Short Note
The offset-midpoint traveltime pyramid in transversely isotropic media

Tariq Alkhalifah

tariq@sep.stanford.edu

ABSTRACT

Prestack Kirchhoff time migration, for transversely isotropic media with a vertical symmetry axis (VTI media), is implemented using an offset-midpoint 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 offset-midpoint traveltime equation for VTI media is highly accurate for even strong anisotropy. It is also strictly dependent on two parameters: the normal-moveout (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 offset-midpoint traveltime equation are replaced by their effective values; the velocity is replaced by the root-mean-squared velocity, whereas $\eta$ is given by a more complicated equation that includes summation of the fourth power of velocity.