Craig Beasley, Walt Lynn, Ken Larner, Hung V. Nguyen
Despite our understanding that depth migration
is a more powerful imaging
tool than time
migration
, time
migration
still constitutes the majority of
migration
done today. In selecting a time-
migration
algorithm, three primary
criteria are of concern: accuracy in imaging steep dips, accuracy in the
presence of vertical
velocity
variation, and computational effort. The ideal
algorithm would be efficient and unlimited in its ability to image steep dips in
arbitrary vertical
velocity
structures. It would also accommodate gentle lateral
velocity
variations deemed acceptable for time-
migration
methods.
A particularly attractive algorithm to consider is Stolt's f-k method: it is
computationally efficient and has unlimited dip accuracy for constant
-
velocity
media. Although Stolt's method can handle moderate vertical variations, errors
become unacceptable for steep dips in the presence of large vertical
velocity
variation. An extension to Stolt
migration
removes its restrictions on vertical
velocity
variation, yielding accuracy comparable to phase-shift
migration
at
only a fraction of the computational time.
This extended Stolt method is based on partitioning the velocity
field in a
manner analogous to that in cascaded finite-difference
migration
and performing
a number of stages of Stolt migrations. In each stage, the
migration
velocity
field is closer to a
constant
--the ideal situation for Stolt
migration
--than
when the
migration
is done conventionally (i.e., in just one stage). Empirical
results and error analyses show that four stages of extended Stolt
migration
are
sufficient to migrate steeply dipping events accurately in nearly any vertically
varying
velocity
field. In fact, for a wide range of
velocity
fields and dips,
as few as two stages will produce phase-shift quality images. The method can be
used for two-dimensional, two-pass three-dimensional, and single-pass
three-dimensio al migrations.
AAPG Search and Discovery Article #91035©1988 AAPG-SEPM-SEG Pacific Sections and SPWLA Annual Convention, Santa Barbara, California, 17-19 April 1988.