## 3 Results
### Comparison of Predictive Abilities of RP Models
For both RP models, the host matrix moduli were selected from the accepted solutions shown in Figure 15. These moduli (bulk and shear) were, respectively, 59.8 and 16.6 GPa for the first RP model (_host_ 1) and 43.4 and 18.5 GPa for the second model (_host_ 2). Below, we call the models _host-models_. Figure 16: Prediction of P-wave velocities for fluid-saturated rocks. For fluid substitution, the Gassmann method was used. Microcrack parameters are constant and correspond to those found for each dataset. Notation (1), (2), (3) signifies the sets of data (Datasets 1–3) used to solve the inverse problem (see the description of the datasets in Section 3.2). Quasi-isometric porosity varies from 0.1 to 20%. The symbols on the curves correspond to porosity values for which the velocities were calculated. The first model assumes that the intergranular material exists between the calcite grains. The second model does not consider any particular reasons for the decreased moduli of the host matrix compared to the calcite polycrystal. These elastic moduli of the matrix in _host 2_ model provide the most probable solution to the inverse problem. The prediction results obtained for these two models are shown in Figure 18 for Sample 1 together with the results found for another two RP models. One of the models is the dual-porosity model with pores and microcracks and the other is an RP model (the \"as simple as possible\" model) with one system of voids (the same as in the upper-left plot in Figure 17). All the results were found for Dataset 1. As seen, the choice of host matrix in the models _host 1_ and _host 2_ did not considerably affect the prediction results. Moreover, the difference between the velocities provided by the dual-porosity model and the _host models_ did not exceed 10% in the whole porosity range. All the predictions based on the tomography significantly differed from those provided by the \"as simple as possible\" model (for a single aspect ratio for all voids). In all the predictions described above, we ignored the existence of the micrite matrix in the samples due to the fact that the porosity was not too high. To analyze when the distribution of porosity between the micrite matrix and \"visible\" pores became noticeable, we performed the following modeling for Sample 1 and Sample 3. In the first model, we fixed the \"visible\" porosity and varied the micrite porosity from 0 to 40%. In the second model, we fixed the micrite porosity and varied the \"visible\" porosity in a wide range. The  
Figure 17: Comparison of the predicted values of fluid-saturated rock velocities obtained from two RP models. The solid lines correspond to the prediction based on the RP model with dual porosity (pores and microcracks). The dashed lines correspond to the RP model prediction with a single aspect ratio for all voids. The parameters of RP models are inverted from Dataset 1.  
fixed values of \"visible\" and micrite porosity corresponded to those found for the sample. This means that the \"visible\" porosity was 7.4% for Sample 1 and 2.2% for Sample 3. The micrite porosity was, respectively, 6.7% and 8.1% for these samples. The total porosity range was up to 35%. The rocks were water-saturated. A comparison of elastic wave velocities obtained with two models is shown in Figure 19. The maximum difference in velocities caused by the redistribution of porosity between the micritic matrix and \"visible\" pores was seen for a porosity of 35%. The difference rapidly increased with porosity and, finally, reached 54% for P-waves and 63% for S-waves, respectively, for Sample 3. This was the sample with the highest micrite content. The difference in the velocities became greater than 5% beginning from a porosity of 17%.