## 4 Analysis and Visualization of Interpolation Results  
### Terrain Modeling  
To develop an accurate model for estimating the spatial distribution of topographic elevation data in the study area, spherical kriging, exponential kriging, Gaussian kriging, linear kriging, IDW (\(p\) = 2), TPS-RBF, RS-RBF, and HS-RBF, were employed to create topographic contour maps (Figure 10). In the interpolation, the neighbor points are selected as 15. Visually, the eight contour maps exhibited minimal differences and effectively represented the undulating nature of the terrain. To quantitatively assess each interpolation algorithm, cross-validation was performed utilizing the mean absolute error (MAE) and root mean square error (RMSE) as evaluation criteria (Table 3). In terms of computation time and memory consumption, there is little difference among the eight interpolation methods. The kriging methods take 51.87-63.10 s, and the IDW and RBF methods take 42.05-49.36 s, which is related to their weighting methods. Kriging-type methods require a  
Figure 8: 25214 workface \(\mathrm{S11}\) gun seismic record time analysis.  
Figure 9: 25214 workface channel wave velocity distribution map.  
relatively long time to fit the variogram, but overall the time is acceptable, with a memory consumption of between 124-212 KB, which is negligible on modern computer hardware.  
The results indicate a high degree of precision for both geostatistical and deterministic interpolation methods, fulfilling the requirement for high-precision modeling. The linear kriging interpolation method demonstrated the highest precision, with MAE = 1.01 m and RMSE = 1.20 m. The linear variogram proved most suitable for fitting the variogram of the topographic elevation points. This suggests that the linear kriging method effectively captures the spatial distribution characteristics of topographic elevation points and represents the optimal interpolation method for this topographic model. A 3D terrain model was generated based on linear kriging interpolation (Figure 11), visualizing the relief characteristics of the surface elevation in the study area. The 3D terrain model and contour map were translated along the \(Z\)-axis, and the 3D terrain model was stretched by a factor of two along the \(Z\)-axis to enhance visual clarity. The details and overall trends of the terrain in the study area were clearly reflected. After selecting the linear kriging method, the sensitivity experiment of its neighbor points parameters is carried out. Figure 12 represents the MAE and RMSE change diagrams of the interpolation results under the condition of different number of neighbor points. It can be seen that when the number of interpolation points is 0-9, the MAE and RMSE values of the model show a rapid downward trend, which is due to the elevation of the terrain interpolation data; the value is large, the terrain points are numerous, the neighbor range of 0-9 points cannot well capture the local differences of the terrain; the neighbor range tends to be stable at 10-25 points of MAE and RMSE, proving that the neighbor range of 10-25 points is able to capture the local variation and undulation  
Figure 10: Terrain interpolation results.  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline  & & **Spherical** & **Exponential** & **Gaussian** & **Linear** & **IDW** & **TPS** & **RS** & **HS** \\ \hline \multirow{4}{*}{Terrain} & MAE (m) & 2.77 & 2.49 & 2.88 & 1.01 & 2.95 & 1.86 & 1.64 & 1.70 \\ \cline{2-10}  & RMSE (m) & 3.39 & 3.61 & 4.17 & 1.20 & 3.87 & 2.41 & 2.67 & 2.84 \\ \cline{2-10}  & Calculate time (s) & 51.87 & 63.10 & 55.63 & 52.26 & 42.05 & 42.99 & 45.94 & 49.36 \\ \cline{2-10}  & \multicolumn{2}{c}{Consume memory (KB)} & 184.00 & 164.00 & 136.00 & 124.00 & 172.00 & 212.00 & 128.00 & 144.00 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Terrain interpolation result error.  
characteristics of the terrain. The parameter sensitivity experiments show that the model is stable when the neighborhood points are more than 10.