Velocity analysis in transversely isotropic media

In transversely isotropic media, the moveout velocity obtained from common-depth-point (CDP) analysis may be significantly different from the horizontal velocity of the pseudo-P wave. In Levin's (1978) paper, he discusses, among other things, the problem of velocity determination in a medium in which the pseudo-P wave surface produced by a point source is an ellipsoid of revolution. He points out that one would expect many sedimentary rocks to be transversely isotropic with a vertical axis of symmetry. In his Appendix he proves that an ellipse (using two dimensions for convenience) is one possible shape for the wave surface in such a medium. He also shows, as have others, that in this case CDP velocity analysis measures the velocity of horizontal propagation.