## 4 Discussion
The authors [31] applied the GSA method for the effective permeability modeling for Barnett shale. They showed that, for this modeling, the permeability of fluid-saturated zones should be also specified (or inverted from the permeability measurements). Besides, it was demonstrated that the \(f\)-parameter inverted from measured permeability has values similar to that inverted from the elastic wave velocities. In another work authors using the modified GSA method with \(f\)-parameter demonstrated prediction of the hydraulic permeability and thermal conductivity of clastic rocks from logging data on \(\mathrm{Vp}\) and electrical conductivity [32]. The predicted permeability is in good agreement with the measured on full-size core samples. The question of the model simplicity is debatable. According to [PERSON] [59], a rock-physics model should be \"as simple as possible but not simpler\". The meaning of this phrase is that the model simplicity is dictated by availability of experimental data and the goal of modeling. Definitely, in a real rock, the pores and cracks exhibit a variety of shapes and sizes. At the core scale we have many tools to examine the rock microstructure (optical and electron microscopy, CT scanning, direct observation of samples). In this case, a rock-physics model can incorporate different type of voids. An example is a very popular the Xu-Payne model [60] of carbonate rocks that includes four types of voids: micropores, clay-related non-isometric voids, cracks, and macropores. Each type of void is described by its specific aspect ratio. This model contains seven parameters of microstructure describing the shape and volume concentration of voids of different types. Another example is the Xu-White model of clayy sandstones containing silt-related and clay-related pores of different aspect ratios [61]. This model contains three microstructural parameters--aspect ratios of silt- and clay-related voids and a parameter describing the porosity distribution between the silt and clayy parts. Commonly, the microstructural parameters are inverted from two elastic wave velocities (Vp and Vs) measured on rock samples or provided by logs. The number of unknowns in these models is greater than the number of measurements which leads to a wide domain of possible solutions. However, constrains provided by microstructural analysis narrow this domain. If the inversion is not supported by microstructural analysis in such complex models the found model parameters have no sense and only play a role in fitting parameters. In this case, simpler models should be applied. However, a model should not be oversimplified. Thus, sometimes the effective elastic properties of carbonate rocks are based on a model consisting of carbonate matrix with a single type of inclusions [62; 63; 64; 65]. A disadvantage of oversimplified models is that they may provide an erroneous prediction. Thus, in the work [66] it is shown that a model with a single aspect ratio used for all voids and a model that distinguishes between the pores and cracks produce different predictions for elastic wave velocities if the fluid type changes. In both models the self-consistent scheme of EMT was applied. If a rock exhibits a hierarchical structure at the scale of consideration and contains several groups of heterogeneities having different sizes, the rock physics model is constructed according to the rule \"from smaller to larger heterogeneities\", and the modeling assumes different stages (like in the Xu-Payne model). At stages when it is necessary to insert connected voids, the \(f\)-models can be applied, which leads to a decrease in the number of model parameters. Note that the replacement of crack characteristics by the \(f\)-parameter is applicable for any matrix, not only for calcite polycrystal. Moreover, we can speak about two approaches to model design: conceptual models and data-driven models.