Anti-aliased Kirchhoff 3-D migration

David E. Lumley, Jon F. Claerbout and Dimitri 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).