## 7 Conclusions  
Based on the statistical characteristics and spatial distribution features of the topographic elevation, strata, and coal seam thickness data within a 300 m range near the 25214 workforce of the Hongliulin coal mine, the accuracies of nine interpolation methods were evaluated through cross-validation. Among these, the topographic and strata data were subjected to eight interpolation methods, while the coal seam thickness interpolation included an additional BME method. A method for accurately delineating areas with missing strata was proposed, and a fine three-dimensional geological model of the 25214 workforce was established using the optimal interpolation methods for each layer.  
Interpolation Results for Terrain Elevation Points: For the terrain elevation data, which is evenly distributed and dense, the performance of eight interpolation methods, including kriging, IDW, and RBF, was generally satisfactory. Among these methods, linear kriging exhibited the highest accuracy (MAE = 1.01 m, RMSE = 1.20 m), capturing the local variations in terrain elevation most effectively.  
Interpolation Results for Stratigraphic Thickness Data: For stratigraphic thickness data with sparse sampling points, the optimal interpolation methods for five strata are as follows: For Q4 stratum, spherical kriging (MAE = 2.13 m, RMSE = 2.83 m); for N2\(b\) stratum, IDW (\(p\) = 2) (MAE = 2.08, RMSE = 2.44); for J2y3 stratum, RS-RBF (MAE = 0.89 m, RMSE = 1.05 m); for J2y2 stratum, TPS-RBF (MAE = 1.96 m, RMSE = 2.25 m); and for J2y1 stratum, HS-RBF (MAE = 2.36 m, RMSE = 2.71 m).  
Method for Handling Missing Stratigraphic Areas: A novel method for addressing missing stratigraphic regions was proposed. By virtually redrawing the zero line of stratum thickness based on negative virtual thickness values, a 3D layer model was constructed. Grid intersection techniques were then employed to eliminate gaps within the model, enabling the accurate definition of missing stratigraphic regions in the 3D geological model.  
Precise Prediction Interpolation Method for Coal Seam Thickness: A precise interpolation method for predicting coal seam thickness based on Bayesian Maximum Entropy (BME) was proposed. This method integrates hard data from boreholes and mine roadway measurements with soft data from channel wave exploration. The interpolation accuracy after integration (MAE = 0.64 m, RMSE = 0.66 m) is significantly superior to that of the other eight methods. Compared to the real 5\({}^{-2}\) coal thickness measurement points, the BME method shows an error range between 0.01 and 0.57 m, with an average error of 0.20 m, demonstrating the highest accuracy.  
Construction of a High-Precision 3D Geological Model: By employing the optimal interpolation methods identified for terrain, individual strata, and coal seams, a high-precision 3D geological model of the coal mining face was constructed using TIN grid modeling. This model provides reliable 3D geological support for intelligent coal mining operations.  
All authors contributed to the concept and design of the study. Data collection and analysis were conducted by [PERSON], E.H. and T.L. On-site construction of coal mine was completed by T.L., and the preparation of charts was carried out by M.C., P.H. and D.F. The first draft of the manuscript was written by [PERSON], and all authors provided comments on the earlier versions of the manuscript. All authors have read and agreed to the published version of the manuscript.  
This work was supported by the National Natural Science Foundation of China (42177174) and a project supported by the scientific research program of Shaanxi Coal Group Co., Ltd. (2021 SMHKJ-BK-J-01).  
Not applicable.  
The raw data supporting the conclusions of this article will be made available by the authors on request.  
The authors declare that this study received funding from Shaanxi Coal Group Co., Ltd. The funder had the following involvement with the study: providing financial support and assisting in data collection at the mining site.