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