## 3 Results
### Rock-Physics-Based Solution of Forward Problem  
When constructing the RPM for the studied samples, the following sets of input data were considered for each sample:  
Dataset 1. The porosity is measured with the porosimeter. The pore aspect ratio is estimated (a) on the small sample and then (b) on the big sample. Dataset 2. The porosity and pore aspect ratio are provided by tomography for the small sample. Dataset 3. The porosity and pore aspect ratio are provided by tomography for the big sample. Moreover, at the initial stage of RP modeling, we took into account the amount of micrite matrix recognized for the samples via thin-section analysis. The elastic moduli of components used for the modeling were as follows. The bulk and shear moduli of the calcite polycrystal were calculated with the self-consistent approximation from the stiffness matrix of the calcite monocrystal presented in [33]. Note that the self-consistent approximation is applicable to the effective elastic properties of polycrystals as well. The bulk and shear moduli were, respectively, equal to 75.1 and 30.3 GPa. The bulk modulus of air was 0.0001 GPa [28]. The density of calcite and air was taken as equal to 2.70 g/cm\({}^{3}\) and 0.001 g/cm\({}^{3}\)[28]. First, we considered a simple model of rocks consisting of the calcite matrix and \"visible\" dry pores of equal shape. We applied the SCA, DEM, and Kuster-Toksoz methods in a rather wide porosity range--from 0 to 35%. Our goals were: (1) to compare the results provided by different theoretical methods and (2) to see the difference between the theoretical and experimental results for this model. The results obtained with the three methods are shown in Figure 8 together with the experimental data. The vertical and horizontal bars show the errors in velocity and porosity determination. The errors are, respectively, \(\pm\)4% and \(\pm\)5% for \(Vp\) and \(Vs\) velocities and \(\pm\)0.5% porosity (in the porosity range up to 16%) as declared in unit test documents. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Parameter** & **Sample 1** & **Sample 2** & **Sample 3** \\ \hline Bulk density (g/cm\({}^{3}\)) & 2.388 (\(\pm\)0.008) & 2.586 (\(\pm\)0.009) & 2.463 (\(\pm\)0.009) \\ S-wave velocity (km/s) & 2.4 (\(\pm\)0.102) & 2.9 (\(\pm\)0.128) & 2.9 (\(\pm\)0.127) \\ P-wave velocity (km/s) & 4.5 (\(\pm\)0.175) & 6.1 (\(\pm\)0.279) & 4.9 (\(\pm\)0.181) \\ Porosity (\(\varphi\)1) (\%) & 11.49 (\(\pm\)0.5) & 3.76 (\(\pm\)0.5) & 7.88 (\(\pm\)0.5) \\ Porosity (\(\varphi\)2) (\%) & 0.43 & 2.16 & 0.13 \\ Porosity (\(\varphi\)3) (\%) & 7.43 & 4.53 & 2.19 \\ Aspect ratio mode (standard sample) & 0.50 & 0.50 & 0.51 \\ Aspect ratio mode (small sample) & 0.50 & 0.55 & 0.52 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Results of laboratory measurement. Figure 5: Volumetric model of (**a**) Samples 1, (**b**) Sample 2, and (**c**) Sample 3 with a diameter of 30 mm according to the results of Computed Tomography. Pores are marked in blue. As can be seen, with the exception of the P-wave velocities for Sample 2, the theoretical velocities obtained with the simple model significantly exceeded the corresponding measured values. Then, we complicated the RP model by bringing it closer to the results of thin-section analysis. Namely, we incorporated the porous micrite matrix in the model. Samples 1 and 3 had large amount of micrite--60% and 70% of the sample volume, respectively. Figure 6: Results of Computed Tomography for (**a**) Sample 1, (**b**) Sample 2, and (**c**) Sample 3. [PERSON] and blue colors on the left pictures show the pores seen, respectively, within big and small samples. The dashed contours on the left indicate the area of small sample. The pictures on the right exemplify the places for cutting the small samples. For Sample 2, the micrite cement was not too high--around 35%. As was mentioned above, the micrite porosity was assumed to be a difference between the measured porosity and porosity provided by the computed tomography.