## 4 Discussion  
As mentioned earlier, samples of different stratigraphic age were studied. Two samples (Sample 1 and Sample 3) were Carboniferous and Sample 2 was Devonian. The Lower Carboniferous samples had lower density and higher porosity than the Upper Devonian sample. This was due to the structure of the pore space. The pores in Sample 1 and Sample 3 were mainly represented by the secondary dissolute type of intergranular porosity, and in Sample 2, the separate cavern's pore space prevailed. According to the results of the RPM, the aspect ratio of microcracks in the Carboniferous samples was lower than in the Devonian sample. Figure 19: Elastic wave velocities vs. porosity calculated for Sample 1 and Sample 3 for two RP models: for fixed “visible” porosity and varying micrite porosity (MICR) and for fixed micrite porosity and varying “visible” porosity (VIS_POR); (**a**) P-wave velocities and (**b**) S-wave velocities. Figure 18: Comparison of the predicted velocities (**a**) _Vp_ and (**b**) _Vs_ for fluid-saturated rocks obtained with four RP models for Sample 1. The solid red lines correspond to the prediction based on the RP model with dual porosity (pores and microcracks). The dashed red lines correspond to the RP model prediction with a single aspect ratio for all voids (“as simple as possible” model). The green and blue curves correspond to predictions for models _host 1_ and _host 2_ described in the text. The parameters of all RP models are inverted from Dataset 1. The tomography studies carried out for the samples demonstrated that the pore space had a hierarchical structure. For two samples (Sample 2 and Sample 3), the tomography performed at different scales (resolutions of 12 microns and 37 microns) indicated a similar pore shape. For all three samples, significantly differing porosity was observed for these two scales. As a rule, the porosity obtained for big samples is much smaller. Thus, for Samples 1 and 3, it was less than 1% (0.58% and even 0.14%). Additionally, for these samples, the porosity measured with the porosimeter was greater, by 3 and 5%, than the porosity provided by tomography for the small scale. This means that a part of the connected porosity could be beyond the tomography resolution. Another possible reason for this discrepancy was that the pores were unevenly distributed within the studied samples. In contrast, for Sample 2, the tomography for small sample exhibited greater porosity as compared to that given by the porosimeter. This could indicate the presence of closed porosity, since the porosimeter measures connected porosity. Moreover, as follows from Figure 5, it also could be due to the uneven distribution of pores in this sample. For each sample, the RPM was performed for three datasets depending on the tomography resolution and the method of obtaining porosity (measured with the porosimeter or provided by computed tomography). When constructing the RP models, the results of thin-section analysis and computed tomography were incorporated into the models. Specifically, first, the porous micrite matrix was taken into account. For the Carbonaceous samples (Sample 1 and Sample 3), the micrite matrix occupied a huge amount of the rock volume (60-70%). However, even for these samples, the results of RP modeling demonstrated that the samples' porosity was too small for the model to be sensitive to the porosity distribution between the micrite matrix and the pores seen with computed tomography. This gave us an opportunity to use a simplified RPM without dividing the quasi-isometric porosity into these two parts. For the RPM, we applied three different methods of EMT including SCA, DEM, and Kuster-Toksoz. We showed that for the range of quasi-spherical porosity of the studied samples (up to 11.5%) and even for higher porosity (up to 20%), all of these methods produce differing results within the experimental error. However, as seen from Figure 8, for greater porosity, the results may differ more markedly. The following question arises: which method gives a more accurate result?