## 5 Results and Discussions
### Results of Compositional Data Analysis  
In this study, the data was first closed to ensure that the sum of all components equals 100% (closure), followed by a clr transformation. Afterward, the characteristics of the data after clr transformation were analyzed through preliminary statistics, and the results are shown in Table 5.  
Compositional data analysis is based on closing the data, followed by log-ratio transformation to reflect a more accurate spatial distribution of the data. The negative values in Table 5 do not represent the actual element content, but rather the relative proportion of that element at the corresponding sampling point. From Table 5, it can be seen that after the clr transformation, the average values of most elements in both the northern and southern regions are now much closer, and the kurtosis and skewness of each element have improved significantly, making the data closer to a normal distribution. From the box plots (Figure 8), it can be seen that after the clr transformation, the spatial distribution scale differences of each element have been significantly reduced, and they are now at roughly the same order of magnitude. The distribution in the box plots is also more uniform. However, for elements such as Sn, Ni, and Co, even after the clr transformation, the data from the southern region still appear more dispersed (with the boxes in the southern region being longer than those in the northern region), suggesting the presence of more outliers. The Q-Q plot (Figure 9) test shows that, after the clr transformation, although there are still some data with long-tail distributions, the data roughly follows a normal distribution. It can be concluded that the clr transformation has effectively reduced the internal heterogeneity and eliminated most of the skewness in the data. The data after clr transformation generally meets the requirements for multivariate statistics. Figure 7: Geochemical maps of the raw data (**a–l**) corresponding to the 12 elements. Figure 8: Box plot of data after clr transformation. \begin{table}
\begin{tabular}{c c c c c c c c c c c} \hline \hline
**Element** & **Region** & **Min** & **25\%** & **50\%** & **75\%** & **Max** & **StdDev** & **Mean** & **Kurt** & **Skew** \\ \hline Ag & North & \(-4.95\) & \(-3.81\) & \(-3.67\) & \(-3.50\) & \(-0.23\) & \(0.33\) & \(-3.64\) & \(12.86\) & \(1.79\) \\  &  
From Table 6, it can be observed that after the CR method transformation using the median, the percentiles of each element are now much closer, and the kurtosis and skewness of all elements have not changed. When considering the corresponding geochemical maps (Figure 10), the results show some improvement compared to the raw data (Figure 7). The shift effect that was present in the raw data for Ag, Mo, and Sb elements has mostly been improved. Among them, Ag and Sb elements show the best results, with almost no shift between map sheets, and the distribution of geochemical anomalies is highly consistent with the distribution of faults, reflecting the fact that faults serve as migration channels for hydrothermal fluids. Figure 9: Q-Q Plot of data from the northern and southern regions after clr transformation: (**a**) northern region; (**b**) southern region. Furthermore, although Mo elements have improved to some extent, there is still a noticeable shift at the boundaries. This may be due to the fact that the CR method levels the data as a whole for each map sheet, without considering the different geochemical backgrounds caused by the large area of the study region. Additionally, a new issue emerged after applying the CR method: data that did not originally exhibit a shift now show one. This is most notable for Sn and Bi elements, followed by Co and Ni elements, which also exhibit a shift problem.