The two phase shift schemes are suitable for use with a constant velocity model or a model which varies only in the direction in which the data is extrapolated. For rectangular coordinates this is a v(z) model, and for polar coordinates it is a v(r) model. When the velocity model is not of a suitable form, a more complicated algorithm must be used.
In many cases a v(z) model is geologically reasonable, but this is rarely true of a v(r) model. One disadvantage of working in polar coordinates is that the simple phase shift algorithm cannot be used for a v(z) model.