## 4 Ultrasonic Measurement  
The P- and S-wave velocity measurements were conducted on an ultrasonic bench-top pulse transmission system at room temperature and an atmosphere pressure suitable for water-saturated conditions. The ultrasonic transducers, which were heavily damped with a central frequency of 500 kHz, were excited by a voltage spike, giving rise to broadband ultrasonic pulses. The transmitted P- and S-wave signals were recorded with a digital oscilloscope and a desktop computer. The time sampling interval for all the experiments was 0.04 us for both P- and S-wave signals. The measurement error was about 0.5% for P-wave velocity and 0.8% for S-wave velocity. Water saturation was obtained by immersing the samples in a water-filled container. The container was placed in a sealed bin to extract the air. To ensure full water saturation, the saturation rate was calculated using the following formula:  
\[Sw(water)=\frac{m_{sat}-m_{dry}}{V\varphi\rho_{f}}\times 100\% \tag{9}\]  
where \(m_{sat}\) and \(m_{dry}\) is the wet and dry mass of the sample, \(V\) and \(\varphi\) represent the volume and helium porosimetry measured porosity of the sample, respectively, and \(\rho_{f}\) is the \begin{table}
\begin{tabular}{c c c c c c c c c} \hline  & \multicolumn{2}{c}{**Group 1**} & \multicolumn{2}{c}{**Group 2**} & \multicolumn{2}{c}{**Group 3**} & \multicolumn{2}{c}{**Group 4**} \\ \cline{2-10}  & **1-B** & **1-F** & **2-B** & **2-F** & **3-B** & **3-F** & **4-B** & **4-F** \\ \hline Fracture density & 0 & 0.06 & 0 & 0.06 & 0 & 0.06 & 0 & 0.06 \\ \hline Fracture aspect ratio & / & 0.018 & / & 0.018 & / & 0.018 & / & 0.018 \\ \hline Porosity (\%) & 14.1 & 15.3 & 20.6 & 22.1 & 25.3 & 26.1 & 30.4 & 30.8 \\ \hline Fracture porosity (\%) & / & 0.75 & / & 0.75 & / & 0.75 & / & 0.75 \\ \hline Bulk density (g/cm\({}^{3}\)) & 2.22 & 2.21 & 2.16 & 2.15 & 2.07 & 2.05 & 2.03 & 2.03 \\ \hline Compression pressure (MPa) & 186 & 186 & 53 & 53 & 21 & 21 & 15 & 15 \\ \hline \end{tabular}
\end{table} 
Table 1: Physical parameters of the three sample groups (water-saturated). Figure 3: (**a**) Four groups of samples with different porosities, (**b**) a section of the fractured sample, (**c**) an SEM image of the pore structure in the section, and (**d**) an SEM image of the fracture structure in the section. bulk density of water. The P-wave velocities were measured both parallel (90\({}^{\circ}\)) and perpendicular (0\({}^{\circ}\)) to the fractures. The S-wave velocities were measured parallel to the fractures, and polarization was performed in two directions (parallel (S1 wave) and perpendicular (S2 wave) to the fractures) by rotating the transducers. Then, the Thomsen parameter (\(\epsilon\)), which represents the difference in P-wave velocity between the parallel and perpendicular directions, was calculated using the following formula:  
\[\epsilon(\%)=100\times(\frac{V_{P}\parallel-V_{P}\bot}{V_{P}\bot}) \tag{10}\]  
where \(V_{P}\parallel\) and \(V_{P}\bot\) represent the P-wave velocities in parallel and perpendicular directions, respectively. Shear wave splitting (SWS) in the parallel direction can be calculated as follows:  
\[SWS(\%)=100\times(\frac{V_{s1}-V_{s2}}{V_{s2}}) \tag{11}\]  
where \(V_{s1}\) and \(V_{s2}\) are fast and slow shear wave velocities. The numerical modelling experiment of wave propagation in anisotropic media by [PERSON] and [PERSON] (1994) showed that if the wave front was propagating parallel or perpendicular to the layering (or in this case, to the fractures) [25], a true phase velocity was measured in laboratory ultrasonic experiments. Therefore, in this study, P- and S-wave phase velocities were measured in both parallel and perpendicular directions. The transmitted signals of the blank samples were analysed using Fourier transform to obtain the dominant frequency and to calculate the wavelength (Figure 4). The ratio of wavelength to fracture diameter (\(\lambda\)/d ratio) was between 5.2 and 10.8 for the P wave and between 3.9 and 12 for the S wave.