## 6 Discussion  
In this study, nine interpolation methods were applied to the spatial interpolation of surface elevation, topography, and coal seam thickness data, with cross-validation to select the best method. A novel approach for redrawing zero lines based on negative virtual thickness values was introduced, addressing the challenge of defining missing stratigraphic regions. For coal seam thickness, a BME interpolation method was proposed, integrating \"soft data\" and \"hard data\" from channel wave exploration, boreholes, and mine roadway data, enabling more accurate identification of abnormal coal thickness variations, which were effectively visualized in the 3D model. The advantage of this study lies in the selection of diverse interpolation methods, including kriging, IDW, RBF, and BME. Compared to other studies, such as [PERSON] et al. [39] and [PERSON] et al. [28], which focused on kriging methods for coal seam interpolation, the methods in this paper demonstrate higher accuracy. While these studies focused on entire mine coal seams, the present study is limited to the mining face, allowing for more detailed results. Additionally, the integration of soft and hard data through BME offers improved results compared to traditional methods like kriging and Bayesian kriging (BK), particularly in handling data gaps and inconsistencies [42]. However, this study also has limitations. The in-seam exploration area does not cover the entire workforce, and the method performs better with evenly distributed and large volumes of data. BME has also been shown to perform well with only soft data [43]. Future research should explore enhanced soft data construction methods, similar to probabilistic soft datasets, and apply machine learning to improve interpolation accuracy, especially  
Figure 23: 3D geological model of 25214 workface (extends 300 m). Figure 22: Modeling sequence partitioning. as data sources increase. At present, small datasets in mining environments may cause machine learning models to overfit, but this approach remains worth exploring [44; 45]. In geologically complex regions, such as fault zones and fractured coal seams, traditional interpolation methods (e.g., kriging, IDW, RBF) often fail to capture local characteristics due to spatial heterogeneity and geological discontinuities. The BME method mitigates this by integrating soft and hard data, allowing for more accurate interval estimates for missing data and reducing errors caused by geological discontinuities. However, BME may face challenges in highly discontinuous environments, particularly in fault zones, where interpolation accuracy may decline. Future improvements could involve increasing auxiliary data (e.g., geophysical exploration) and optimizing search radii to limit data influence from across faults, ensuring more accurate results in fault and fracture zones. In three-dimensional geological modeling, real-time updates are crucial for mining accuracy, particularly for coal seam models. While terrain and strata data are updated less frequently, coal seam models must be continuously updated with real-time data from mining operations. Despite its high accuracy, BME's computational complexity can cause delays in real-time updates. However, coal seam changes are generally stable, except in areas with abnormal geological structures (such as fault zones). In stable conditions, the model updated during mining progress can provide valuable guidance for subsequent mining cuts, especially as mining typically advances 8-12 cuts per day. To mitigate these delays, future research could focus on accelerating the BME calculation process via parallel computing or GPU acceleration. Additionally, machine learning could be applied to predict coal thickness trends, enabling faster and more precise real-time updates. Although this article studies the mining operations that are currently being extracted, the proposed interpolation methods are also highly applicable to closed coal mines, such as those in Europe.