## 4 Results and Discussion
### Quantifying Aspect Ratio and Crack Density  
The measured elastic wave velocities for each sample were substituted in Equations (1) and (2) to produce two separate equations parameterized with only aspect ratio and crack density as unknowns. Both of these resultant equations were combined and solved simultaneously to obtain sample-specific aspect ratio and crack density values, which are shown in Figures 8 and 9. Equations (6) and (7) show that Equations (1) and (2) can be reformulated simply using the relationship between the elastic wave velocity and the porosity, which contains 10 different parameters. The measured values were used for  
Figure 7: Different reduction ratios for compressional and shear wave velocities. The 1, 2, 3, 4, 5, 6, 7, 8, 9, and 10 denote samples albite 1, albite 2, albite 3, albite 4, quartz 1, quartz 2, quartz 3, biotite, calcite, and chlorite, respectively. Each difference was calculated by subtracting the shear wave reduction ratio from the compressional wave reduction ratio. As such, a negative value shows that shear wave velocities significantly decreased due to weathering. elastic wave velocities, and both [PERSON]'s modulus (E) and Poisson's ratio (\(\
u\)) were calculated in terms of compressional (V\({}_{\rm p}\)) and shear wave (V\({}_{\rm S}\)) velocities, as shown in Equations (11) and (12):  
\[v=\frac{\rm{Vp}^{2}-2\rm{Vs}^{2}}{2\Big{(}\rm{Vp}^{2}-\rm{Vs}^{2}\Big{)}} \tag{11}\]  
\[\rm{E}=\frac{-4\rm{Vs}^{4}\gamma-3\rm{Vp}^{2}\rm{Vs}^{2}\gamma}{\rm{Vp}^{2}- \rm{Vs}^{2}} \tag{12}\]  
The bulk moduli for grain (K\({}_{\rm g}\)), skeleton (K\({}_{\rm sk}\)), and fluid (K\({}_{\rm f}\)) phases in all samples were assumed to be \(15\times 109\) Pa, \(7.78\times 106\) Pa, and \(2.18\times 109\) Pa, respectively, as reported by [PERSON] and [PERSON] (2016). The grain (G\({}_{\rm S}\)) shear modulus and mass density (\(\gamma\)) were assumed to be \(13\times 109\) Pa and \(2800\) kg/m\({}^{3}\), respectively ([PERSON] et al., 2016). Unaltered rock columns had calculated aspect ratios and crack densities in the ranges 0.1872-0.1948 and 0.1829-0.2120, respectively, although post-weathering values changed to 0.014-0.133 and 0.1131-0.2220, respectively. Figure 10 shows absolute change ratios based on pre- and post-weathering values of aspect ratio and crack density. These change ratios are \(-2\)-\(14\%\) and \(9\)-\(1021\%\), respectively, revealing that crack density showed a significantly greater difference due to weathering, whereas the aspect ratio remained almost constant. [PERSON] et al. (2016) suggested similar behavior during an increase in effective stress (i.e., the aspect ratio of a rock remains constant despite the crack density changing). The number of cracks per unit volume thus increases as weathering progresses, which greatly influences the crack density. However, the aspect ratio of a crack, which is the ratio of its short and long dimensions, shows a relatively small percentage change because simply opening a crack via weathering does not change its longitudinal and transverse orientations. Unlike the elastic wave velocity, it is difficult to determine a sample's tendency of composed mineral via calculation of aspect ratio and crack density. The total porosity (\(\phi\)) consists of equant porosity (\(\phi_{\rm ep}\)) and crack porosity (\(\phi_{\rm cp}\)), and the relative proportions of both in most rocks are thought to be about 95% and 5%, respectively ([PERSON], 2016; [PERSON], 2016). Therefore, the total porosity is often dependent on the equant porosity, which influences elastic wave propagation. Further, elastic wave velocity shows a good tendency with composed mineral in specimens as the weathering process continues. Nonetheless, aspect ratio and crack density limit our ability to characterize some sample properties, such as seismic velocity, as they are related to equant porosity, which forms a relatively small proportion of the total porosity and only weakly influences microstructural behaviors.