## 3 Numerical Experiments
### Robustness to Other Wave Components
Figure 21h shows the MVSS beamforming result excluding direct  
Figure 20: Imaging amplitude curves at \(x=15\) m and the Hilbert transform of each. (**a**,**b**) model B-2; (**c**,**d**) model A-3. waves and surface waves. Compared with Figure 21g, the artifact at the top of the image disappears, but the interferences beneath the deeper interface still exist. These comparisons suggest that the main consequence of direct waves and surface waves is the presence of artifacts at the top of the image. S-waves (or converted waves) are another main factor causing artifacts and interference in seismic imaging. S-wave signals and converted waves (reflected S-waves converted from P-waves at interfaces) have similar in-phase axes as P-wave signals. However, the velocities of S-waves and converted waves do not match the estimated velocity (P-wave velocity), so the use of S-waves (or converted waves) can cause errors. Figure 21c shows the Kirchhoff migration imaging result ignoring S-waves. Compared with Figure 21a, artifacts at the top of the image still exist, but the artifacts are thinner and weaker. Moreover, the interferences across the shallower interface and beneath the deeper interface both disappear. Figure 21f shows the DAS beamforming result ignoring S-waves. Compared with Figure 21d, the artifacts at the top of the image still exist but are weaker, and the interferences beneath the deeper interface and on both sides of the shallower interface disappear. Finally, Figure 21i shows the MVSS beamforming result ignoring S-waves. Compared with Figure 21g, the artifacts at the top of the image still exist, albeit with weaker energy, and the interference beneath the deeper interface disappears. In addition, compared with Figure 21f, the artifacts on both sides of the interfaces disappear. From this discussion, we have found the following:  
1. The horizontal artifacts at the top of the images are caused by surface waves, while the artifacts beneath the interfaces are caused by S-waves, probably P-S waves;
2. When S-waves are eliminated, the direct wave still exists, but the surface wave does not. This greatly weakens the artifacts at the top of the image;  
Figure 21: Imaging results after eliminating either surface waves or S-waves. (**a**) Kirchhoff migration result using the original signals. (**b**) Kirchhoff migration result using signals without surface waves. (**c**) Kirchhoff migration result using signals with only P-waves. (**d**) DAS beamforming result using the original signals. (**e**) DAS beamforming result using signals without surface waves. (**f**) DAS beamforming result using signals with only P-waves. (**g**) MVSS beamforming result using the original signals. (**h**) MVSS beamforming result using signals without surface waves. (**i**) MVSS beamforming result using signals with only P-waves. 3. The ability of MVSS beamforming to suppress surface wave artifacts at the top of the image and the S-wave artifacts on both sides of the interfaces is superior. However, the S-wave artifacts beneath the interfaces still affect MVSS beamforming as much as they do the other methods.