3.2.2. Layer Models

The imaging results of model B-1 are shown in Figure 13. In the MVSS beamforming imaging result (Figure 13b), two interfaces can be clearly observed. There is some light interference on both sides of the image (Mark 2) and between the interfaces (Mark 1). Furthermore, some parts of the deeper interface are missing (Mark 3).

In the Kirchhoff migration imaging result (Figure 13c), the interfaces between the layers can be observed clearly, but artifacts appear between the two layers and on both sides of the image (Mark 1), and some arc-shaped interferences can be observed on both sides of the image (Mark 2). The DAS beamforming imaging result is shown in Figure 13d; the interfaces can be observed, but arc-shaped interferences and a massive surface wave artifact at the top of the image can also be observed.

**Figure 13.** Model B-1. (**a**) True velocity model. (**b**) Imaging result of MVSS beamforming. (**c**) Imaging result of Kirchhoff migration. (**d**) Imaging result of DAS beamforming.

Comparing the three imaging methods reveals interferences between the different interfaces in the Kirchhoff migration and DAS beamforming imaging results. In the MVSS beamforming image, the amplitude of the surface wave artifact is weak, and the interferences between the interfaces are suppressed. The thickness of the interface between the two layers is approximately 0.4 m. The best resolution given the wavelength of the wavelet is 0.24 m. In contrast, the interfaces are thicker (approximately 1.6 m on the deeper interface) in the Kirchhoff migration and DAS beamforming images, which means that the vertical resolution of MVSS is higher in this layer model. However, artifacts caused by the superposition of S-wave energy still exist and caused interference between the interfaces. Kirchhoff migration and DAS beamforming suffer from similar intersecting interferences (Mark 4) caused by S-waves. However, at shallow depths, these intersecting interferences are replaced by vertical bars in the Kirchhoff migration image.

Compared with the MVSS beamforming imaging results obtained for the cave models, the interfaces can be readily determined, but the amplitudes of the interfaces in this layer model seem weaker than the amplitudes of those in the cave models (using the same imaging and display parameters in every model). In addition, the layers are missing on two sides of the image because the shots range horizontally from 5 m to 25 m.

The imaging results of model B-2 are shown in Figure 14. Figure 14b shows the imaging result of MVSS beamforming. The interfaces between the layers can be observed, and the location of a fault can be inferred from the shapes of the interfaces, but the details of the fault are difficult to discern. Lightly surface wave artifact can be observed (Mark 1).Dislocations in the shallow interface can be observed. For the deeper interface, although the upper and lower stratigraphic boundaries can be seen, the dislocations cannot. Slight interferences can be observed on the sides of the image and beneath the interface (Mark 2).

Figure 14c shows the imaging result of Kirchhoff migration. The artifact caused by surface waves can be observed at the top of the image. At the same time, interferences can be observed above the shallower interface and beneath the deeper interface.

**Figure 14.** Model B-2. (**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 14d shows the imaging result of DAS beamforming. Likewise, the artifact caused by surface waves can be observed at the top of the image (Mark 1). In addition, artifacts caused by S-waves are present on both sides of the image. We also detected interferences between the two interfaces and beneath the deeper interface. The interferences above the shallower interface appear with different shapes in the Kirchhoff migration and DAS beamforming imaging results (Mark 3).

Compared with the RTM (Figure 14e), there were less interferences beneath the interfaces in RTM but MVSS beamforming showed a higher vertical resolution. Still, the surface wave caused an intensive artifact at the top in the RTM result.

Compared the imaging results of the three methods, the artifacts caused by direct waves and surface waves are weaker in the MVSS beamforming result. Similarly, the artifacts on both sides of the image and beneath the deeper interface are also weaker. The dislocations across the deeper interface are missing because the reflection angles generated at such dislocations are large, and thus, the signal could not be recorded by the receiver array.

In summary, compared with the imaging results in model B-1, the shallower interface is complete, and the fault dislocation is well determined. However, the dislocation of the deeper interface is missing because the reflected waves were not received by the receiver array.

Both model B-3 (Figure 15) and model B-4 (Figure 16) contained low-velocity areas near the dislocation. The imaging results of model B-3 are not very different from those of model B-2. The weak layer results in more S-wave interferences above the shallower interface (Mark 1). The reason is that when seismic waves arrive at the weak layer, the reflected waves are not recorded by the receivers. Thus, because of the shadow created by the weak fault layer, the layer beneath the shallower interface is distorted (Mark 2).

