Acoustic transversely isotropic (TI) media are defined by artificially setting the shear-wave velocity in the direction of symmetry axis, VS0, to zero. Contrary to conventional wisdom that equating VS0 = 0 eliminates shear waves, we demonstrate their presence and examine their properties. Specifically, we show that SV-waves generally have finite nonzero phase and group velocities in acoustic TI media. In fact, these waves have been observed in full waveform modeling, but apparently they were not understood and labeled as numerical artifacts.

Acoustic TI media are characterized by extreme, in some sense infinite strength of anisotropy. It makes the following unusual wave phenomena possible: (1) there are propagation directions, where the SV-ray is orthogonal to the corresponding wavefront normal, (2) the SV-wave whose ray propagates along the symmetry axis is polarized parallel to the P-wave propagating in the same direction, (3) P-wave singularities, that is, directions where P- and SV-wave phase velocities coincide might exist in acoustic TI media.

We also briefly discuss some aspects of wave propagation in low-symmetry acoustic anisotropic models. Extreme anisotropy in those media creates bizarre phase- and group-velocity surfaces that might bring intellectual delight to an anisotropic guru.

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