## 4 Analysis and Visualization of Interpolation Results
### Formation Modeling  
For the strata (Q\({}_{4}\), N\({}_{2}b\), J\({}_{2}y^{3}\), J\({}_{2}y^{2}\), and J\({}_{2}y^{1}\)), the optimal interpolation method was selected (Table 4) using the same eight interpolation methods as for terrain interpolation and evaluated through cross-validation (MAE and RMSE). Taking the Q\({}_{4}\) stratum as an example, its best result was spherical kriging (MAE = 2.13 m, RMSE = 2.83 m). From the eight interpolation results in Figure 13, the spatial distribution of the spherical kriging image is also more reasonable, without abnormal breakpoints or irregular polylines. The same indicators and criteria were used to determine the optimal interpolation methods for the other four strata, N\({}_{2}b\) was IDW (\(p\) = 2), J\({}_{2}y^{3}\) was RS-RBF, J\({}_{2}y^{2}\) was TPS-RBF, and J\({}_{2}y^{1}\) was HS-RBF.  
\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{2}{*}{Q\({}_{4}\)} & MAE (m) & 2.13 & 2.88 & 2.82 & 2.86 & 2.45 & 3.73 & 3.41 & 2.67 \\ \cline{2-10}  & RMSE (m) & 2.83 & 3.51 & 3.34 & 3.65 & 3.24 & 4.43 & 3.98 & 3.28 \\ \hline \multirow{2}{*}{N\({}_{2}b\)} & MAE (m) & 3.71 & 3.68 & 3.33 & 3.77 & 2.08 & 5.47 & 4.56 & 4.53 \\ \cline{2-10}  & RMSE (m) & 4.23 & 4.13 & 3.79 & 4.24 & 2.44 & 6.19 & 5.34 & 5.80 \\ \hline \multirow{2}{*}{J\({}_{2}y^{3}\)} & MAE (m) & 1.39 & 1.63 & 1.78 & 1.65 & 1.55 & 1.05 & 0.89 & 1.06 \\ \cline{2-10}  & RMSE (m) & 1.64 & 1.83 & 1.95 & 1.80 & 1.67 & 1.2 & 1.05 & 1.19 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Strata interpolation result error.  
Figure 11: 3D model of terrain (linear kriging).  
Figure 12: Neighbor point sensitivity experiment.  
The data source of stratum interpolation is borehole data, which is less distributed. Figure 14 shows that the change of MAE and RMSE is very small when the number of neighbor points is 3-10, which is between 0.05 and 0.1 m. It proves that the number of neighbor points has little effect on the interpolation of strata and the model is stable. Because the number of formation interpolation boreholes is small, the calculation time and memory consumption are very small, so the statistical analysis is not carried out separately.  
For certain formations (such as Q4 and N2_b_), a virtual thickness assignment method addressed missing borehole data. Specifically, the missing zone is determined by the contour map generated by the optimal interpolation method, and the thickness of the missing zone is assigned to a negative value, then the interpolated surface is regenerated,  
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline  & & **Spherical** & **Exponential** & **Gaussian** & **Linear** & **IDW** & **TPS** & **RS** & **HS** \\ \hline \multirow{2}{*}{\(\text{lay}^{2}\)} & MAE (m) & 2.74 & 2.72 & 2.8 & 2.77 & 2.38 & 1.96 & 2.17 & 2.42 \\ \cline{2-10}  & RMSE (m) & 3.28 & 3.19 & 3.25 & 3.15 & 2.79 & 2.25 & 2.45 & 2.83 \\ \hline \multirow{2}{*}{\(\text{lay}^{3}\)} & MAE (m) & 2.72 & 2.96 & 2.72 & 3.78 & 2.55 & 2.60 & 2.43 & 2.36 \\ \cline{2-10}  & RMSE (m) & 3.01 & 3.22 & 2.80 & 4.32 & 2.79 & 2.74 & 2.81 & 2.71 \\ \hline \end{tabular}
\end{table}
Table 4: _Cont._  
Figure 14: Sensitivity experiment of stratigraphic parameters.  
Figure 13: Q4 interpolation result graph.  
while the missing line (0 line) is drawn automatically. During 3D layer modeling, grid intersection eliminated these areas of missing stratum data, allowing for accurate definition of these zones (Figure 15). Employing the optimal interpolation method in conjunction with this stratum deletion method produced the layer models for the Q\({}_{4}\), N\({}_{2}b\), and J\({}_{2}y^{3}\) strata (Figure 16), verifying the effectiveness and scientific basis of the missing data handling procedure.