## 2 Materials and Methods
### Experimental Samples
\begin{tabular}{c} **Total** \\ **Porosity** \\ **(\%)** \\ \end{tabular}  } & \multicolumn{2}{c}{**P-Wave**} & \multirow{2}{*}{ \begin{tabular}{c} **Quartz** \\ **(\%)** \\ \end{tabular}  } & \multirow{2}{*}{\ \begin{tabular}{c} **Feldspar** \\ **(\%)** \\ \end{tabular}  } & \multirow{2}{*}{ \begin{tabular}{c} **Debris** \\ **(\%)** \\ \end{tabular}  } \\  & & & & & \\ \hline
1 & 1.79 & 5.49 & 57 & 11 & 27 \\
2 & 2.46 & 5.37 & 64 & 15 & 17 \\
3 & 3.26 & 5.47 & 61 & 23 & 12 \\
4 & 3.63 & 5.13 & 62 & 16 & 14 \\
5 & 4.84 & 5.3  
In order to observe the distribution of microscopic pore system, we sliced the three-dimensional digital core of the rock sample. The result of rock sample slicing is shown in Figure 3a. We found from the rock section that there were so many kinds of pores with different size, shape and connectivity, the tight sandstone can be regarded as a kind of medium with multiple pore structures under ellipsoid inclusion theory [28]. Therefore, the pores in the rock section were fitted to ellipses with different pore aspect ratios using an image processing algorithm [29]. It was calculated that the pore aspect ratio distribution range of rock samples was 0.01-0.65, with an average of 0.21 and a standard deviation of 0.16. Figure 3b shows the equivalent slicing of the rock pore structure after digital image processing. According to the equivalent slicing of the rock pore structure, different types of pores in the rock were represented by some ellipsoids with different aspect ratios. Thus, we set the initial pore aspect ratio of the primary intergranular pores, secondary dissolution pores and micro-fractures at 0.25, 0.45, and 0.05, respectively. This provided a reference for the parameter settings of the subsequent rock physical modeling. Tight sandstone reservoirs tend to exhibit strong elastic anisotropy resulting from fluid-filled aligned fractures. Since the wavelength of a seismic wave is much larger than the fracture aperture, we can ignore the opening degree of the fracture aperture and the  
Figure 3: The internal microscopic pore system of rock samples. (**a**) Main pore types of rock samples under two-dimensional slicing. (**b**) The equivalent diagram of rock pore structure after digital image processing. Figure 2: 3D reconstruction of some tight sand samples: (**a**) NO.2 rock sample; (**b**) NO.10 rock sample. The yellow area in the map is rock skeleton, and the blue area is pore space. details of fracture spatial distribution, and treat the fracture equivalently as an anisotropic solid in the rock physics modeling [30]. The anisotropic characteristics of the rock will depend on the development direction and intensity of the fractures, the elastic properties of the material filling the fracture, and the elastic modulus of the surrounding rock. The statistical results of 318 structural fractures in the study area are shown in Figure 4. It can be seen from the figure that vertical fractures and sub-vertical fractures were mainly developed, and the number of low angle fractures and horizontal fractures was less in the study area. Moreover, vertical or sub-vertical fractures were mostly effective fractures with good opening degrees and partial fracture width up to 0.1-0.5 cm. In contrast, the low-angle fractures were mostly ineffective and closed due to the gravity of the overlying strata. Fractured reservoir rocks filled with vertical or sub-vertical arranged fractures may exhibit horizontal transverse isotropic (HTI) characteristics based on the fracture equivalent medium theory [31; 32]. According to the statistical results, the Xu-2 Member reservoir can be assumed to be an HTI medium, which is formed by a group of vertically arranged non-interactive fractures embedded in a pure isotropic background medium. This assumption helps us to describe the propagation characteristics of seismic waves in tight sandstone of study area [33].