The problem of theoretical prediction of the elastic stiffness parameter C13 is important, as well as proper establishment of its theoretical bounds, which is extremely useful in the reliable C13 estimation. We revise a formula for the lower bound C13_min, empirically derived by F. Yan with coauthors, based on their empirical inequality between two Poisson’s ratios in a transversely isotropic elastic medium; i.e., ν13>ν12. In doing this, we consider a theoretical counterexample derived on theoretical grounds by J. Sarout leading to the opposite inequality ν13<ν12. Our analysis on shale anisotropy (using published data on various shale samples) proves both inequalities to be true. Therefore, we can divide shale data into two groups: 1 and 2; i.e., group 1 we define by the inequality ν13<ν12, and group 2 by ν13>ν12. In the framework of the linear slip (LS) model, we found another restriction on two Poisson’s ratios ν13=ν12, which must be satisfied in the LS model. In addition, we found that the theoretical formula for the C13LS in the LS model and the bound C13_min should be equal: C13_minC13LS. Also, we found that C13 depends on the normal fracture compliance ZN. We postulate that there is a critical compliance ZNLS predicted by the LS model that marks the transition between two inequalities of Poisson’s ratios: ν13<ν12, and ν13>ν12. These inequalities become a part of a broader interpretation, in which the compliance ZNLS acts as a transitional intermediate response (i.e., ν13=ν12) between the two shale groups 1 and 2. Each shale group (i.e., ν13<ν12, and ν13>ν12) is assigned to different ZN (i.e., ZN<ZNLS and ZN>ZNLS), which imply differentiation of rock properties in two groups, such as different fluid saturation, as an example.

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