**6. Discussion**

The pore structure of the tight carbonates is involved to help analyze and explain the relationship between the porosity and the wave speeds of both P- and S-waves. Seen from the constructed pore space of the tight carbonates, the pore spaces of the tight carbonate samples vary significantly and fractures and vugs are well developed causing the relationship between the porosity and the wave speeds to be scattered.

The pores and vugs possess the majority of the pore space for most of the samples, except those fractured tight carbonates. Thus, the porosity of the samples is positively related to the sum of the volume fraction of the vugs and pores (Figure 11). The existence of vugs and pores improves the porosity of the tight carbonate samples. However, considering the wave speeds, the fractures are key compared to the pores and the vugs because the vugs are distributed heterogeneously in the samples, and some of them are on or near the sidewall of the core plugs that might not affect the path of the waves.

**Figure 11.** The cross plot of the sum of the volume fractions (VF) of vugs and pores against the He gas porosity.

If a fracture is perpendicular to the wave path, the wave has to transit through the fracture and consequently, its speed is slower. However, a fracture can merely affect the wave speed if it is parallel to the wave path. This kind of fracture adds to the total porosity but will not reduce the wave speed. Thus, the heterogeneity in the spatial distribution of the vugs and the fractures with high orientation angles are the main causes of the scatterings in the porosity and wave velocity relationship. On this consideration, the wave speeds of both the P- and S-waves are related to the porosity of the fractures as shown in Figure 12. Removing the samples with a limited amount of low-oriented fractures (the fractures having their surface perpendicular or nearly perpendicular to the direction of wave propagation), the wave velocity of the remaining samples is negatively related to the fracture porosity indicating that the wave velocity of the tight carbonate samples is more sensitive to the fractures, especially those intersecting its wave path. The Pearson coefficient of S-wave velocity with fracture porosity is about two times that of the P-wave velocity with fracture porosity indicating that the S-wave is more sensitive to the fracture porosity compared to the P-wave.

**Figure 12.** The cross plots of (**a**) P- and (**b**) S-wave porosity against fracture porosity. For the convenience in referring the dots to the micro-CT images, the number of the samples are marked on the figure. The red solid and black empty dots represent the data collected from the samples possessing fractures with low and high orientation angles, respectively. Decreasing trends of the wave speeds with porosity are observed for both P- and S-waves in the samples mainly containing low orientation fractures.
