In this paper, I consider the simplest and probably most practical anisotropic model,
that is a transversely isotropic (TI)
medium with a vertical symmetry axis. Such a medium is given
the same importance in the anisotropic world
that *v*(*z*) velocity variation has in the inhomogeneous world.
Although more complicated anisotropies can exist (such as orthrohombic anisotropy), the large
amount of shales Banik (1984)
present in the subsurface makes the TI model the most influential for P-wave data.

In homogeneous transversely isotropic media with a vertical symmetry axis (VTI media),
*P*- and *SV*-waves ^{} can be described by the vertical velocities
*V*_{P0} and *V*_{S0} of *P*- and *S*-waves, respectively, and the two
dimensionless parameters and Thomsen (1986), as follows:

Alkhalifah and Tsvankin (1995) further demonstrated that a new representation in terms of just two parameters is sufficient for performing all time-related processing, such as normal moveout correction (including nonhyperbolic moveout correction, if necessary), dip-moveout removal, and prestack and post-stack time migration. These two parameters are the normal-moveout velocity for a horizontal reflector

(1) |

(2) |

However, if depth is of concern, as in this paper, the vertical
*P*-wave velocity (*v*_{v} or *V*_{P0}) is also needed to characterize the medium. Again,
the vertical shear wave velocity has little influence on *P*-wave propagation in such media,
and as a result, it is set to zero with little loss in the accuracy of the VTI equations.

10/9/1997