A new asymptotic formula for S waves propagating near the symmetry axis in transversely isotropic elastic media derived by Popov et al. [Wave Motion 42 (2005) 191-201] is discussed and commented. It is shown that the formula is a modification of the previously published formula by Vavrycuk [Geophys. J. Int. 138 (1999) 581-589]. The formula of Popov et al. is less accurate and valid under more restrictive conditions than that of Vavrycuk.
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