Migration of non-zero-offset sections for a constant velocity medium
, by Dave Hale
The first step in migrating a zero-offset seismic sections p(h=o,y,t) via the
Stolt (1978) algorithms is a two-dimensional Fourier transform over midpoint y
and time t. Assuming that the midpoint transform is performed first, we show
that migration of non-zero-offset (h not equal 0) sections may be accomplished
by replacing the temporal Fourier transform with the more general transform:
EQUATION
where
EQUATION
and where w is temporal frequency, k subscript y is midpoint-wavenumber, h is
half-offset, and v is velocity assumed constant. q(k subscript y, w) is then
migrated as if it were the two-demensional Fourier transform of a zero-offset
setion. One can readily verify that the general transform reduces to the
Fourier transform in the limit of zero-offset h=o, and that it reduces to the
Fourier transform of normal-movemout-corrected data in the limit of zero-dip,
k subscript y=0. In fact, the above transform is accurate for all offsets and
all dips.
STANFORD