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First, we show that for flat reflectors and VTI
media, vertical velocities cannot be estimated from reflection
seismic data only. These results are consistent with
Tsvankin (2001), who shows
that P-wave signatures depend only on two combinations of
*V*_{V}, and , and that vertical velocities cannot be
estimated from reflection seismic data only.
For elliptical media, we demonstrate that the
first-order derivative of the image-point depth with
respect to vertical velocity perturbations is independent of the
aperture angle so that the residual moveout is independent of the
vertical velocity perturbations:

| |
(8) |

| |
(9) |

As a consequence, vertical velocity perturbations cannot be estimated
from RMO transformation.
For anelliptical media, we show numerically that the first-order
derivative of the RMO with respect to vertical velocity
perturbations is not significantly different from zero and does not
allow the estimation of vertical velocity perturbations.

** Next:** Estimation of the horizontal
** Up:** Anisotropic migration velocity analysis
** Previous:** Anisotropic migration velocity analysis
Stanford Exploration Project

5/6/2007