## 4 Discussion  
We analyze several methods of rock physics that give a possibility of taking into account the effect of pore space connectivity in carbonate rock. Some of these methods,  
\begin{table}
\begin{tabular}{c c c} \hline \hline \(\mathbf{\varphi_{\text{pore}}\)\% & **Equation** & \(\mathbf{R^{2}}\) \\ \hline  & Berryman-SC – Berryman-\(f\) and GSA-SC – GSA  
namely, GSA-SC, Berryman-SC, and DEM, allow us to do that implicitly. Thus, the derivation schemes of formulas for GSA-SC and Berryman-SC methods assume that each inclusion of ellipsoidal shape is placed in a matrix with effective properties thereby implicitly allowing the inclusions to be in a contact with each other. The DEM method, at each step, requires placing a portion of inclusions in a medium that already contains several portions of inclusions embedded in the previous steps. The elastic properties of this medium change after each step. This means that the inclusions of every new step can be in a contact with previously embedded inclusions. The other two methods considered in our work, GSA-\(f\) and Berryman-\(f\), can quantify the effect of pore space connectivity via a special dimensionless parameter \(f\) varying from 0 to 1. This parameter controls the properties in so-called comparison body in Formulas (3), (5), (8), and (9), being a coefficient in the linear combination of stiffness tensors of the stiffest and softest materials composing a rock. The comparison body serves as a host medium for other inclusions. The case \(f=0\) is related to a matrix having properties of the stiffest component with isolated ellipsoidal inclusions of other components. The opposite limiting case \(f=1\) is related to the medium where the softest component plays the role of the host matrix. In the case of porous rock, the first case corresponds to completely isolated inclusions in a mineral matrix. The second limiting case comprises an exotic medium with a fluid matrix with ellipsoidal solid particles of mineral matter, kerogen, etc. The \(f\) values between 0 and 1 are related to intermediate cases met in reality. The increase in this parameter means that the voids become more connected and vice versa. This parameter is non-measurable and can be evaluated by inversion from experimental data with the use of rock-physics modeling [36; 43]. To clarify the physical meaning of the \(f\)-parameter, we compare two simple rock-physics models of carbonate rock. Porous-cracked limestone is considered. The first model (Type 1 model) is a double porosity model representing isotropic calcite polycrystal with two types of voids: spherical pores and randomly oriented cracks having various aspect ratios. To calculate the effective elastic properties of this model we apply two methods based on the self-consistent approach of the effective medium theory including GSA-SC, Berryman-SC, and DEM. The second model (Type 2 model) is the same isotropic calcite polycrystal with spherical pores whose connectivity is described by the \(f\)-parameter according to formulas of GSA-\(f\) and Berryman-\(f\) methods (Equations (1)-(5) and (6)-(9), respectively). Our idealized models (Figure 1) reflect specific microstructure that could be met for isotropic carbonates in practice [43; 52; 53; 54]. These idealized models are often used to estimate the effective elastic properties of reservoir rocks. Specifically, these are simplest models for porous-fractured carbonate reservoir rocks that are of vital interest for prospecting geophysics. These idealized models have predictive power and help to assess the elastic wave velocities change if: (1) the crack porosity increases (or decreases), (2) the crack relative opening increases (decreases), (3) crack density increases (decreases), (4) the fluid type varies and so on. Specifically, these models are applied for well-log and seismic data in order to localize and characterize the fractured zones [55; 56].