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The simplest effective-medium model of fractured rocks known as the Linear Slip (LS) model of Schoenberg (1980) represents a single fracture set in an isotropic background rock. In the LS model, the stiffness C 13 is not independent as in the overall transversely isotropic (TI) model, but it is related to other stiffnesses by the equation, C 11 C 33-C 2 13 = 2C 66 (C33+C13). We have studied a physical sense of this constraint on the C 13 and found out that in terms of the TI elastic compliance tensor S it leads to the equality 12 = 13 , where 13 and 12 are the two different horizontal Poisson's ratios. In contrast to the Linear Slip model, in the overall TI model, one of these Poisson's ratios, 13 , is always greater than the other one, 12 , that is validated by numerous static and dynamic laboratory measurements of these Poisson's ratios in VTI-type rocks. Thus we have revealed a contradiction and inconsistency in the constraint on the C 13 for the LS model. Moreover, the restriction on C 13 for the LS model doesn't work for the overall TI medium in which there are physical constraints on the C 13 , namely, C 13_min < C 13 < C 13_max (e.g., Yan et al., 2013). We have revealed that mathematical expression for its lower bound, C 13_min , coincides with that for the constraint on the C 13 for the LS model. This means that the restriction on C 13 for the LS model, C 13 = C 13_min , does not satisfy the physical constraint for the overall TI model that is inequality C 13 > C 13_min. The LS model is not a universal model for real rocks. It may work successfully only in several special cases, or under certain conditions, for example, when the normal fracture weakness Δ N =0 (fluid-saturated cracks), or in the case of Δ N = Δ T (dry cracks). Also we have revealed that the LS model may suit better for sandstones and carbonates than for shales.

—The paper considers the results of a series of laboratory experiments (more than 100) on the formation of synthetic sand samples containing water/ice and methane or tetrahydrofuran hydrates in the pore space and of the measurement of their acoustic properties (velocities and attenuation of acoustic waves). The main aim of the experiments was to establish the relationship between the velocities of acoustic waves and the ice or hydrate saturation of the samples. An increase in the content of ice and hydrates always leads to a velocity increase. However, the rate of the velocity increase is determined by the localization of ice and hydrates in the samples: at the contacts between the sand grains (“cementing” model) or in the pore space (“filling” model). It has been established that the “cementing” model, characterized by a drastic initial increase in velocities, works for ice or gas hydrates formed from free methane and localized in the pores. On the contrary, tetrahydrofuran hydrates form by the “filling” model and cause a slow increase in velocities.