## 3 Numerical Experiments
### Simple Isotropic Elastic Model  
We first use a simple isotropic elastic model, which is shown in Figure 4, to demonstrate the effectiveness and feasibility of our developed method, and the density of this model is a constant in our work. During the training process of this model, we first define an explosive source located at (2.56 km, 0.02 km) of this model which can be mainly represented by P-wave incident energy and simulate the coupled elastic seismic wavefields at different times by discretely solving the elastic wave equations, and then we separate the vector P- and S-wave modes from these coupled wavefields using the vector decomposition algorithm in the wavenumber domain. Finally, we randomly select fifty pairs of time slices from these coupled elastic wave modes and the corresponding decoupled vector P-wave modes for training our neural network, and all remaining time slices for this given source position are used for testing our neural network. Additionally, we randomly crop 100 patches with a size of 256 \(\times\) 256 for each training sample, and therefore we have a total of 5000 training samples in the training dataset, and the batch size is defined as 32. The decomposition results of P- and S-wave modes from the coupled elastic seismic wavefields at \(t=0.9\) s, which are not included in training dataset, using different methods are shown in Figure 5. The horizontal and vertical components of the coupled elastic seismic wavefields are shown in Figure 5a,b, the decomposed P- and S-wave modes using the Helmholtz decomposition algorithm are shown in Figure 5c,d, the horizontal and vertical components of the decomposed vector P- and S-wave modes using the wavenum  
Figure 4: The simple isotropic elastic model which has a constant density: (**a**) P-wave velocity, and (**b**) S-wave velocity. ber domain decomposition algorithm are shown in Figure 5e-h, and the corresponding horizontal and vertical components of the decomposed vector P- and S-wave modes using our developed method are shown in Figure 5i-l. The corresponding wavenumber spectrums of these time slices (Figure 5a-l) are, respectively, shown in Figure 6a-l. From Figures 5 and 6, the Helmholtz decomposition algorithm can generate the decomposed P- and S-wave modes from the coupled elastic seismic wavefields, but it cannot generate all components of the decomposed vector P- and S-wave modes and will damage their amplitude and phase characteristics, which will seriously affect the imaging quality of different wave modes from ERTM. The wavenumber domain decomposition algorithm can effectively generate the horizontal and vertical components of the decomposed vector P- and S-wave modes from the coupled elastic seismic wavefields and accurately preserve the amplitude and phase characteristic of different wave modes, but there is still some weak residual energy of other wave modes in these decomposed wave modes. Our developed method can accurately generate the horizontal and vertical components of the decomposed vector P- and S-wave modes from the coupled elastic seismic wavefields which are similar to the decomposition results separated by the vector decomposition algorithm in the wavenumber domain, which verifies the correctness and effectiveness of the intelligent data-driven vector decomposition method using SADCGANs. To compare the performance of different methods more intuitively, we further extract and compare the amplitude of the decomposed P- and S-wave modes (Figure 5c-l) at depth = 1.28 km which are shown in Figure 7a-d. From Figure 7, we can draw the same conclusion: our developed method can effectively achieve the vector decomposition of P- and S-wave modes from the coupled elastic seismic wavefields and accurately preserve the amplitude and phase characteristic of different wave modes which are similar to the wavenumber domain decomposition algorithm, whereas the Helmholtz decomposition algorithm cannot achieve this goal.