The main problem considered in the previous sections was how the
limited view of the measurements affect our ability
to estimate velocities in different directions. By assuming
elliptic anisotropy it was necessary to estimate only two velocities:
horizontal and vertical. Of course, this is too simple
to describe the real complexities of the velocities in
many cases but still, it is the first step beyond fitting
the data with circles (isotropic tomography).
We have seen that unless we constrain considerably the inversion
(layered models) or we have measurements from a wide range of angles,
it is difficult to estimate *accurately* and *simultaneously*
*S*_{x} and *S*_{z}. Unfortunately, even if these conditions are satisfied,
many other factors may affect the results.
Among this factors we have:

- Picking errors. These errors may increase or decrease systematically
the velocities,
depending on which part of the first
arriving wavelet has been picked. Picking before
the correct value speeds up velocities whereas picking later
slows them down. This may explain why
in Figure 15
*V*_{z}is systematically 1 or 2 % faster than the sonic log. - Well deviation. As we said before, the wells deviate in 3-D but
we decided to work in 2-D. If the real 3-D variations
in the medium are moderate, this is a good approximation
but it may not be otherwise. When first testing our
algorithm with real data the well deviation was
not considered. We just substituted each well by a vertical
one located at its average surface location.
The results were (not shown) higher velocities (than those shown
in Figure 12)
where the wells were actually closer and lower
velocities where the wells were actually farther apart.
Considering the well deviation
affected
*S*_{x}more than*S*_{z}. - Head waves vs. body waves.
Although this may be considered a picking error,
it affects primarily traveltimes at near offsets (small ray angles)
in low velocity layers. These errors affect mainly
the estimation of
*S*_{x}because*S*_{z}does not use information from rays that travel at small angles. In principle, when head waves are inverted like body waves the estimated horizontal velocity turns out to be faster than the real one. - Ray bending.

All the previous factors, when not considered appropriately, may produce artificially anisotropic results. For this reason and the ill-conditioning of the problem studied later, the estimation of small scale variations in velocity anisotropy is a difficult task.

12/18/1997