## 4 Discussion
Once trained, the computational cost for the prediction process of the neural network is comparatively inexpensive. During our numerical experiments, the central processing unit (CPU) which is used for elastic wavefield decomposition is the Intel Xeon Gold 5218 16-core 2.30 GHz processor, and the graphics processing unit (GPU) which is used for elastic wavefield decomposition is the 32G NVIDIA Tesla V100 processor. To obtain the decomposed wave modes from the coupled elastic seismic wavefields, the computing time of the Helmholtz decomposition algorithm is so small that it can be ignored, the vector decomposition algorithm in the wavenumber domain usually takes approximately 12 to 16 s, and our developed method based on SADCGANs with 5000 training samples requires approximately 48 h for the training process and 10 to 15 s for the subsequent prediction process. Based on these statistical time data, the significant computational cost of our developed vector decomposition algorithm based on SADCGANs is mainly caused by the training process. With the rapid development of advanced hardware, such as CPUs, GPUs and computer clusters, the computational cost will not be a problem for our developed method based on SADCGANs in the future. With the rapid development of deep learning methods, more and more neural networks are widely used in seismic data processing, such as DCNN, DenceNet, ResNet and GANs, etc. To achieve the vector decomposition of coupled elastic seismic wavefields, we use SADCGANs which are an improvement of conventional GANs in this paper. Compared with other generative models, GANs are a type of generative model with several advantages. Firstly, GANs can be well generalized without requiring a large amount of annotated training data [38]. Secondly, Markov chains may have a lower efficiency in high-dimensional spaces because their convergence rate may be slower, and therefore GANs have the advantage of not requiring Markov chains. Most of the other neural networks either use stochastic approximations to select the training samples to minimize the objective function or use Markov chains to repeatedly extract samples from the distribution and update them to ultimately converge to the true model [38,46]. Thirdly, GANs can use multimodal outputs where a single input may correspond to multiple correct answers. Compared with conventional machine learning models, this significant advantage can minimize the mean squared error (MSE) between the predicted and the desired outputs and thus lead to the blurring of the detailed features because of the averaging effect [38,46]. Finally, the GAN framework is a promising alternative to the neural networks operating on MSE because it provides a rich internal representation of the structural information of the datasets without any blurring or averaging effect [38,47]. However, the conventional GANs also have some disadvantages, the most serious problem of which is the difficulty of training. To effectively alleviate this problem, we use the more effective SADCGANs instead of the conventional GANs to stabilize the entire training process and obtain better wavefield decomposition results. At present, we only study the developed vector decomposition method based on SADCGANs, and in future work, we will test other neural networks used in elastic wavefield decomposition and conduct a comprehensive comparative analysis of their performance, such as DCNN, DenceNet and ResNet, etc.