# Mountain Muon Tomography Using a Liquid Scintillator Detector
## 3 Results and Discussion
### Internal Imaging of the Mountain Using Simulated Data
#### 3.2.1 Scenario 1: The Detector Is Placed inside the Mountain  
Figure 6 shows the shapes and locations of the density variation regions. The mountain height is set to 1 km, and the detector is placed at the center of the bottom surface of the mountain. In actual imaging, this is suitable for mountains with traffic tunnels, in which the detector can be placed. The eight density variation regions are set to be located within the same cylinder, which has a height of 0.2 km, a diameter of 2 km, and a center located at 0.5 km above the detector and is completely wrapped in the mountain. The setting of multiple small regions helps to study whether the position of each small region can be displayed in the radar image to better reflect the imaging capability of this MT. Through the method described in Section 2.4, we obtain the ratio radar image of the density variation, as shown in Figure 7.  
For the six-month data taking time and at least a 50% (\(\leq\)1.4 or \(\geq\)4.2 g/cm\({}^{3}\)) density variation from the reference one, we find that the colored areas in the radar image successfully show the locations of the density variation regions and that some small regions can be identified, indicating that the MT can identify the geometric structure on a hundred-meter scale. The size of the density variation regions is defined as the average muon trajectory length when the regions' density is set to the reference density. Calculations show that the size is 0.16 km. We propose to determine whether the colored areas are caused by density variations by whether the colored bins are clustered in the radar image. This criterion can distinguish the false signals caused by statistical fluctuations where the bins are randomly distributed in the radar image. The greater the density deviation, the greater the number of colored bins, the darker the color, and the better the imaging performance. The extraction of the numerical value of the density from the color, i.e., the ratio \(r\) of the event numbers, needs to be studied further. However, we can ascertain whether the density is larger or smaller than the reference one, as this corresponds to the ratio \(r\) being smaller or larger than one. The locations of the density variation regions displayed on the radar image can guide subsequent prosp  
Figure 6: The mountain (grey) with artificially embedded density variation regions (cyan) and their shapes and locations. The height and diameter of the detector are enlarged 100 times for display convenience. The regions are located in the same cylinder, the center of which is 500 m above the detector. Figure 7: The ratio radar images of the density variation regions, assuming a six-month data acquisition with the detector placed inside the mountain. The radial dimension is the \(\cos\theta_{\rm{zen}}\) of the muon direction; the innermost point and the outermost circle correspond to \(\cos\theta_{\rm{zen}}=1\) (vertical upward direction) and \(\cos\theta_{\rm{zen}}=0.2\), respectively. We do not draw the regions with a \(\cos\theta_{\rm{zen}}<0.2\), in which the MT is not sensitive due to the low event rate. The densities of **(a–h)** are 0, 0.7, 1.4, 2.1, 3.5, 4.2, 4.9, and 5.6 g/cm\({}^{3}\), respectively. The color shows the ratio \(r\) of the number of muons passing through the mountain with the density variation regions to the number of muons passing through the reference mountain. The division is weighted according to the data acquisition time. We set the \(r\) of the bins with a statistical significance \(<3\sigma\) to 1, which means no difference from the reference one, when plotting. The ratio uncertainty \(r_{\rm{unc}}\) of the colored bins satisfies \(r_{\rm{unc}}\leq|r-1|/3\). The total event numbers are 19.5 k, 15.5 k, and 13.1 k when the regions' densities are set to 0, 2.8 (reference), and 5.6 g/cm\({}^{3}\), respectively. The difference between the event number and the reference one can be used to test the ability of the MT to distinguish the density variation regions.