The generalized screen propagator (GSP) is a fast and accurate method for c
omputing wave propagation in laterally varying velocity media. The method s
olves the acoustic one-way wave equation by shuffling FFTs between frequenc
y-space and frequency-wavenumber domain. The velocity model is decomposed i
nto a vertically varying reference velocity and a laterally varying perturb
ation. Downward continuation of the wavefield is performed with a phase shi
ft in a background medium followed by a correction that accommodates the la
teral velocity variations. All frequencies of interest are migrated and sum
med to produce an image at each depth level. The screen propagators are app
licable to both poststack and prestack depth migrations. We illustrate the
method with the SEG-EAGE salt model and Marmousi data set. The image result
s show that the pseudo-screen propagator is a big improvement over the phas
e-screen propagator for steeply dipping events in strong-contrast heterogen
eous media.