The application of McClellan transformations considerably reduces the
computational cost of 3D wavefield depth extrapolation by explicit con
volutional methods. The accuracy of migration methods based on McClell
an transformation depends on how well the transformation filter (cos \
k\) is approximated; errors in this approximation cause anisotropy in
the extrapolation operator and frequency dispersion in the migrated re
sults. The anisotropy can be greatly reduced by rotating the approxima
te filter by 45 degrees and averaging the rotated filter with the orig
inal filter. The application of the rotated filter yields a migration
method that correctly images very steep dips, with little or no additi
onal computational cost. McClellan migration with the improved circula
r response enhances the imaging of synthetic and real data.