## 3 Numerical Experiments
### Robustness to Other Wave Components  
This numerical experiment was carried out based on elastic wave propagation theory, in which the signals received contain various components, such as P-P, P-S, and S-S waves, surface waves, and direct waves (Figure 19). For these imaging methods, we employed the P-P signal. Other components in the signal were considered to be noise or interference in imaging, and S-waves and surface waves were significant causes of imaging artifacts. Figure 19: Components in a seismic signal. Figure 18: Model C-2. (**a**) True velocity model. (**b**) Imaging result of MVSS beamforming. (**c**) Imaging result of Kirchhoff migration. (**d**) Imaging result of DAS beamforming. Figure 20 shows the normalized amplitude curves and Hilbert transforms at \(x=15\) m in model B-2 (Figure 20a,b) and model A-3 (Figure 20c,d). The curves indicate the following: (1) The amplitude in the shallow parts of the Kirchhoff curve and DAS curve is high (greater than the reflection amplitude). This is the result of a surface wave. However, in the MVSS curve, the surface wave amplitude is suppressed. The surface wave is suppressed because the MVSS method amplifies the reflected wave by using the CF matrix. (2) From the Hilbert transform, it can be noted that the MVSS beamforming method can recognize two close interfaces, while the Kirchhoff and DAS methods might combine these interfaces as one. Thus, MVSS beamforming has a better vertical resolution than the other two methods. (3) In the MVSS curve, the reflection amplitudes are greater than those in the Kirchhoff migration and DAS beamforming curves; this is also partly due to the suppression of surface waves. This means that MVSS beamforming offers a better contrast than the other two imaging methods. Figure 21a shows the imaging result of Kirchhoff migration with all signal components. The interfaces between the layers at depths of 5 m and 15 m are clear. However, massive horizontal artifacts can be detected at the top of the image; in addition, artifacts obliquely penetrate the shallower interface, and noise exists beneath the interface at a depth of 15 m. Likewise, Figure 21d shows the imaging result of DAS beamforming with all signal components. The two interfaces are clear, but horizontal artifacts can again be observed at the top of the image, and there are slight artifacts on both sides of the interfaces. Noise also appears beneath the interface at a depth of 15 m. Figure 21g shows the imaging result of MVSS beamforming with all wave components. The two interfaces are clear at depths of 5 m and 15 m. However, horizontal artifacts remain near the top of the image, and noise can be observed beneath the deeper interfaces. Nevertheless, compared with the imaging results of Kirchhoff migration and DAS beamforming, MVSS beamforming can suppress both the horizontal artifacts caused by surface waves and the artifacts on both sides of the image caused by S-waves. These results confirm that the MVSS beamforming method can significantly suppress artifacts caused by direct waves and surface waves. The suppression of surface waves in reflection seismic exploration has long been a topic of interest [32]. Strong surface waves are significant causes of artifacts in imaging. Hence, to determine how surface waves impact the imaging results, we performed image processing by excluding direct waves and surface waves and then compared the results with the original imaging results. Figure 21b shows the Kirchhoff migration imaging results excluding direct waves and surface waves. Compared with Figure 21a, the surface wave artifact at the top of the image disappears, and the interference across the shallower interface is weaker. However, the artifacts on both sides of the interfaces and beneath the deeper interface still exist. Figure 21e shows the DAS imaging result excluding direct waves and surface waves. Compared with Figure 21d, the surface wave artifact at the top of the image disappears, but the S-wave artifacts across the interfaces still exist.