## 4 Analysis and Visualization of Interpolation Results
### Coal Modeling  
Considering that the interpolation results inform the three-dimensional geological model and recognizing that the channel wave exploration does not consist of the entire workforce, the spatial distribution of 5\({}^{-2}\) coal thickness was analyzed across the entire 25214 workforce, as well as in the channel wave exploration area, to ensure accurate representation. Assessment of coal thickness distribution across the entire workforce employed eight interpolation methods. Low MAE and RMSE values indicate the reliability of these methods (Table 5). Among these methods, spherical, exponential, and linear kriging demonstrated comparably high precision. Visual inspection of the interpolated distributions (Figure 17) indicates a more uniform color distribution and aesthetically preferable representation from spherical kriging in the 25214 workforce. Therefore, spherical kriging was selected as the optimal interpolation method for 5\({}^{-2}\) coal thickness in this workforce. Figure 16: 3D layer model (stratum missing). Figure 15: Formation missing treatment process (Q\({}_{4}\)). In addition to the eight methods described above, Bayesian Maximum Entropy (BME) interpolation was employed to estimate the spatial distribution of coal thickness specifically in the channel wave exploration area. BME interpolation was implemented utilizing Seksgui V1.0.9, an open-source MATLAB R2020a-based software package available at Spatiotemporal Epistematics Knowledge Synthesis Graphical User Interface. Construction of \"soft data\" is central to BME interpolation. In this study, interval \"soft data\" were constructed based on the error analysis of channel wave exploration. Specifically, considering a 20% error in the retrieved coal thickness near roadway exposures, interval \"soft data\" [lb, up] were generated. For instance, a measured coal thickness of 4.6 m yields corresponding \"soft data\" of [3.68 m, 5.52 m], thus offering comprehensive input for the BME interpolation. Eight interpolation methods, including kriging, IDW, and RBF, cannot accommodate data uncertainty during the interpolation process. Therefore, when interpolating coal thickness, data from channel wave inversion, borehole data, and mine roadway data were incorporated as input sources. The MAE and RMSE values for the nine interpolation methods are lower (Table 6) accordingly with the uniform distribution and gridded output of the geophysically inverted coal thickness data. The BME method has the highest accuracy but consumes more time and memory than the other eight algorithms, which is determined by the computational complexity of the BME algorithm itself. The time consumption is 83.57 s and the memory consumption is 387 KB. Figure 18 illustrates that BME interpolation offers greater precision in areas where the coal seam thins and in the vicinity of the maximum coal thickness of 7.04 m, effectively capturing localized differences in the coal seam. This enhanced performance is attributed to the inability of the other eight methods to utilize coal thickness data uncertainty; thus, these data are treated as \"Hard Data\" during  
Figure 17: 25214 workface 5\({}^{-2}\) coal thickness interpolation results (hard data). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & **Hard Data** & **Spherical** & **Exponential** & **Gaussian** & **Linear** & **IDW** & **TPS** & **RS** & **HS** \\ \hline
5\({}^{-2}\) & MAE (m) & 0.85 & 0.85 & 0.89 & 0.86 & 1.06 & 1.03 & 1.01 & 0.91 \\ \cline{2-10} Coal & RMSE (m) & 1.06 & 1.06 & 1.13 & 1.06 & 1.37 & 1.51 & 1.30 & 1.27 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: 5\({}^{-2}\) coal interpolation result error (hard data). interpolation, leading to greater discrepancies between interpolated and observed values. BME interpolation, in contrast, incorporates both \"Hard Data\" and \"Soft Data\", utilizing uncertainty intervals and analyzing interpolation weights at various locations to achieve an optimal solution.