## 3 Results
### Rock-Physics-Based Solution of Forward Problem
We took the porosity given by the computed tomography performed for the small samples. We found that the porosity of the micrite matrix was 6.7% for Sample 1 and 8.1% for Sample 3. The tomography porosity for Sample 2 was smaller than the measured porosity. Therefore, we considered that the micrite porosity was very low or even absent in this sample. We compared the results obtained with the simple model described above in this section with the two-step model of rocks with porous micritic cement presented in Section 2. The comparison showed that the difference in elastic wave velocities provided by these two models did not exceed 1% for all samples. The reason was that the total porosity was not high. In this case, a distribution of porosity between \"visible\" and micrite pores did not produce a noticeable effect. Therefore, for further computations performed for the studied samples, we applied the model without a micrite matrix. However, in Section 4, we again consider the micrite-based model for the prediction of elastic properties for higher porosity. We performed a numerical analysis that allowed us to conclude that an RP model incorporating ten systems of voids characterized by histograms (Figure 4) can be replaced by a model with a single system of voids. The aspect ratio of the voids was equal to the mode values of the histogram (0.50-0.55). Thus, the difference between the \(\mathcal{V}p\) and \(Vs\) velocities for Sample 1, calculated with the two models for porosity provided by the porosimeter (11.49%), was around 1%. This was much smaller than the experimental errors for \(\mathcal{V}p\) and \(Vs\) (4% and 5%, respectively). From the analysis of the obtained modeling results, it follows that for the voids' aspect ratio, provided by the tomography, and in the range of porosity of the samples 0.58-11.5%, all methods showed similar results. Therefore, only the Berryman self-consistent method was chosen for further modeling. The overestimated values of the theoretical elastic wave velocities compared to their experimental analogs may be due to the presence of smaller voids, the size of which was beyond the resolution of the tomographic study. However, the volume concentration of these voids should not be too high. Otherwise, the porosity of the rock will not correspond to the experimental data. The voids whose small amount may produce a significant drop in the velocities are microcracks. We assumed that the microcracks were randomly oriented. Even a small content of microcracks (within the experimental error of porosity) can cause a significant decrease in the elastic wave velocities. As a rule, it is not possible to measure  
Figure 7: Porosity-based analysis of Representative Elementary Volumes (REV) of studied big samples. the microcrack porosity and estimate their aspect ratio in the experiment. In this case, RPM can be used to estimate these parameters, including not only quasi-isometric voids but also microcracks in the model. Such a model will contain two unknown parameters--microcrack porosity and their aspect ratio. These parameters can be determined by minimizing the discrepancy between theoretical and experimental elastic wave velocities. Note that microcracks not seen by the computed tomography were also incorporated in an RP model of carbonate rocks by [PERSON] et al. (2018) in order to explain the experimental P-wave velocities. [PERSON] (2018) investigated thin-section images of carbonate rocks with confocal laser scanning microscopy. The porosity and permeability were independently measured for the rocks. It was found that numerical simulations based on image analysis captured the porosity but not the permeability. This may also indicate the presence of invisible voids in carbonate rocks. When incorporating microcracks in the RP model, again, the question arises about the ambiguity of the simulation results due to the choice of the method.