The offset-midpoint traveltime pyramid in transversely isotropic media

Prestack Kirchhoff time migration for transversely isotropic media with a vertical symmetry axis (VTI media) is implemented using an offset-midpoint traveltime equation, Cheep's pyramid equivalent equation for VTI media. The derivation of such an equation for VTI media requires approximations that pertain to high frequency and weak anisotropy. Yet the resultant offset-midpoint traveltime equation for VTI media is highly accurate for even strong anisotropy. It is also strictly dependent on two parameters: NMO velocity and the anisotropy parameter, eta. It reduces to the exact offset-midpoint traveltime equation for isotropic media when eta = 0. In vertically inhomogeneous media, the NMO velocity and eta parameters in the offset-midpoint traveltime equation are replaced by their effective values: the velocity is replaced by the rms velocity and eta is given by a more complicated equation that includes summation of the fourth power of velocity.