Ak. Benson, PHASE-SHIFT MIGRATION WITH A VARIABLE-LENGTH SPATIAL TRANSFORM - AN ALGORITHM FOR MODERATELY VARYING LATERAL VELOCITIES, Geophysical prospecting, 43(6), 1995, pp. 729-741
A migration algorithm appropriate for moderately varying lateral veloc
ity changes is developed as an extension of phase-shift migration by u
sing a variable-length spatial transform. This process significantly r
educes the number of lateral wavenumbers necessary to downward continu
e the data, and it replaces the spatial FFT with a simple recursion re
lationship. For a given frequency and position x, ten lateral wavenumb
ers are typically sufficient, and the migration algorithm produces acc
urate images when the velocity structure v(x, z) changes over a few de
pth intervals of thickness Delta z, with lateral velocity gradients up
to 1.4 to 1.0.