Having approximated the square root by a polynomial ratio,
Table .4 or Table .5 can be inverse transformed
from the horizontal wavenumber domain *k*_{x} to the
horizontal space domain *x* by substituting
.The resulting extrapolation equations have a
wide range of validity for *v* = *v*(*x*,*z*) even though the
derivation would not seem to permit any change of velocity with *x*.

Ordinarily will be chosen
to be some kind of horizontal average of *v*(*x*,*z*).
Permitting to become a function of *x* generates many
new terms.
The terms are awkward to implement and ignoring them introduced
unknown hazards.
So is usually taken to depend on *z* but not *x*.

12/26/2000