## 4 Methods
### Data Leveling Methods
#### 4.2.2 BL Method  
Principle of BL Method  
As seen from the definition of the CR method, it has obvious advantages: it is simple and quick. However, this method also has a significant drawback: it treats a block as a whole. This approach is suitable and reasonable when the study area is small, the samples do not span many regions, and there is no significant change in geological conditions. However, if the study area is large or the geological conditions are complex within the study area, the processed data may become \"distorted\".  
Therefore, to address the issues with the CR method, we use the data leveling method for multiple map sheets (BL) proposed by [PERSON] in 1998 [6].  
The method assumes that at the boundary between two map sheets, a shift in data measurement occurs--since the geological conditions at the boundary are theoretically similar, the data should remain consistent. As shown in Figure 5, a and b, as adjacent boundaries, have similar geological conditions, so the data characteristics should generally remain consistent. Therefore, we choose samples with as similar geological conditions as possible, calculate the percentiles of elements, and perform line fitting in a scatter plot. The fitting curve parameters can then be used to adjust the data at one map sheet boundary to the adjacent map sheet, and data outside the boundary can also be leveled accordingly. The specific calculation parameters can be 0.05, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 0.95 [6]. This method avoids the uncertainty caused by leveling using only the 0.5 percentile, making the results more reliable.  
Specifically, determining the critical range is crucial. If it is too small, it may not be representative; if it is too large, geological conditions may have changed. Therefore, when determining the boundary size, it is important to refer to the attributes of the geological units. At the same time, this method is based on multivariate statistics, requiring the data to be as close to a normal distribution as possible. Consequently, this operation is performed on the basis of compositional data analysis.  
Determination of Minimum Boundary Distance  
In the BL method, the key step is determining the minimum boundary. In this study, different boundary distances (bandwidths) are selected for the calculation of \(D\)-values to choose the most suitable bandwidth. Specifically, this can be calculated using Equation (2).  
\[D=\sum w_{i}[(q_{i})_{\rm e}-(q_{i})_{\rm e^{\prime}}]^{2} \tag{2}\]In this formula, \(D\) represents the degree of difference between two data sets (northern and southern) at a specific bandwidth; \(w_{i}\) is the weight assigned to the \(i\)-th percentile--if the data follow a normal distribution, the probability density at the 50 th percentile is \(\frac{1}{\sqrt{2n}}\approx 0.39\)[6,31]. The standard weight of 1 is assigned to the 50 th percentile's probability density (0.39), and the weights for other percentiles are scaled proportionally to the ratio with the 50 th percentile's probability density. \((q_{i})_{\text{e}}\) represents the i-th percentile in the northern bandwidth e, and \((q_{i})_{\text{e}^{\prime}}\) represents the i-th percentile in the southern bandwidth e\({}^{\prime}\).