Both equivalent-offset migration and dipmoveout-prestack imaging are prestack-time-migration techniques. While EOM is only a partial reversal of the standard processing sequence, DMO-PSI fully reverses the process and so is independent of velocity. EOM is shown to be conceptually and asymptotically identical to the PSI part of DMO-PSI. Both PSI and EOM perform the imaging step on constant time-slices by diffracting energy over appropriately defined curves. The PSI curves are much simpler than those for EOM and so are significantly easier to implement.

Theoretically, EOM is equivalent to PSI when
the input data have been DMO corrected. In that case, the equivalent-offset formula for offset (*h*_{e})
as a function of midpoint, scatterpoint, velocity, *v*, and time, *T*,
has no dependence on *v ^{2}T^{2}* and, the underlying curves are circles rather than hyperbolas. There
are many alternative formulations of DMO-PSI, but the fact that the entire process can
be completed in the frequency-wavenumber domain implies the existence of a very fast algorithm that
is computationally superior to diffraction stacking.

Separation of prestack-constant-velocity migration into two steps, DMO and PSI, has an advantage over EOM in that it allows free choice of the DMO algorithm. The utilization of more sophisticated DMO techniques prior to PSI, e.g. Alfaraj and Larner (1991, 1992), ; Anderson and Tsvankin 1994; Anderson et al. 1994; Miller and Burridge 1989; Liner (1990, 1991), may improve both image quality and velocity estimates. Inclusion of reasonable isotropic velocity variations are possible in DMO-PSI. As anisotropic techniques mature it will also be possible to include anisotropic velocity variations in the imaging equation. This separability also allows one to apply a 3D DMO-PSI sequence followed by inverse 2D DMO to regularize irregular data sets and use 2D prestack-depth migration to achieve a 3D result Canning and Gardner (1993).

Velocity independence is definitely a powerful feature of any prestack technique. The inherent dependence of EOM on velocity estimates reduces its potential as a competitive alternative to DMO-PSI.

10/10/1997