## 3 Numerical Experiments
### Simple Isotropic Elastic Model
Figure 5: The decomposition results of P- and S-wave modes at = 0.9 s using different methods for the simple isotropic elastic model with the source position located at (2.56 km, 0.02 km): (**a**,**b**) horizontal and vertical components of the coupled elastic seismic wavefields, (**c**,**d**) decomposed P- and S-wave modes using the Helmholtz decomposition algorithm, (**e**–**h**) horizontal and vertical components of decomposed vector P- and S-wave modes using the wavenumber domain decomposition algorithm, and (**i**-**l**) horizontal and vertical components of decomposed vector P- and S-wave modes using our developed method. These subgraphs (**a**–**l**) indicate different wave modes, which are listed within the subgraphs in white text. Figure 6: The corresponding wavenumber spectrums for these time slices which are shown in Figure 5. These subgraphs (**a**–**l**) indicate different wave modes, which are listed within the subgraphs in white text. Figure 7: The amplitude comparisons of these time slices which are shown in Figure 5c-l at depth = 1.28 km: (**a,b**) horizontal and vertical components of decomposed P-wave mode, and (**c,d**) horizontal and vertical components of decomposed S-wave mode. These different color lines in each subgraph indicate different wave modes, which are listed in the subgraphs using black text. To test the adaptability of our neural network, the time slices for another source position located at (2.56 km, 1.28 km) of this simple isotropic elastic model are also used to test our neural network. It is worth noting that all the time slices for this source position simulated by the elastic wave equations are not included in the training dataset. The horizontal and vertical components of the coupled elastic seismic wavefields at \(t=0.4\) s are shown in Figure 8a,b, and then we separate the P- and S-wave modes from the coupled wavefields using different methods. The decomposed P- and S-wave modes using the Helmholtz decomposition algorithm are shown in Figure 8c,d, the horizontal and vertical components of the decomposed vector P- and S-wave modes using the wavenumber domain decomposition algorithm are shown in Figure 8e-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 8i-l. The corresponding wavenumber spectrums of these time slices (Figure 8a-l) are, respectively, shown in Figure 9a-l. From Figures 8 and 9, even if the source position changes, our developed method can still effectively and 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 those of the vector decomposition algorithm in the wavenumber domain, which reveals that our developed method also has good adaptability when the source position changes. To compare the performance of different methods more clearly, the amplitude comparisons of the decomposed P- and S-wave modes (Figure 8c-l) at depth \(=2.0\) km are shown in Figure 10a-d. From Figure 10, we can also find that our developed method can effectively separate the vector P- and S-wave modes from the coupled elastic seismic wavefields for different source positions and accurately preserve their amplitude and phase characteristic when using the time slices for a given source position as a training dataset. Figure 8: The decomposition results of P- and S-wave modes at \(t=0.4\) s using different methods for the simple isotropic elastic model with the source position located at (2.56 km, 1.28 km): (**a,b**) horizontal and vertical components of the coupled elastic seismic wavefields, (**c,d**) decomposed P- and S-wave modes using the Helmholtz decomposition algorithm, (**e–h**) horizontal and vertical components of decomposed vector P- and S-wave modes using the wavenumber domain decomposition algorithm, and (**i–l**) horizontal and vertical components of decomposed vector P- and S-wave modes using our developed method.