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ARTICLES
Subsalt
imaging with semirecursive Kirchhoff migration
By Dimitri Bevc and A.
Mihai Popovici, 3DGeo Development Inc.
Summary
Kirchhoff migration is generally accepted to be the most practical
and efficient method of imaging 2-D and 3-D prestack seismic
data. However, in practice, standard Kirchhoff algorithms
often do a poor job of imaging complex structures such as
subsalt targets. We present a new semirecursive Kirchhoff
migration algorithm which is capable of obtaining accurate
images of complex subsalt structures by combining Kirchhoff
datuming and Kirchhoff migration. By datuming to the top of
salt, or even through the salt, and then imaging below the
salt, a greatly improved image is obtained.
Introduction
Kirchhoff algorithms using first-arrival traveltimes do a
poor job of imaging complex structures (Audebert et. al.,
1995; Gray and May, 1993; Geoltrain and Brac, 1993). Even
traveltime methods which calculate multivalued arrivals and
most energetic arrivals along with estimates of amplitude
and phase do not always result in satisfactory images. It
is generally accepted that migration algorithms which use
recursive wavefield continuation to backwards propagate the
received wavefield produce the best images. Unfortunately
these methods often require regular spatial sampling and are
computationally intensive. That is why nonrecursive methods
based on the Kirchhoff integral are attractive, especially
for 3-D prestack imaging objectives. Kirchhoff algorithms
can easily accommodate irregular sampling and they can be
applied in a target-oriented fashion.
This semirecursive migration
method presented here, and illustrated in Figure 1a has two
major components: (1) Kirchhoff datuming, and (2) Kirchhoff
migration. The data are Kirchhoff datumed to some imaging
horizon, from which the data are migrated. The datuming depth
step can be varied, and multiple depth steps (Figure 2b) can
be performed between migration steps.
The imaging improvement
occurs because the complicated effects of propagation across
the salt boundary are mitigated. In addition, the semirecursive
method is successful because breaking up the complex velocity
structure into smaller depth regions allows traveltimes to
be calculated in simple regions where they are well behaved,
and where they correspond to energetic arrivals. Because traveltimes
are computed for simple depth regions, the adverse effects
of caustics, headwaves, and multivalued arrivals do not develop.
Figure 1. Subsalt imaging
example for the semirecursive migration method. The seismic
data are first redatumed to the top of salt. Then the target
is imaged by migrating the data from the imaging surface at
top of salt. The datuming can be done (a) in one step to the
top of salt, or (b) in multiple steps with intermediate datums
between the acquisition surface and top of salt. Two intermediate
datums are shown in the right-hand figure, corresponding to
three datuming steps.
Semirecursive
migration
The premise of the semirecursive method is that data can be
re-synthesized at any subsurface datum by downward continuation
with a Kirchhoff datuming algorithm (Berryhill, 1979; Berryhill,
1984; Bevc, 1995). The depth step of the datuming is limited
so that the first-arrival traveltimes are calculated in such
a way that they accurately parameterize the most energetic
portions of the wavefield (Bevc, 1997). In this way, the downward
continued data are accurately synthesized at a datum which
is closer to the imaging target. Traveltimes can then be calculated
from the new datum, and the data can either be downward continued
again or migrated from the new datum. Since all the traveltimes
in this process are calculated over a smaller portion of the
velocity model, the final outcome is a more accurate image.
The semirecursive migration
method can be thought of as a hybrid algorithm that incorporates
some of the advantages of recursive migration with the efficiency
of Kirchhoff migration. It is called semirecursive because
the datuming depth step is much greater than the depth step
used in phase-shift or finite-difference shot-profile migration.
Because the data are re-synthesized at one or more depth levels
in the subsurface, the method has the added advantage of implicitly
handling multivalued arrivals. In each datuming and imaging
step the traveltime tables are single valued, but because
the data are repropagated at every step, the semirecursive
method captures the same energy that is accounted for by using
multivalued traveltime tables.
Discussion
The semirecursive Kirchhoff method has the advantage of being
able to use any simple first-arrival traveltime algorithm,
thus benefiting from the computational efficiency, robustness,
and simplicity of such methods. Because it is a Kirchhoff
method, it accommodates varied marine acquisition geometries.
The methods economical
benefits are two-fold: (1) The imaging algorithm is efficient
and offers substantial cost advantages over conventional methods.
(2) The imaging result is superior to widely used standard
Kirchhoff migration using first-arrival traveltime methods,
and therefore facilitates interpretation, reduces risk, and
cuts exploration costs.
References
Audebert, F., Nichols, D., Rekdal, T., Biondi, B., Lumley,
D., Nichols, D., and Urdaneta, H., 1997, Imaging complex geologic
structure with single-arrival Kirchhoff prestack depth migration:
Geophysics (Scheduled for publication in September-October
issue.
Berryhill, J. R., 1979,
Wave equation datuming: Geophysics, 44 1329--1344.
Berryhill, J. R., 1984,
Wave equation datuming before stack: Geophysics, 49 2064--2067.
Bevc, D., 1995, Imaging
under rugged topography and complex velocity structure: Ph.D.
Thesis, Stanford University.
Bevc, D., 1997, Imaging
complex structures with semirecursive Kirchhoff migration:
Geophysics, 62, 577--588.
Geoltrain, S. and Brac,
J., 1993, Can we image complex structure with first-arrival
traveltime?, Geophysics 58, 564--575.
Gray, S. H., and May,
W. P., 1993, Kirchhoff migration using eikonal equation traveltimes,
Geophysics 59, 810--817.
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