- 1.
- We can simplify the FFD migration equation by ignoring the
spatial variability of the slowness function for the terms of the summation,
and ,which gives the following equation Biondi (1999):
(7) - 2.
- In the next simplification, we consider, in addition to the earlier
approximations, that the ratio , which leads to the
*split-step Fourier*method a.k.a.*phase-screen*method Stoffa et al. (1990):(8) - 3.
- Finally, the simplest method of the family is
*phase-shift*Gazdag and Sguazzero (1984); Gazdag (1978), for which we further assume that*s*-*s*_{o}=0, therefore(9)

For most of these methods, we can separate approximations of various *orders* ,
depending on the number of terms in the sum (*n*).
We can also have versions that use several values of the reference slowness (*s*_{o}),
followed by *interpolation* of the continued wavefield.

The bottom line is that all these simplified methods are just particular cases of the
*Fourier finite-difference* method mathematically
described by Equation (2). Similarly, we can derive all these simplified methods
from the *generalized screen* method, mathematically described by
Equation (5).

9/5/2000