P-wave reflections from horizontal interfaces in transversely isotropic (TI) media have nonhyperbolic moveout. Alkhalifah and Tsvankin (1995) showed that such nonhyperbolic moveout as well as all time-related processing in TI media with a vertical symmetry axis (VTI media) as a whole depend on only two parameters, called Vnmo and They also showed that these two parameters can be estimated from the P-wave dip moveout behavior of surface seismic data. Alternatively, one could use the nonhyperbolic moveout for parameter estimation. Conveniently, nonhyperbolic moveouts in media with typical anisotropies 1) are larger than those in media with typical vertical inhomogeneities, and therefore they are more observable, as well as measurable. The stability of the nonhyperbolic-moveout inversion depends largely on the range of offsets used in the inversion procedure. Larger offset-to-depth ratios (X/D) provide more nonhyperbolic information, and therefore, increased stability and resolution in the inversion. Likely, such X/D values (e.g., X/D > 1.5) needed for obtaining stability and resolution are within the conventional acquisition limits, especially for early zero-offset times. Application of the nonhyperbolic inversion to data from offshore Africa demonstrates its usefulness, especially in estimating lateral and vertical variations in.