Here, I consider the simplest and probably most practical anisotropic model, that is, a transversely isotropic (TI) medium with a vertical symmetry axis. Although more complicated kinds of anisotropies can exist (i.e., orthrohombic anisotropy), the large amount of shales present in the subsurface implies that the TI model has the most influence on P-wave data Banik (1984).
In homogeneous transversely isotropic media with a vertical symmetry axis (VTI media), P- and SV-waves can be described by the vertical velocities VP0 and VS0 of P- and S-waves, respectively, and two dimensionless parameters and Thomsen (1986).
Alkhalifah (1997a) demonstrated that P-wave velocity and traveltime are practically independent of VS0, even for strong anisotropy. This implies that, for practical purposes, P-wave kinematic signatures is a function of just three parameters: VP0, , and .
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 non-hyperbolic moveout correction, if necessary), dip-moveout correction, and prestack and post-stack time migration. These two parameters are the normal-moveout velocity for a horizontal reflector