Spatial aliasing of Kirchhoff migration operators occurs when the migration summation surface slices through the input data volume at moveouts greater than the spatial and temporal dip Nyquist frequency. This operator aliasing can severely degrade the quality of the final subsurface image. The aliasing can become worse for 3-D surveys since crossline trace spacings are often at least twice as long as inline spacings. Additionally, scattered energy from steep-dip reflectors, such as faults and salt flanks, magnifies the aliasing problem.
Conventionally, some degree of anti-aliasing of Kirchhoff operators can be partially effected by a combination of trace interpolation, migration aperture control, operator dip filtering, and offset-dependent lowpass filtering (e.g., Gray, 1992). Trace interpolation decreases the spatial sample interval and thus increases the spatial Nyquist frequency, but at the potentially prohibitive cost of increasing the total migration input load. Migration aperture control and operator dip filtering effectively represent ad hoc methods to suppress (aliased) steep dips contributions to the output image. Unfortunately, these steep dips may be precisely the events of interest when imaging salt flanks or vertical faulting. Source/receiver offset-dependent lowpass temporal filtering is an approximation to steep-dip operator anti-aliasing, but does not fully take into account the true time and dip variant nature of the problem, as exemplified by considering a simple zero offset (poststack) migration.
The outline of this paper is as follows. I first briefly review the anti-aliasing method by triangle filtering as proposed by Claerbout (1992). Next I discuss my implementation of the method and practical numerical aspects with regard to parallel computation on the SEP Connection Machine. Finally, I discuss an application of the method to a 3-D poststack data set from the Gulf of Mexico, and show that the anti-aliased Kirchhoff migration resolves steep dips on salt-sediment interfaces and faults better than a conventional aperture-weighted Kirchhoff migration.