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Since the layer-stripping algorithm
is a Kirchhoff method, it is readily applicable to 3-D
data sets. The most efficient mode of application will depend on
the particular acquisition parameters and there will be intermediate
data volumes. Many of the same sampling and coverage issues that
arise in 3-D migration will be issues in 3-D datuming also.
Depending on the acquisition geometry, the intermediate volume
could turn out to be larger than the original volume because out-of-plane
propagation must be accommodated and saved at intermediate depth levels.
In some cases, a common azimuth approach can be applied.
This is easy to do with the Kirchhoff formulation, because it only amounts to
3-D downward continuation in what could be termed a target-oriented manner.
If the cross-line lateral velocity variation is not too severe, marine data
can be downward continued to a grid with the same geometry as the
original acquisition geometry. In this case, some energy will be lost,
but this may be acceptable.
As in the case of rugged topography, the handling of
land data acquired by shooting into patches of receivers is fairly
straightforward: source and receiver gathers can be
extrapolated using reciprocity.
In this case, source spacing will be a critical parameter in determining
if the common receiver gathers will be adequately sampled.
There are several factors that can make this approach very attractive in
three dimensions. All of these computational factors
hold for 2-D data also, but their
effects should be more dramatic in 3-D applications.
The following items could offer significant efficiency in three dimensions:
- Traveltimes for 3-D imaging are usually calculated
in spherical coordinates. For a given cube of desired traveltimes,
this calculation requires a spherical volume with a radius equal
to the longest cube diagonal. Therefore, if the velocity model
is subdivided, the number of traveltimes that need to be calculated
is dramatically reduced. The reduced volume also significantly
reduces the storage space required during the calculation.
- After each depth step, the resynthesized data traces
get progressively shorter. This means that the computation and
the amount of storage per trace is reduced after each depth step.
- After each depth step, both the migration and
datuming aperture can be reduced. This not only cuts down on
the number of calculations, but it can be used to limit the
amount of input data kept in memory for any
given output location.
- As mentioned in Chapter , a key
algorithmic difference between migration and wave-equation datuming
is that each input trace is statically shifted rather than dynamically.
This means that the computation can be done quickly and efficiently
as a complex multiplication in the Fourier-domain, where the
derivative operator is applied. This is the primary reason why
an optimized Kirchhoff datuming algorithm
is potentially much faster than Kirchhoff migration.
The layer-stripping migration algorithm has
great potential for efficiency, and
for some geometries it is more efficient
than standard Kirchhoff migration.
Next: Summary
Up: Implications for velocity estimation
Previous: Velocity estimation
Stanford Exploration Project
2/12/2001