In my preceding paper (Zhang,1990b), I showed that
If the traveltime table is calculated with polar coordinates ,instead of Cartesian coordinates (x,z), then we can simply change x and z in equations (3) and (4) to and r, respectively.
With equations (3) and (4), we can extrapolate the operators in both the horizontal and vertical directions. Because the operators are usually known at the surface, one can use equation (4) to extrapolate the operators vertically to each depth. The next section shows how this extrapolation is done.