}\) values for the elements indicate that the fitting in both the northern and southern regions is quite good (all above 0.9), showing that the data for each element in both regions exhibit linear correlation, making boundary-based leveling a viable approach. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Elements** & **Formula** & **R\({}^{2}\)** \\ \hline Ag & \(y=0.43x-2.06\) & 0.93 \\ Cu & \(y=1.49x-1.14\) & 0.96 \\ Pb & \(y=0.95x-0.17\) & 0.90 \\ Zn & \(y=1.19x-0.37\) & 0.95 \\ W & \(y=0.99x+0.00\) & 0.98 \\ Sn & \(y=0.72x-0.04\) & 0.95 \\ \hline \hline \end{tabular}
\end{table} 
Table 7: Fitted curve parameters for each element within the 1000 m north–south range for BL. Figure 11: Line chart for determining optimal boundary range. Figure 12: Fitted curves for each element within the 1000 m north–south range (**a**) Ag; (**b**) Cu; (**c**) Pb; (**d**) Zn; (**e**) W; (**f**) Sn; (**g**) Mo; (**h**) As; (**i**) Bi; (**j**) Ni; (**k**) Co; (**l**) Sb. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Elements** & **Formula** & **R2** \\ \hline Mo & \(y=0.85x+0.11\) & 0.94 \\ As & \(y=1.25x-0.57\) & 0.90 \\ Bi & \(y=0.88x-0.49\) & 0.98 \\ Ni & \(y=0.94x+0.10\) & 0.98 \\ Co & \(y=1.16x-0.11\) & 0.96 \\ Sb & \(y=1.19x-0.69\) & 0.93 \\ \hline \hline \end{tabular}
\end{table}