## 3 Test Results
### Ultrasonic Velocity Change  
As shown in Figure 4, assuming that the matrix quantity of all rock samples and the horizontal thickness of each matrix were the same, the thickness of the matrix in the axial direction was also different for sandstones with different bedding dip angles. The relationship between the horizontal thickness of the matrix and the axial thickness of the matrix under different dip angles is shown in Formula (2):  
\[d=\frac{l}{cos\beta} \tag{2}\] \begin{table}
\begin{tabular}{c c c c c} \hline \(T\)\({}^{\circ}\)C & \(L\) & \(a\) * & \(b\) * & \(\Delta E\) \\ \hline
25 & 54.3 & 5.28 & 3.52 & 0 \\
200 & 56.33 & 5.81 & 4.84 & 2.479 \\
400 & 56.36 & 6.42 & 5.83 & 3.298 \\
600 & 58.37 & 14.8 & 12.46 & 13.679 \\
800 & 58.79 & 11.2 & 10.83 & 10.423 \\
1000 & 60.98 & 12.42 & 14.32 & 14.569 \\ \hline \end{tabular}
\end{table} 
Table 1: Variations in sandstone \(L\), \(a\) *, \(b\) *, and \(\Delta E\) with temperature. Figure 3: Sandstone samples heated to different temperatures. where \(l\) is the horizontal thickness of the matrix, \(d\) is the axial thickness of the matrix, and \(\beta\) is the angle between the matrix and the horizontal line. According to the formula, d increases with the increasing bedding dip angle, and the change rate within the range of \(\beta\) = 45-90\({}^{\circ}\) is greater than that within the \(\beta\) = 0-45\({}^{\circ}\) interval. Since the height of the sample is fixed, if the thickness of the matrix distributed in the axial direction is larger, the thickness of the bedding plane distributed in the axial direction is smaller. By measuring the P-wave velocity (\(v_{p}\)) and S-wave velocity (\(v_{s}\)) of sandstone with different bedding angles, the change rate of the \(v_{p}\) and \(v_{s}\) waves of the sandstone can be calculated according to the formulas defining \(\eta_{p}\) and \(\eta_{s}\):  
\[\eta_{p}=\frac{v_{pT}-v_{p0}}{v_{p0}}\times 100\% \tag{3}\]  
\[\eta_{s}=\frac{v_{sT}-v_{s0}}{v_{s0}}\times 100\% \tag{4}\]  
where \(v_{pT}\) and \(v_{sT}\) represent the P- and S-wave velocities, respectively, of sandstone samples after heat treatment at different temperatures. \(v_{p0}\) and \(v_{s0}\) are the corresponding P- and S-wave velocities of sandstone samples at room temperature. The change rule of \(\eta_{p}\) with temperature is shown in Figure 5a. With increasing temperature, the P-wave velocity of sandstone shows a significant downwards trend. When \(T\) < 400 \({}^{\circ}\)C, it can be observed that the \(v_{p}\) of sandstone decreases slightly, and \(\eta_{p}\) is approximately 10%. As the temperature continues to rise, \(v_{p}\) decreases rapidly, showing a fast-decreasing trend. When \(T\) = 600 \({}^{\circ}\)C, \(\eta_{p}\) reaches approximately 45%, and when \(T\) = 1000 \({}^{\circ}\)C, \(\eta_{p}\) is close to 70%. Temperature has a significant reduction effect on the P-wave velocity of sandstone. Figure 4: Schematic diagram of sandstone stratification with different bedding angles. Figure 5: (**a**) Change trend of the P-wave velocity change rate with temperature for rock samples with different bedding dip angles; (**b**) change trend of P-wave velocity with dip angles for rock samples treated at different temperatures. Figures 5b and 6b show that at the same temperature level, the ultrasonic velocity of sandstone generally increased with the increasing bedding dip angle. When \(\beta=60^{\circ}\) and \(90^{\circ}\), the ultrasonic velocity of sandstone was obviously higher than that of sandstone with other bedding dip angles. It can be seen from Figures 5a and 6a that the wave velocity variation trend with temperature can be divided into two groups. When \(\beta=0^{\circ}\), \(30^{\circ}\) and \(45^{\circ}\), the ultrasonic velocity curve trend with temperature is similar, and when \(\beta=60^{\circ}\) and \(90^{\circ}\), the wave velocity change curve is relatively similar because the distance of ultrasonic wave propagation in the matrix is relatively small in the sandstone with two bedding angles.