## 5 Results and Discussions  
### Laboratory Results  
Table 2 shows the P- and S-wave velocities of the blank samples. The P-wave velocity in the parallel direction was slightly higher than that in the perpendicular direction, and the S1 velocity (polarized parallel to the fractures) was slightly higher than the S2 velocity (polarized perpendicular to the fractures). This was due to layering and uniaxial loading during the manufacturing process.  
Figure 5 shows the measured P- and S-wave velocities in the water-saturated fractured samples. Significant velocity anisotropy was evident in all the fractured samples, with the faster P-wave being measured parallel and the slower one perpendicular. The measured velocity anisotropy is discussed further in the following paragraphs. When the porosity increased from 15.3% to 22.1%, the P-wave velocities (both parallel and perpendicular) dropped sharply. However, as the porosity continued to increase, the decreasing trend in the perpendicular direction was slower than that in the parallel direction, narrowing the difference between the parallel and perpendicular directions and indicating a decrease in anisotropy. However, when porosity increased from 15.1% to 30.8%, the decrease observed in both S1 and S2 wave velocities was generally similar.  
Figure 6 shows the P-wave anisotropy parameter (\(\varepsilon\)) and SWS in all the blank samples. Both the \(\varepsilon\) parameter and SWS decreased with increasing porosity in the blank samples. Because the higher porosity samples suffered lower uniaxial loading (Table 1), they exhibited weaker anisotropy.  
We aimed to investigate the effect of background porosity on fracture-induced P-wave anisotropy and SWS. Because the blank samples exhibited transverse isotropy, we inferred that the background matrix in the fractured samples had the same anisotropy as the blank samples. In fractured samples, the measured anisotropy was a superposition of background matrix anisotropy and fracture-induced anisotropy. To model the anisotropy caused by fractures, the anisotropy of the background matrix had to be considered. Therefore, we approximately represented the fracture-induced P-wave anisotropy and SWS by subtracting the measured \(\varepsilon\) parameter and SWS of the blank samples from that of the fractured ones. Figure 7 depicts the measured results of the fracture-induced \(\varepsilon\) parameter and SWS, as well as the theoretical predictions. When porosity increased from 15.3% to 22.1%, both the measured \(\varepsilon\) parameter and SWS exhibited small fluctuations. In this porosity range, the \(\varepsilon\) parameter and SWS are not so sensitive to porosity changes. However, when porosity increased to 26.1%, P-wave anisotropy dramatically declined from 4.5% to 3.5%, whereas SWS remained fairly constant. Afterwards, as porosity increased to 30.8%, P-wave anisotropy continued to decline from 3.5%to 2.2%, but SWS fluctuated very slightly.  
\begin{table}
\begin{tabular}{c c c c c c} \hline  & **Porosity** & \multicolumn{2}{c}{**P-Wave Velocity (m/s)**} & \multicolumn{2}{c}{**S-Wave Velocity (m/s)**} \\ \cline{2-6}  & **(\%)** & **Parallel** & **Perpendicular** & **S1** & **S2** \\ \hline
1-B & 14.1 & 3930 & 3896 & 2170 & 2120 \\ \hline
2-B & 20.6 & 3442 & 3420 & 1857 & 1820 \\ \hline
3-B & 25.3 & 3128 & 3005 & 1583 & 1495 \\ \hline
4-B & 30.4 & 2817 & 2811 & 1397 & 1390 \\ \hline \end{tabular}
\end{table}
Table 2: P- and S-wave velocities in the blank samples (water-saturated).  
Figure 5: P-wave (**a**) and shear wave (**b**) velocities in water-saturated fractured samples (the P-wave velocity measurement error is smaller than the size of the labels).  
Figure 6: P-wave anisotropy and shear wave splitting (SWS) in water-saturated blank samples.