## 4 Results  
Figures 3a-5a show P-wave velocity variation with the propagation angle in three samples. The P-wave velocity was the fastest in the 90\({}^{\circ}\) direction and the slowest in the 0\({}^{\circ}\) direction in all samples. Figure 2: SEM images of artificial fractured sandstones. (**a**) Pore structure; and (**b**) aligned fractures. Figure 3: Measured velocity and theoretical predictions of the Galvin model for the 1# sample (fracture density 0). (**a**) P-wave (P-wave velocity measurement error is smaller than the size of labels); (**b**) SH-wave; and (**c**) SV-wave. Figure 4: Measured velocity and theoretical predictions of the Galvin model for the 2\(\#\) sample (fracture density 0.0312). (a) P-wave (P-wave velocity measurement error is smaller than the size of labels); (b) SH-wave; and (c) SV-wave. Figure 5: Measured velocity and theoretical predictions of the Galvin model for the 3# sample (fracture density 0.0624). (**a**) P-wave (P-wave velocity measurement error is smaller than the size of labels); (**b**) SH-wave; and (**c**) SV-wave. The P-wave velocity variation with the direction in the 1\(\#\) sample indicated some anisotropy in the background matrix in all samples; this is due to layering in the construction process and has been frequently encountered in previous experimental studies [25; 26; 27; 28]. For P-wave propagation at oblique (45\({}^{\circ}\)) and perpendicular (0\({}^{\circ}\)) angles in the fractured samples, the aligned fractures can increase the compliance of rocks and reduce P-wave velocity. In the 90\({}^{\circ}\) direction, the measured P-wave velocity in samples 2\(\#\) and 3\(\#\) was higher than 1\(\#\) in the dry condition, and lower than 1\(\#\) in the water-saturated condition. Theoretical and experimental studies indicated that, in the 90\({}^{\circ}\) direction [28], P- and SH-wave velocity only decrease very slightly with the increase of fracture density, because fractures are hard to compress in this direction. Therefore, the difference of the measured P-wave between different fracture density samples in the 90\({}^{\circ}\) direction is mainly due to both the background matrix property differences within the three samples and the velocity measurement error. In dry conditions, theoretical predictions fit well with the measured P-wave in the 90\({}^{\circ}\) direction. However, in fractured samples 2\(\#\) and 3\(\#\), theoretical predictions underestimated the P-wave velocity at 45\({}^{\circ}\) and 0\({}^{\circ}\), indicating the predicted P-wave anisotropy was larger than the measured data. In water-saturated conditions, the predicted P-wave velocities were well below the measured results. In the [PERSON] (2015) model, the fluid-saturated background matrix modulus is calculated by Gassmann theory [38]. The results for the 1\(\#\) sample indicated that Gassmann theory significantly underestimated P-wave velocity in the water-saturated background matrix in the three samples. Meanwhile, the measured P-wave velocity showed 20 periodicity while the predicted P-wave velocity showed 40 in the propagation direction. Figures 3b-5b show comparisons of the SH-wave velocities with measured data versus the propagation direction angle in samples with different fracture densities. In dry conditions, the predicted SH-wave velocity qualitatively fit the measured data, and some underestimation was found in the 45\({}^{\circ}\) and 0\({}^{\circ}\) directions. In water saturation, for sample 1\(\#\), the measured SH-wave velocity was higher than in dry conditions, while in theoretical prediction water saturation can reduce the SH-wave velocity from dry conditions. The Gassmann theory assumes that water saturation does not influence shear modulus, \(\mu_{dry}=\mu_{sat}\). Since water saturation can increase the bulk density but has no effect on shear modulus in theoretical prediction, the predicted water-saturated SH- and SV-wave velocities were lower than those in dry conditions.