Compared with Kirchhoff migration and DAS beamforming, MVSS beamforming still suppressed the S-wave interferences more effectively and provided a better contrast.

In model B-4, the fault angle is shallower than that in model B-3. The shallow part of the weak layer can be observed, but the deep part could not because the imaging results were disturbed by the weak layer. Arcuate interferences (Mark 1) and artifacts along the fault (Mark 2) can be observed. Furthermore, the imaging results were disturbed by the complicated structure due to the fault dislocation (Mark 2). However, the position of the deeper interface was not influenced by the weak fault layer.

**Figure 15.** Model B-3. (**a**) True velocity model. (**b**) Imaging result of MVSS beamforming. (**c**) Imaging result of Kirchhoff migration. (**d**) Imaging result of DAS beamforming.

**Figure 16.** Model B-4b. (**a**) True velocity model. (**b**) Imaging result of MVSS beamforming. (**c**) Imaging result of Kirchhoff migration. (**d**) Imaging result of DAS beamforming.

Comparing MVSS beamforming with Kirchhoff migration and DAS beamforming reveals that the artifacts (Mark 2) in the latter two methods were more intensive than those in the former. For the deeper interface, Kirchhoff migration provided a better contrast than MVSS beamforming.

### 3.2.3. Cave-Layer Hybrid Models

The imaging results of model C-1 are shown in Figure 17. The imaging result of MVSS beamforming is shown in Figure 17b. The shapes and locations of the interfaces and caves can be clearly observed. There were some interferences between the layer interfaces and

the cave boundaries. On both sides of the layer beneath the shallower interface, some artifacts caused by S-waves can be observed.

**Figure 17.** Model C-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.

The imaging result of Kirchhoff migration is shown in Figure 17c, indicating that some interferences appeared near (Mark 1) and between (Mark 2) the layer interfaces. The DAS beamforming imaging result is shown in Figure 17d, revealing multiple arcuate interferences between the two interfaces (Mark 2) and above the shallow interface (Mark 3).

When the three imaging methods are compared, the imaging results of Kirchhoff migration and DAS beamforming still exhibit artifacts of direct waves and surface waves, and there are more interferences between the layers and near the interfaces. Nevertheless, the MVSS method achieved the best resolution and most effectively suppressed the direct and surface waves.

Compared with those for model B-1, the imaging results for model C-1 display more interferences between the interfaces and on both sides of the caves because of the increased stacking of S-waves from different reflection interfaces. In addition, compared with model A-1, it can be noted that the image of the cave in model C-1 is more precise.

Compared with the RTM (Figure 17e), in the composed model of cave and fold, MVSS beamforming still made a better vertical resolution. There was a strong artifact caused by a surface wave in the RTM result.

Model C-2 comprises a combination of a fault, multiple layers, and a cave (model A-1 and model B-2). The imaging results are shown in Figure 18, where Figure 18b shows the imaging result of the MVSS beamforming method. The shallower interface of the layer can be clearly observed, and the cave between the layers can be detected as well. However, the deeper interface is not complete at widths of 10 m to 20 m (Mark 4).

Comparing the three methods makes it evident that the artifacts caused by surface waves are still noticeable in the Kirchhoff migration and DAS beamforming imaging results. Furthermore, the incompleteness of the deeper interface is as notable as it is in the MVSS beamforming imaging result, while the interferences between the layers and on both sides of the image (Mark 2) are weaker in the MVSS beamforming imaging results. However, the disturbances on the deeper interface (Mark 3) are similar among all three methods.

**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.

Compared with model B-2, a part of the deeper interface of the layer is blurred in model C-2. There are two main reasons for this blurriness. The structure is particularly complicated in the middle of the area due to the coexistence of the fault and cave, which causes the wave to reflect back and forth between those structures; this produces many multiples. Thus, the reflected waves from the deeper interface are seriously disturbed by multiples from the complex structure in the middle of the model. Moreover, compared with the features of model A-1, the cave's roof and floor are not clear (Mark 1) because the waves are disturbed by the fault.
