## 4 Experimental Results
### The Reconstruction of CSNGAN-ASPP
#### 4.3.1 Reconstruction for Nonstationary Delta Facies Model  
Referring to the parameter settings in Table 1, the 2D network was trained. After training, conditioning data from 10 different distribution patterns in the testing set of the nonstationary delta model were randomly selected as inputs to the generator. The corresponding reconstruction results are shown in Figure 7. The simulation results clearly reproduce the channel connectivity and its nonstationary patterns within the reservoir domain, with no significant noise present. Furthermore, all the simulation results comply with the given well data constraints, with a high reconstruction accuracy for the facies attribute types at the conditioning point locations. To further quantitatively assess the simulation performance of the network, this paper uses the variogram and the connectivity functions to evaluate the reconstruction results. The variogram, in particular, can characterize the spatial variability of the regionalized variables in a certain direction, which can be mathematically expressed as follows:  
\[\gamma(x,h)=\frac{1}{2}E[Z(x)-Z(x+h)]^{2} \tag{11}\]  
where \(Z(x)\) represents the attribute value at position \(x\), and \(h\) is the lag distance. The variogram is defined as the variance of the difference between two regionalized variables, \(Z(x)\) and \(Z(x+h)\), separated by \(|h|\), which is used to characterize the local changes in the spatial structure in a particular direction. Additionally, the connectivity function measures the degree of connectivity between multiple points in a given direction, which can be mathematically expressed as follows:  
Figure 7: Reconstruction results for nonstationary delta model. \[MPC(n) =E\{S(u)\cdot S(u+1)\cdot\cdots\cdot S(u+(n-1)\cdot h)\} \tag{12}\] \[=E\{\prod_{i=0}^{n-1}S(u+i\cdot h)\}\]  
where \(S(u)\) represents the attribute value at position \(u\), \(h\) is the lag distance, and \(n\) denotes the number of points (pixels or voxels) in a given direction. This function is used to assess the structural properties of the reconstruction result. Figure 8 illustrates the distribution of strain function curves corresponding to 50 stochastic simulation results. Compared to the reference line, these curves maintain a similar direction and distribution trend, indicating that CSNGAN-ASPP can effectively reproduce the spatial variability of regionalized variables at different lag distances. Figure 9 presents the connectivity function curves in the x direction for the 50 stochastic simulation results and the reference model. It can be seen that the difference between the connectivity curves of the simulation results and the reference line is small, which proves that the river facies in the simulation results maintain a high level of connectivity. Figure 8: The variogram plots for the 50 realizations of delta model generated by CSNGAN-ASPP and the corresponding reference. Figure 9: The connectivity function distribution along x-directions for the 50 realizations of delta model and the corresponding reference. To further statistically analyze the facies attribute information in the simulation results, this paper calculates the facies ratios for the 50 reconstructions and their corresponding reference. The distributions, maximum, minimum, and medians of these ratios are visualized using scatter plots and box plots, as shown in Figure 10. The results reveal that the statistical characteristics of the facies attributes in the reconstructions closely match those of the reference model, indicating that CSNGAN-ASPP effectively reproduces the proportional distribution characteristics of different facies attributes. Additionally, to quantify the overall dissimilarity between the simulation results and the reference model, the Euclidean distance between them is first calculated and then mapped onto a 2D Cartesian coordinate system for visualization. This means that a smaller distance between the two points corresponds to a greater similarity in spatial structural features.