3.2.1. Cave Models

The imaging results of model A-1 are shown in Figure 10. In the MVSS beamforming imaging (Figure 10b), the cave roof and floor can be observed, but the right and left sides of the cave are missing. A slight artifact caused by surface waves is observed at the top of the image (Mark 1). The ceiling and floor can be observed, but the walls on both sides are missing. The reason is that the roof is convex and reflects the waves to both sides. Some of these reflected waves exceed the range of the receiver array, resulting in a lack of information from the roof. In contrast, the concave floor can better reflect all arriving waves toward the receiver array, forming a better image. The imaging results of the three methods show that the imaged cave is slightly larger in the vertical direction than the cave actually is.

Figure 10c shows the imaging result via Kirchhoff migration. There is a massive artifact (Mark 1) at the top of the image caused by surface waves. Some minor artifacts can be observed between the top of the image and the cave (Mark 2). Arcuate noise signals caused by S-waves are present on both sides (Mark 4). The upper roof is formed as a dot (Mark 3).


**Table 2.** Model list.

**Table 3.** Elastic parameters of the model media.


Figure 10d shows the DAS beamforming imaging result. The artifacts caused by surface waves are still present at the top of the image (Mark 1). The roof of the cave is also formed as a dot shape (Mark 3). The artifact caused by S-waves is again observed (Mark 4) and is stronger than that in the Kirchhoff migration results.

Compared with RTM (Figure 10e), the advantage for suppressing the artifact caused by the surface wave and S-waves remains in MVSS beamforming. The cave location in MVSS beamforming is more accurate than that in RTM.

The imaging results of model A-2 are shown in Figure 11. In the MVSS beamforming imaging result shown in Figure 11b, the locations of the two caves are well determined, and the roofs and floors of both caves can be observed. In addition to the same surface

wave artifacts detected in model A-1, some interferences were found beneath the floors of the caves (Mark 1) due to the superposition of different S-waves.

**Figure 10.** Model A-1. (**a**) True velocity model. (**b**) Imaging result of MVSS beamforming. (**c**) Imaging result of Kirchhoff migration. (**d**) Imaging result of DAS beamforming. (**e**) Imaging result of RTM.

**Figure 11.** Model A-2. (**a**) True velocity model. (**b**) Imaging result of MVSS beamforming. (**c**) Imaging result of Kirchhoff migration. (**d**) Imaging result of DAS beamforming.

Compared with MVSS beamforming, in addition to the same interferences and artifacts in model A-1, the two floors overlap (Mark 1) in the Kirchhoff migration result (Figure 11c). This overlap appears again in the DAS beamforming result. This finding indicates that MVSS beamforming has a higher horizontal resolution than the other two methods. These imaging results further demonstrate that the imaging of these caves did not suffer from signal interference because the propagation paths of the waves reflected from the cave

boundaries do not overlap with each other. Besides, the S-wave artifacts appears in Kirchhoff migration and DAS beamforming (Mark 2).

Compared with those in model A-1, the interferences in the Kirchhoff migration and DAS beamforming results in model A-2 are more intensive due to the more complicated structure (Mark 3). However, these interferences are still much weaker in the MVSS beamforming result, which means that MVSS beamforming exhibits better S-wave suppression.

The imaging results of model A-3 are shown in Figure 12, in which two caves are aligned vertically in the middle of the area (a beaded cave model). The surface wave artifacts and S-wave interferences are similar to those in model A-1 and model A-2. In addition, there is some overlap between the roof of the shallower cave and the floor of the deeper cave (Mark 1), which means that the three methods have similar vertical resolutions in this cave model.

**Figure 12.** Model A-3. (**a**) True velocity model. (**b**) Imaging result of MVSS beamforming. (**c**) Imaging result of Kirchhoff migration. (**d**) Imaging result of DAS beamforming.

Compared with the MVSS beamforming imaging result, the Kirchhoff migration imaging result suffers from more intensive and complicated interferences on both sides of the image caused by S-waves. These S-wave interferences are also relatively intensive in the DAS beamforming result.
