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Acoustic transversely isotropic models are widely used in seismic exploration for P-wave processing and analysis. In isotropic acoustic media only P-wave can propagate, while in an acoustic transversely isotropic medium both P and S waves propagate. In this paper, we focus on kinematic properties of S-wave in acoustic transversely isotropic media. We define new parameters better suited for S-wave kinematics analysis. We also establish the travel time and relative geometrical spreading equations and analyse their properties. To illustrate the behaviour of the S-wave in multi-layered acoustic transversely isotropic media, we define the Dix-type equations that are different from the ones widely used for the P-wave propagation.