ABSTRACT
Prestack phase-shift migration is implemented by evaluating
the offset-wavenumber (kh) integral using the
stationary-phase method. Thus, the stationary point along kh must be calculated prior
to applying the phase shift.
This type of implementation allows for migration of separate offsets, as opposed to
migration of the whole prestack data when using the original formulas.
For zero-offset data, the stationary
point (kh=0) is known in advance, and, therefore, the phase-shift migration can be implemented
directly. For non-zero-offset data, we first evaluate kh that corresponds
to the stationary point solution
either numerically or through analytical approximations.
The insensitivity of the phase to kh
around the stationary point solution (its maximum) implies that even an imperfect kh obtained analytically can
go a long way to getting an accurate image.
In transversely isotropic (TI) media, the analytical solutions of the stationary point (kh) include more
approximations than those corresponding to isotropic media (i.e., approximations corresponding to
weaker anisotropy). Nevertheless, the resultant equations, obtained using Shanks transforms,
produce accurate migration signatures for strong anisotropy (
|