## 3 Numerical Experiments
### Imaging Results  
#### 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 \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Value** \\ \hline Receiver spacing interval & 0.2 m \\ Source frequency & 600 Hz \\ Sampling frequency & \(2\times 10^{5}\) Hz \\ Background P-wave velocity & 1500 m/s \\ Receiver array length & 30 m \\ Number of receivers & 151 \\ Signal length & 0.05 s \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Numerical experiment parameters. Figure 9: Geological model generation workflow. 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 \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **Geological** & \multirow{2}{*}{**Caves**} & **Cave Center** & \multirow{2}{*}{**Cave**} & \multirow{2}{*}{**Map**} & \multirow{2}{*}{**Description**} \\  & **Structure Type** & & & **Location (m)** & & \\  & & & **(Horizontal, Vertical)** & & & \\ \hline A-1 & - & 1 & 15, 11 & 1.8 & \multirow{4}{*}{A model with two horizontally aligned caves.} \\ A-2 & - & 2 & 13, 11 and 17, 11 & 1.8 & & \\ A-3 & - & 2 & 15, 11 and 15, 16 & 1.8 & & \\ \hline B-1 & Syncline fold & - & - & - & - & Syncline model with a fold depth of 4 m. \\ B-2 & Fault & - & - & - & Fault model with a dislocation of 2 m and a great angle (_arctan1.5_). \\ B-3 & Fault & - & - & - & Fault model with a great angle weak fault layer. \\ B-4 & Fault & - & - & - & Fault model with a small angle weak fault layer (_arctan0.5_). \\ \hline C-1 & Syncline fold & 1 & 15, 11 & 1.8 & Syncline model composed of three layers with a cavity. \\ C-2 & Fault & 1 & 15, 11 & 1.8 & & Fault model composed of three layers with a cavity. \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Model list. \begin{table}
\begin{tabular}{c c c c} \hline \hline \multicolumn{1}{c}{**Sequence**} & **P-Wave Velocity (m/s)** & **S-Wave Velocity (m/s)** & **Density (kg/m\({}^{3}\))** \\ \hline Cave 1 & 1400 & 700 & 1600 \\ Layer 1 & 1500 & 800 & 1800 \\ Layer 2 & 1600 & 900 & 2000 \\ Layer 3 & 1800 & 1000 & 2200 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Elastic parameters of the model media.