Anisotropy introduces error into seismically-estimated velocities. In a homogeneous, elliptically anisotropic medium with a single flat reflector, standard velocity analysis measures vH, the horizontal wave velocity, rather than the vertical velocity vV. An elliptically anisotropic medium is defined by the parameter
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 y, solely from the vertical seismic/well log misfit.
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 vH in the overlying medium. At other locations, the (x,y) from Equation (8) gives a reasonable estimate of vH.
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.