## 4 Experimental Results
### The Reconstruction of CSNGAN-ASPP
#### 4.3.3 Reconstruction for Heterogeneous Aquifer Model  
The CSNGAN-ASPP was trained according to the hyperparameter settings in Table 1. Upon completing training, 12 models from the heterogeneous aquifer testing set were randomly selected, and the corresponding cross-section data were input into the network. The corresponding simulation results are displayed in Figure 18.  
The results of Figures 18 and 19 reveal that the aquifer structure distribution is continuous and effectively reproduces the heterogeneous characteristics of the reservoir domain. This also proves that CSNGAN-ASPP has good simulation performance for heterogeneous structural models.  
In Figure 20, four cross-section data with their corresponding realization models were compared in order to visualize the control effect of the conditioning data. The locations of the conditioning mudstone in the realizations are highlighted in red. The results show that the mudstone locations in the conditioning cross-section data are consistently represented as mudstone in the realizations, which indicates that the realization results are not only consistent with the geological laws within the model but are also fully constrained by the conditioning data.  
Figure 16: The boxplots of the facies ratios for the 50 realizations of lithofacies-fold structure model and their corresponding references.  
Figure 17: The MDS scatter plots for the relationship between the 50 realizations of lithofacies-fold structure model and their corresponding references.  
Figure 19 illustrates the channel distribution characteristics of the aquifer model between one set of simulation results and the corresponding reference.  
Figure 19: The internal distribution between one set of realizations of heterogeneous aquifer structural model and the corresponding reference.  
Figure 20: Conditioning cross-section data and the corresponding realization models.  
Figures 21 and 22 present the variogram and connectivity function curves for the 50 reconstruction results and their corresponding models, respectively.  
Additionally, Figure 23 illustrates the statistical analysis of facies proportion characteristics for 50 randomly selected reference models and their corresponding simulation results, and the corresponding MDS visualization presented in Figure 24.  
Figure 21: The variogram plots for the 50 realizations of heterogeneous aquifer model and the corresponding reference.  
Figure 22: The connectivity function distribution along x-directions and y-directions for the 50 realizations of heterogeneous aquifer structure model and the corresponding reference.  
As illustrated in Figures 21 and 22, the gray curve closely follows the reference line with the change of lag distance, indicating that the simulation results effectively capture the spatial variability and channel connectivity of the aquifer model. Figure 23 shows that, except for a few outliers, there is minimal variability in the statistical information between the two data sets. Figure 24 reveals that the Euclidean distance between the blue and red point clusters is small, signifying a high degree of similarity between the simulation results and their reference model.  
In conclusion, the simulation results generated by CSNGAN-ASPP are consistent with the conditioning data and maintain similar geometric and structural properties to the reference model. The method successfully reproduces the spatial variability, channel connectivity, and facies proportion statistics in the 3D heterogeneous aquifer structural model.