This paper examines the meaning of the anelliptic terms in relation to the processes of approximating the ray velocity surface of transversely isotropic media recently introduced by Muir (1985) and Byun et al. (1989). Compared with stacking velocity obtained by simple hyperbolic velocity analysis, the additional parameters estimated by the non-hyperbolic method contain more physically meaningful geologic information regarding the anisotropy of the subsurface. Synthetic ¶-wave model experiments demonstrate that the non-hyperbolic moveout formulas yield an excellent fit to time-distance curves over a wide range of ray angles. Thus the measurement parameters adequately reflect the characteristics of velocity dependence on ray angle, in other words, velocity anisotropy.