Anisotropy introduces error into
seismically-estimated velocities. In a homogeneous, elliptically anisotropic
medium^{} with a single
flat reflector,
standard velocity analysis measures ** v_{H}**, the horizontal wave velocity, rather
than the vertical velocity

(10) |

Equation (3) appears to be a complicated way to express the
vertical misfit between and , but it can be shown that in Equation
(3) is equivalent to in
Equation (10) for the simple medium discussed above. Given the
flat reflector and constant assumptions, Equation
(8) computes for all ** x** and

Though I have not yet been able to prove it, I believe that in a more
complex medium, the **( x,y)** from Equation (8)
is an ``RMS'' . From Equation (10) we
obtain at the well locations the horizontal wave velocity

For multiple , one could imagine vertically
interpolating the **( x,y)** surfaces corresponding
to each one, thus yielding a 3-D cube which could
then be subjected to a Dix-like inversion to obtain a 3-D ``interval''
cube.
The RMS cube could be, after
conversion back to time, used as a direct multiplicative correction on the
stacking velocities.

7/5/1998