## 3 Results
### Experimental Calibration
#### 3.2.1 Case of One Single Filled Joint  
When a P wave obliquely impinges on a single filled joint, there are reflected P and SV waves as well as transmitted P and SV waves as shown in Figure 4.  
Figure 5 shows reflection-transmission coefficients versus the filled thickness \(h_{\text{f}}\) considering different water contents of the filled medium. It displays that \(R_{\text{P}\to\text{P}}\) first increases abruptly with the increase in \(h_{\text{f}}\), then its increase tends to be gentle while \(T_{\text{P}\to\text{P}}\) decreases basically in a negative exponential form. For the conversion waves, \(R_{\text{P}\to\text{P}}\) first increases sharply with \(h_{\text{f}}\) increasing then it basically increases in a linear manner while \(T_{\text{P}\to\text{P}}\) basically keeps invariant. In general, \(R_{\text{P}\to\text{P}}\) varies more violently with the increase in \(h_{\text{f}}\) compared with \(T_{\text{P}\to\text{P}}\). As the water content increases, \(T_{\text{P}\to\text{P}}\) decreases evenly, and corresponding curves become divergent; \(R_{\text{P}\to\text{P}}\) and \(R_{\text{P}\to\text{P}}\) have an increasing trend on the whole; \(T_{\text{P}\to\text{P}}\) curves for different water contents basically overlap with each other. Figure 4: Reflected and transmitted waves when a P wave obliquely impinges on a single filled joint. Figure 5: Reflection–transmission coefficients of a P wave impinging on a single filled joint versus the filled thickness \(h_{\text{f}}\) considering different water contents. The incident P wave has the frequency of 50 Hz and the incident angle of 20\({}^{\circ}\). Figure 6 shows the reflection-transmission coefficients varying with wave frequency \(f\). We can see that \(T_{\mathrm{P\to p}}\) decreases basically in a negative exponential form with increasing \(f\). \(R_{\mathrm{P\to p}}\) and \(R_{\mathrm{P\to sv}}\) first increase abruptly with increasing \(f\), then they only have slight changes. Compared with the other three types of coefficients, \(T_{\mathrm{P\to sv}}\) is relatively insensitive to \(f\). Cases of different water contents present similar variation of reflection-transmission coefficients versus \(f\) except for the magnitude difference. As the water content increases, \(T_{\mathrm{P\to p}}\) decreases evenly and corresponding curves become divergent; Both \(R_{\mathrm{P\to p}}\) and \(R_{\mathrm{P\to sv}}\) generally have an increasing trend of which the variation is smaller than that of \(T_{\mathrm{P\to p}}\); \(T_{\mathrm{P\to sv}}\) curves for different water contents basically overlap with each other which indicates that it is independent of the water content of the filled medium. Figure 7 shows the reflection-transmission coefficients versus the incident angle \(\theta\) when a P wave obliquely impinges on a single filled joint considering the different water contents. It shows that \(T_{\mathrm{P\to p}}\) does not change much with increasing \(\theta\) until \(\theta\) approaches the critical angle \(90^{\circ}\), and it suddenly decreases to 0. When \(\theta\) is smaller than around \(40^{\circ}\), \(R_{\mathrm{P\to p}}\) first decreases with increasing \(\theta\). As \(\theta\) is larger than around \(40^{\circ}\), it gradually increases to a peak and then it deceases instead. When \(\theta\) is larger than around \(83^{\circ}\), \(R_{\mathrm{P\to p}}\) increases rapidly. \(T_{\mathrm{P\to sv}}\) changes gently with the increase in \(\theta\). \(R_{\mathrm{P\to sv}}\) first increases to the maximum value at \(\theta\) of approximately \(40^{\circ}\) and then it decreases with increasing \(\theta\) instead. Generally, \(T_{\mathrm{P\to sv}}\) is much smaller than \(T_{\mathrm{P\to p}}\).