## 3 Results
### Comparison of Predictive Abilities of RP Models  
Each of the constructed RP models was used to predict the elastic wave velocities in rocks saturated with formation water in the range of 0-20% quasi-isometric porosity. The bulk modulus and density of formation water were taken as equal to 2.82 GPa and 1.1 g/cm\({}^{3}\)[28], respectively. The microcrack parameters were considered constant and corresponded to the most probable solutions found for each dataset. These parameters are shown in Table 2. For the fluid substitution, the Gassmann method was used [28; 37], i.e., a prediction of velocities for the frequencies of the field experiment was assumed. Figures 16 and 17 show the prediction of longitudinal and transverse wave velocities obtained for each sample as a function of the total porosity. The total porosity is equal to the sum of the quasi-isometric and microcrack porosity. The prediction was carried out for the microcrack parameters obtained for the Datasets 1-3 shown in Table 2.  
As follows from the analysis of the results, the estimates of elastic wave velocities obtained for the same value of total porosity differed by no more than 14 and 16% for the _Vp_ and _Vs_ velocities, respectively. Moreover, the maximum discrepancy in the predicted velocities was observed for the sample with the highest porosity (Sample 1) and between the datasets exhibiting the maximum difference in the porosity values. A similar inversion was carried out for an RP model containing only one type of voids, without dividing them into pores and microcracks. In this case, the data of tomography were not taken into account. For all samples, Dataset 1 was selected for the inversion of model parameters. It is interesting to note that for all three samples, the inverted aspect ratio of voids was almost the same and varied around 0.1, which was much less than the \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Name** & **Crack Porosity, \%** & **Aspect Ratio** & **Crack Density** \\ \hline Sample 1, Dataset 1 & 0.01 & 0.0001 & 0.23 \\ Sample 1, Dataset 2 & 0.85 & 0.0078 & 0.26 \\ Sample 1, Dataset 3 & 0.02 & 0.0001 & 0.39 \\ Sample 2, Dataset 1 & 0.07 & 0.0024 & 0.07 \\ Sample 2, Dataset 2 & 0.23 & 0.0100 & 0.05 \\ Sample 2, Dataset 3 & 0.25 & 0.0066 & 0.09 \\ Sample 3, Dataset 1 & 0.10 & 0.0016 & 0.15 \\ Sample 3, Dataset 2 & 0.15 & 0.0016 & 0.22 \\ Sample 3, Dataset 3 & 0.03 & 0.0003 & 0.26 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Microcrack parameter corresponding to the most probable solutions. Figure 15: Surfaces of characteristic _Discrepancy measure_ (%) versus elastic moduli of the host matrix for Sample 1.  
aspect ratios provided by the tomographic studies (0.50-0.55). As for the previous case, the inverse problem had more than one solution (on the order of 10-20). However, the values of the aspect ratio in all solutions were obtained in the vicinity of 0.1. For Sample 1, the solutions were obtained at a given error level of 5%. For Sample 2 and Sample 3, the error levels that made it possible to obtain solutions for the voids' aspect ratio were 7.5 and 8%. These error values were comparable to those used for the model with two types of voids discussed above. A comparison of the predicted velocities is shown in Figure 17. The single aspect ratio model gave greatly overestimated elastic wave velocities. The discrepancy in the estimates of velocities for the two models could reach 30%. Moreover, the maximum discrepancy was observed for the rock with the highest porosity (Sample 1). The use of such a \"rough\" model with one type of voids, not verified by tomography data, can lead to significant errors in the interpretation of field experiment data. A similar prediction was carried out for two RP models in which the elastic moduli of the host matrix were assumed to be unknown and inverted from the elastic wave velocities. These models did not contain microcracks. The models were constructed for Sample 1. Dataset 1 was used for the inversion of the model parameters.