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 anisotropies can exist (i.e. orthorhombic anisotropy), the large amount of shales present in the subsurface makes the TI model the most influential on P-wave data Banik (1984).
In homogeneous transversely isotropic media with vertical symmetry axis (VTI media), P- and SV-waves (I omit the qualifiers in ``quasi-P-wave" and ``quasi-SV-wave" for brevity) can be described by the vertical velocities vv and vsv of P- and S-waves, respectively, and two dimensionless parameters and Thomsen (1986).
Tsvankin (1996) and Alkhalifah (1997b) demonstrated that P-wave velocity and traveltime are practically independent of vsv, even for strong anisotropy. This implies that, for practical purposes, P-wave kinematic signatures can be considered a function of just three parameters: vv, , 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 removal, and prestack and post-stack time migration. These two parameters are the normal-moveout velocity for a horizontal reflector