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ARTICLES
Anti-aliased
Kirchhoff 3-D migration
By D. E. Lumley, J. F.
Claerbout, and D. Bevc
A significant degradation
in the quality of Kirchhoff migration images can arise
when the migration operator summation trajectory is too
steep for a given input seismic trace spacing and frequency
content. This phenomenon is called ``operator aliasing''
and is strictly distinct from and independent of data aliasing.
Unfortunately, the conditions which lead to significant
operator aliasing are common in most 3-D Kirchhoff migration
work, due to the sparse and irregular nature of 3-D acquisition
geometries, and the need to minimize the size of 3-D migration
input data volumes.
We anti-alias the migration
operators ``on the fly'' with N-point triangle filters.
Using a Z-transform representation, we reduce each N-point
triangle filter operation to an efficient three-point filter
operation, with the added minor overhead of a causal and
anticausal integration of the input trace data prior to
migration. Our anti-aliased migration is computationally
efficient since it requires about the same number of floating
point operations as a conventional Kirchhoff migration,
and is conservative in its memory use since it does not
require storage of multiple trace-data copies to implement
the anti-aliasing. Our anti-aliased migration is accurate
in that it applies local anti-alias filters separately
for each of the many migration operators which pass through
a given input data point.
We demonstrate our method
with a 3-D implementation on a massively parallel Connection
Machine CM-5, and compare our new anti-aliased Kirchhoff
migration to a conventional aperture-weighted Kirchhoff
migration in an application to a 3-D marine seismic data
example. Our results indicate that our anti-aliasing method
greatly enhances the 3-D resolution of steep salt-sediment
interfaces and faults, and suppresses false reflections
caused by conventional Kirchhoff-migration aliasing artifacts.
Our method is applicable to other space-time Kirchhoff
operations such as NMO velocity-stacking and DMO.
64th Ann. Internat. Mtg.,
Soc., Expl. Geophys., Expanded Abstracts, 1282-1285, (1994).
56th Ann. Internat. Mtg.,
European Assoc. Expl. Geophys., (1994)
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