## 4 Analysis and Visualization of Interpolation Results
### Coal Modeling
Accordingly, BME interpolation was chosen for accurate coal thickness predictions in the channel wave exploration area, while spherical kriging was applied to predict coal thickness in other sections of the 25214 workface. According to the results of BME parameter sensitivity experiments (Figure 19), the accuracy of the model (MAE and RMSE) tends to be stable when the number of neighbor points exceeds 5, and it performs best at 10 neighbor points. This result shows that there is a sensitivity between the interpolation accuracy of the BME method and the number of neighbor points, and in this experiment, 10 neighbor points were selected as the best balance points. The BME method considers both soft data and hard data in the process of interpolation, and uses these data to model uncertainty. Due to the large number of points in the in-seam wave inversion data, selecting 10 neighbor points can effectively capture the spatial variation of the data and provide enough local information for accurate interpolation. After this point, adding more neighbor points has little effect on the accuracy improvement, indicating that the BME method has a limited demand for the number of neighbor points, and 10 neighbor points are sufficient to ensure the stability and accuracy of the model. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **Data** & **BME** & **Spherical** & **Exponential** & **Gaussian** & **Linear** & **IDW** & **TPS** & **RS** & **HS** \\ \hline \multirow{4}{*}{\(5^{-2}\) Coal} & MAE (m) & 0.64 & 0.99 & 1.01 & 0.98 & 1.00 & 1.20 & 1.96 & 2.00 & 1.58 \\ \cline{2-10}  & RMSE (m) & 0.66 & 1.18 & 1.18 & 1.12 & 1.13 & 1.27 & 2.05 & 2.11 & 1.63 \\ \cline{2-10}  & Calculate time (s) & 83.57 & 75.45 & 69.03 & 61.70 & 70.13 & 45.21 & 72.07 & 64.02 & 67.28 \\ \cline{2-10}  & Consume memory (KB) & 387.00 & 207.00 & 191.00 & 157.00 & 163.00 & 183.00 & 218.00 & 154.00 & 201.00 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: \(5^{-2}\) Coal interpolation result error (hard and soft data). Figure 18: Channel wave area \(5^{-2}\) coal thickness interpolation results (hard and soft data). In the actual recovery process of the trough wave exploration area, three measurement lines were conducted at distances of 2409 m, 2515 m, and 2632 m from the starting recovery direction to measure the coal thickness, totaling 39 actual coal thickness measurement points to validate the interpolation results (Figure 20). Table 7 provides a quantitative error analysis comparing BME with other interpolation methods (such as spherical, exponential, Gaussian, linear, IDW, TPS, RS, HS) against the actual coal seam thickness measurement points. Among the minimum errors, Gaussian kriging and linear kriging performed the best with 0.00 m, followed by BME, exponential kriging, TPS-RBF, RS-RBF, and HS-RBF methods with 0.01 m. In terms of maximum error, the BME method performed the best with 0.57 m, while the other methods ranged between 0.81 m and 1.86 m. For average error, the BME method also performed the best with 0.20 m, while the other methods slightly lagged behind BME, ranging from 0.25 m to 0.35 m. These results indicate that BME has high accuracy in predicting coal seam thickness and can effectively integrate soft and hard data information for predictions  
Figure 19: BME neighbor points sensitivity experiment. Figure 20: Comparison of BME coal thickness interpolation results with real data. The BME and spherical kriging interpolation results were combined to create a 3D geological model of the \(5^{-2}\) coal seam (Figure 21). The yellow area represents the BME interpolation domain, while the gray surface depicts the spherical kriging results. The BME results lie beneath the gray surface, offering a more accurate representation in the coal seam thinning zone.