## 4 Discussion
It is not so easy to answer this question since all the methods are approximate. Note that the formulas of these methods were derived under different assumptions of what a heterogeneous medium looks like. Thus, SCA assumes that all heterogeneities have an ellipsoidal shape and are embedded in an effective matrix. The DEM proposes a step-by-step scheme of embedding inclusions in the effective matrix obtained in the previous step. This model can produce good results in the case when inclusions differ in size, and inclusions of each next portion are larger than the previous ones. The Kuster-Toksoz method considers a model of a host matrix with isolated inclusions. When applying these methods in practice, the difference in the models should be taken into account. The calculation results should be verified on experimental data. However, the data may contain experimental errors. An interesting and helpful theoretical verification of these methods was presented by [PERSON] and [PERSON] [38; 39]. The authors of these works compared the quadratic terms with respect to the concentration of inclusions in the virial expansion formulas [40] and SCA and DEM formulas. The results obtained by the authors allowed them to conclude that DEM was the most accurate approach. The theoretical velocities obtained for dry samples are, in general, significantly higher than their experimental analogs. This result indicates that the carbonate rocks may also contain voids whose size is beyond the tomography resolution. The microcrack parameters (aspect ratio and microcrack porosity) were inverted from the measured \(Vp\) and \(Vs\) velocities. It was shown that a wide domain of solutions for pairs of these parameters existedor each sample. However, if the microcracks were characterized by a single parameter, namely, the crack density, the solution was rather stable. Note that the existence of microcracks that were not seen with the tomography studies was debatable. However, their occurrence was quite realistic in Samples 1 and 2 that were characterized as packstones, according to previous lithological studies in this area [4; 5]. It is interesting that the crack density found for Samples 1 and 3 had similar values that varied between 0.15 and 0.39 depending on the dataset used for inversion (see Table 2 and Figure 12). These values were much higher compared to Sample 2 for which the crack density varied from 0.05 to 0.09. The rocks represented by Samples 1 and 3 were of the Lower Carboniferous period whereas Sample 2 was rock from the Upper Devonian age. Does a relation exist between the microcrack parameters and the age of carbonate rocks? Or is this, perhaps, a coincidence? This is a debatable question to be answered in future works. The microcrack parameters obtained for different datasets together with the pores' aspect ratio provided by computed tomography were used for the RP-based prediction of elastic wave velocities (_Vp_ and _Vs_) for rocks saturated with formation water. The prediction was performed for a porosity up to 20%. It was demonstrated that the predicted velocity values can differ within 16% depending on the dataset used for the microstructural parameters and porosity evaluation. In our study, we also considered another RP model of the studied rocks which was called \"as simple as possible\". This simple model did not take into account either the data of thin-section analysis or the computed tomography data. This model contained only one type of void with the same aspect ratio. The aspect ratio was inverted only on the basis of elastic wave velocities and porosity measured using a porosimeter. Note, that this type of pore shape evaluation is often met in practice. Our modeling showed that all the samples had voids of a similar aspect ratio of around 0.1. Note that this value has nothing in common with those provided by the computed tomography for pores.