# Exploration of Kastification and Characterization Based on Borehole Image
## 4 Characterization and Analysis of the Karst Pore Structure
### Analysis of the Karst Pore Structure  
The 38 pore structures in the image are characterized as described above, and the obtained results are demonstrated in Figure 7. Figure 7a-c presents the pore radius, pore area, and shape factor, respectively. As can be seen from Figure 7, the corresponding values of the radius, area, and shape factor vary between various pore structures. By calculating the pore radius, pore area, and pore shape factor, the scale and morphological characteristics of the pore structure could be reasonably characterized. Figure 7: Plots of the karst pore structure parameters: (**a**) pore radius distribution, (**b**) pore area distribution, and (**c**) shape factor distribution. After completing the characterization of the pore structure, the corresponding statistical analyses of the regional pore structure are performed from different angles. In the statistical analysis of the karst pore structure, the quantitative statistical analyses of pores and area statistics are mainly included. The number of pores in the karst hole (\(h\)) is recorded as \(n(h)\), and the pore area in the karst hole (\(h\)) is recorded as \(S(h)\). In the depth direction, the number-ratio function \(N_{\text{p}}(z)\) and the area-scale function \(S_{\text{p}}(z)\) of the pore are established through the following definitions:  
\[N_{V}(z)=\frac{\sum\limits_{i=z\atop h_{2}}^{z+\Delta h}n(i)}{\sum\limits_{i= h_{1}}^{h_{2}}n(i)},\hskip 28.452756 ptS_{V}(z)=\frac{\sum\limits_{i=z\atop i =z}^{z+\Delta h}S(i)}{\sum\limits_{i=h_{1}}^{h_{2}}S(i)}, \tag{15}\]  
where \(z\) is the statistical region depth number, \(h_{1}\) and \(h_{2}\) denote the minimum and maximum values of the statistical region depth, and \(\Delta h\) represents the length of the statistical region \(z\). Equation (15) indicates the projection of the pore number ratio and the area ratio in the depth direction. The proportion of the pore area in the 5.0-5.5 m depth direction is demonstrated in Figure 8a. It can be seen from Figure 8 that at a borehole depth of 5.085 m, the nearby pore structure is moderately small, revealing that the pore structure at a borehole depth of 5.085 m is chiefly manifested as cracks, which is more consistent with the actual situation. In the circumferential direction, the number ratio function \(N_{\text{c}}(z)\) and the area ratio function \(S_{\text{c}}(z)\) of the pore could be established as follows:  
\[N_{\text{C}}(\alpha)=\frac{\sum\limits_{i=z\atop i=0}^{\alpha+\Delta\theta}n( i)}{\sum\limits_{i=0}^{2\pi}n(i)},\hskip 56.905512 ptS_{\text{C}}(\alpha)= \frac{\sum\limits_{i=z\atop i=0}^{\alpha+\Delta\theta}S(i)}{\sum\limits_{i=0}^ {2\pi}S(i)}, \tag{16}\]  
in which angle \(\alpha\) corresponds to the borehole image of the statistical area, and \(\Delta\theta\) is the unit angle of the statistical area. Equation (16) indicates the projection of the pore number ratio and the area ratio in the circumferential direction. The proportion of the pore area in the depth interval of 5.0-5.5 m through the circumferential direction is presented in Figure 8b. The results for the borehole orientation 53\({}^{\circ}\) indicate that the corresponding pore structure is densely distributed, which is more consistent with the actual situation. Statistical analysis of borehole images at borehole depths 5.0-5.5 m is performed based on Equations (14) and (15). In the depth direction, the borehole depth is divided into five sections, i.e., the statistical unit depth is set as 0.1 m, and the corresponding quantity proportion and area proportion distribution are presented in Figure 9a. As can be seen  
Figure 8: Area ratio projection: (**a**) depth direction and (**b**) circumferential direction. from Figure 9a, in terms of quantity, pore structure in the depth range of 5.3-5.4 m and the number of pore structures in at depth intervals of 5.0-5.1 m and 5.4-5.5 m are almost equal to zero.