Alkhalifah and Tsvankin (1995) show that P-wave normal-moveout (NMO) velocity for horizontal and dipping reflectors, as well as time migration, in transversely isotropic (TI) media with a vertical symmetry axis depends just on the zero-dip NMO velocity and a parameter that is a combination of Thomsen's (1986) parameters. Their inversion procedure makes it possible to obtain and reconstruct the NMO velocity as a function of ray parameter using moveout velocities for two different dips. This means that inversion of dip-dependent information allows one to perform all time-processing in TI media using only surface P-wave data. The layered TI media NMO equation for dipping reflectors (Alkhalifah and Tsvankin, 1995) provides the basis for extending TI velocity analysis to vertically inhomogeneous media. The multi-layered NMO equation is based on a root-mean-square (rms) average of modified interval velocities corresponding to a single ray parameter, that of the dipping event. Therefore, modified interval velocity values can be extracted from the stacking velocities using a Dix-type differentiation procedure. In addition, the inversion is performed simultaneously with the interval velocity evaluation in each layer. Time migration, like DMO, depends on two parameters in vertically inhomogeneous media, namely the NMO velocity and both of which can vary with depth. Therefore, the NMO velocity and estimated using the dip dependency of P-wave moveout velocity can be used in a TI time migration. An application of anisotropic processing to seismic data from offshore Africa demonstrates the importance of considering anisotropy, especially as it pertains to focusing dipping events.