## 4 Discussion
Therefore, the decomposition results of our developed method based on SADCGANs will be as close as possible to that of the vector decomposition algorithm in the wavenumber domain, because the training results of the neural network can only be as close to the sample labels as possible. There is still some weak residual energy of S-wave modes in these decomposed vector P-wave modes as sample labels for our neural network, and therefore each wave mode generated by our developed method contains other weak wave modes which are similar to those of the wavenumber domain vector decomposition algorithm. In other words, the accuracy of sample labels largely determines the accuracy of our developed method. Thus, studying how to effectively improve the accuracy of the decomposed vector P-wave modes as training sample labels as much as possible is worth considering. Our developed method is currently applied to the elastic wavefield extrapolation and decomposition process of ERTM to obtain the multi-wave imaging results, and therefore its application object is the time slices of coupled elastic seismic wavefields at different times. In our work, we mainly use the time slices at some certain times for two theoretical elastic models as training sample labels, and therefore the training data have the following main limitations. Firstly, the training results of the neural network theoretically improve as the number of sample labels gradually increases, but we can only select the simulated wavefields at some certain times as training data for a given elastic model, and therefore this number needs to be carefully considered. Secondly, due to only testing two models, the training dataset we used in our work lacks diversity, which may result in our developed method not achieving good vector decomposition results for more complex elastic models, and this problem can be effectively solved by introducing various theoretical elastic models. Thirdly, various theoretical models are only the approximation of the real geological models, and therefore the simulated wavefields with fixed simulation parameters as training data are different from the real elastic seismic wavefields in subsurface media, such as time and space grid sizes, source and receiver positions, etc., which may lead to the fact that our developed method cannot effectively and accurately separate the horizontal and vertical components of the vector P- and S-wave modes from the real elastic seismic wavefields. Fourthly, at present, there is no effective method to completely separate the vector P- and S-wave modes from the coupled elastic seismic wavefields, and therefore the training dataset which we use in our work is not absolutely perfect. In future work, our developed method will be applied to multicomponent seismic data to effectively and accurately separate the seismic data of different wave modes, so that it can promote the development and practical application of multicomponent seismic exploration technology. Compared with the simulated seismic data, the wavefield characteristics of real multi-component seismic data are more complex, and therefore how to generate the corresponding training sample labels is also a key consideration. Because the elastic wavefield extrapolation of ERTM itself requires a huge computing time, using deep learning methods to achieve the vector decomposition of coupled elastic seismic wavefields will require more computing time, and therefore one practical limitation of our developed method is its computational efficiency. In other words, among the three decomposition algorithms used in our numerical experiments, the Helmholtz decomposition algorithm has the highest computational efficiency, the vector decomposition algorithm in the wavenumber domain requires a longer computing time than the previous algorithm, and our developed algorithm based on SADCGANs requires the longest computing time. The biggest concern of using SADCGANs is the computational cost of the training process.