## 3 Application Effect
### Generation of Homogeneous Training Images  
On the basis of the training dataset in Section 2.1.2, 10,000 uniform training images of fan delta facies, straight river facies, and meandering river facies are generated. The training image generation result 1 and result 2 in Figure 10 show two implementations of the training image for the homogeneous fan delta facies. From 200 to 3200 steps,  
Figure 8: Generation results of braided river delta facies training images: (**a**) 200 steps; (**b**) 2200 steps; (**c**) 4200 steps; (**d**) 6200 steps; (**e**) generation result 1; (**f**) generation result 2 (yellow represents a river region, blue represents background). Figure 9: Generation results of anastomosing river facies training images: (**a**) 200 steps; (**b**) 2200 steps; (**c**) 4200 steps; (**d**) 6200 steps; (**e**) generation result 1; (**f**) generation result 2 (yellow represents a river region, blue represents background). the boundary of divergent channel microfacies and interdivergent bay microfacies became clear, and the divergent channel microfacies spread out in a fan shape. After 3200 steps, it is possible to generate a fan delta facies training image similar to the one in the training image library. The training image generation result 1 and result 2 in Figure 11 show two implementations of the training image for the homogeneous smooth river facies. From 200 to 2000 steps, the boundary of river sediment subfacies and flood bank subfacies is clarified, and the continuity of river is strengthened gradually. After 2000 steps, it is possible to generate the training image of the straight stream facies, which is the same as in the training image database. In Figure 12, the training image generating result 1 and result 2 show two implementations of the training image for the homogeneous meandering river facies. From 200-3200 steps, the sediment subfacies boundary becomes distinct, the river continuity is strengthened, and the width of the river becomes uniform. After 3200 steps, it is possible to generate the training image of the meandering stream, which is the same as that in the training image library. Figure 11: Generation results of smooth river facies training images: (**a**) 200 steps; (**b**) 1200 steps; (**c**) 2200 steps; (**d**) 3200 steps; (**e**) generation result 1; (**f**) generation result 2 (yellow represents a river region, blue represents background). Figure 10: Generation results of fan delta facies training images: (**a**) 200 steps; (**b**) 1200 steps; (**c**) 2200 steps; (**d**) 3200 steps; (**e**) generation result 1; (**f**) generation result 2 (yellow represents a river region, blue represents background). Comparison between the Proposed cDCGAN-Based Approach and Traditional Methods for Training Image Library Construction  
In order to elaborate on how this method addresses the limitations of traditional methods, we also compare the generation efficiency with traditional methods. The Facies Modeling function of Schlumberger's Petrel modeling software can achieve various sedimentary facies modeling functions, among which Object-Based Facies Modeling can be combined with the workflow function to achieve target-based training image batch generation. Stanford University's SGeMS modeling software can achieve simple modeling functions, with TIgenerator specifically used for batch generation of training images for multi-point geostatistics. Overall, as shown in Figure 13, on the one hand, the cDCGAN-based training image generation approach is capable of producing a training image for a particular type of sedimentary facies in comparison with a conventional GAN-based unconditioned simulation. The cDCGAN-based approach, on the other hand, can produce a larger batch of training images, faster, and with more diversity than conventional training methods. Under the same calculation conditions, as shown in Table 6, with the goal of generating 1000 training images, Petrel, SGeMS, and cDCGAN took 634.6 s, 177.5 s, and 22.5 s, respectively.