## 3 Numerical Experiments
### Hess Isotropic Elastic Model  
We then use the Hess isotropic elastic model, which is shown in Figure 11, to demonstrate the effectiveness and feasibility of our developed method in the complex elastic model with an anomalous body, and the density of this model is also a constant in our work. The experimental process for this Hess isotropic elastic model is similar to the previous model. To obtain an effective training dataset, we first simulate the coupled elastic seismic wavefields at different times by discretely solving the elastic wave equations, and this source wavelet is an explosive source which is located at (3.5 km, 2.2 km) of this model and can be mainly represented by the P-wave incident energy. We then use the vector decomposition algorithm in the wavenumber domain to generate the decomposed vector P- and S-wave modes from these coupled wavefields. Finally, we also randomly select fifty pairs of time slices from these coupled elastic wave modes and the corresponding decomposed vector P-wave modes for training our neural network. Additionally, we also 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 also defined as 32. After training, all remaining time slices for this given source position are used for testing our neural network. Figure 12a,b show the horizontal and vertical components of the coupled elastic seismic wavefields at \(t=0.6\) s for this Hess isotropic elastic model, and then we use different methods to separate the decomposed P- and S-wave modes from the above coupled wavefields and further compare their decomposition results. Figure 12c,d show the decomposed P- and S-wave modes using the Helmholtz decomposition algorithm, Figure 12e-h show the horizontal and vertical components of the decomposed vector P- and S-wave modes using the wavenumber domain decomposition algorithm, and Figure 12i-l show the corresponding horizontal and vertical components of the decomposed vector P- and S-wave modes using our developed method. Figure 13a-l show the corresponding wavenumber spectrums of these time slices shown in Figure 12a-l. According to Figures 12 and 13, similar to the previous elastic-model testing process, our developed method can also effectively separate the horizontal and vertical components of the decomposed vector P- and S-wave modes from the coupled elastic seismic wavefields when using the time slices which have the same source position as the training samples as the testing samples for complex isotropic elastic models, and these decomposition results of different wave modes are close to that of the vector decomposition algorithm in the wavenumber domain. However, although the Helmholtz decomposition algorithm can generate the decomposed P- and S-wave modes, it will damage their amplitude and phase characteristics. Figure 14 show  
Figure 11: The Hess isotropic elastic model which has a constant density: (**a**) P-wave velocity, and (**b**) S-wave velocity. the amplitude comparisons of the decomposed P- and S-wave modes shown in Figure 12c-1 at depth = 2.5 km. As shown in Figure 14, similar to the vector decomposition algorithm in the wavenumber domain, our developed method can also accurately preserve the amplitude and phase characteristics of the decomposed vector P- and S-wave modes when it is applied to complex elastic models, whereas the Helmholtz decomposition algorithm cannot achieve this goal. Next, the time slices for this Hess isotropic elastic model with another source position located at (3.0 km, 0.2 km) are further used to test the adaptability of our neural network to variations in source position. It is noteworthy that all the time slices for this source position are excluded from the training dataset and are obtained using the elastic wave equations.