# GeoSAE: A 3D Stratographic Modeling Method Driven by Geological Constraint
## 3 Experimental Verification and Results
### Construction of Three-Dimensional Geological Models  
The stratigraphic surface sampling points, with coordinates normalized to the range \([-1,1]\), are entered into the constructed stacked autoencoder to predict the potential field values. Section 2.1 provides a comprehensive introduction to the stacked autoencoder model used for 3D geological modeling. The stacked autoencoder model used in this study is defined by several key parameters. The batch size is set to 128 samples per iteration, with an initial learning rate of 0.001, which is halved every 500 iterations. Pre-training is performed using planar geometry, as shown in Figure 7, and after 5000 iterations, the network parameters are loaded into each autoencoder. The model incorporates various loss functions, including stratigraphic sequence relationship loss, global smoothing loss, stratigraphic surface potential field bias, variance, and polarity-related losses. A parameterized Softplus function is used as the activation function, and the weight (\(\lambda\)) for the global smoothing loss is set to 0.1. After 5000 iterations, when the training reaches convergence, the values of each loss function are presented in Table 4. The stratigraphic consistency loss measures how well the model-generated stratigraphic surfaces align with the geological sequence. A low value indicates that the model accurately reflects the stratigraphic distribution, maintaining continuity and relative positioning of the surfaces. The global smoothing loss evaluates the model's spatial smoothness, aiming to prevent abrupt or unnatural changes in the stratigraphic surfaces. A low value suggests that the model maintains smooth transitions throughout and avoids excessive local fluctuations. The potential field deviation loss quantifies the difference between the predicted and actual potential fields. A slightly higher value indicates that the model may underperform in some regions, requiring further optimization to reduce discrepancies with real data. The potential field variance loss measures the variability in the predicted potential field, reflecting the stability and consistency of the model. A very small value suggests that the model is stable across most areas, with high consistency in its predictions. The 3D potential field is shown in Figure 12, with isosurface extraction performed using the PyVista open-source library [40]. The resulting 3D stratigraphic surface model is displayed in Figure 13. The model's spatial resolution is 50 m in the x and y directions and 10 m in the z direction, enabling detailed capture of stratigraphic variations and ensuring the model accurately represents the geological structure. Figure 14 presents a \(3\times 3\) section of the model, illustrating the fit of the data within the model. The fit between each modeled stratigraphic surface and its corresponding sampling points is shown in Figure 15, with panels a to g representing seven strata, ordered from youngest to oldest. The modeled surfaces and the sampling points generally align well, with most points overlapping the surfaces. However, a few points lie outside the surfaces due to significant stratigraphic undulations, which make full constraint difficult. The core method for constructing geological models using the PyVista library involves extracting a series of consecutive isosurfaces from the potential field and processing them iteratively, from oldest to youngest. When processing an older stratigraphic surface, the algorithm \begin{table}
\begin{tabular}{c c} \hline \hline
**Model Loss Metrics** & **Worth** \\ \hline Loss of stratigraphic consistency & 0.00336 \\ Global smoothing loss & 0.02705 \\ Potential field bias loss & 0.05635 \\ Potential field variance loss & 0.00114 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Details of each loss function for 3D stratigraphic surface modeling of stratigraphic points in Jiangdong new district. identifies any younger unconformity surfaces above it that intersect with the current surface.