Having approximated the square root by a polynomial ratio, Table .4 or Table .5 can be inverse transformed from the horizontal wavenumber domain kx 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.