Conclusions

The offset-midpoint traveltime equation for transversely isotropic media is derived from its Fourier domain equivalent using the stationary phase method. Perturbation theory and Shank transforms we needed to arrive at a relatively simple analytical form. This Cheop's pyramid equation for VTI media provides accurate traveltimes for practically any strength of anisotropy. It can be used in vertically inhomogeneous media by replacing the medium parameters in the equation by their effective values.