Resolution versus antialiasing in wavelet migration
Yu Zhou, John Etgen, Uwe K. Albertin, David N. Whitcombe · 2007
A common method used to protect Kirchhoff migration operators from aliasing is to apply an operator-dip-dependent lowpass filter to each input trace during summation. This can reduce resolution because higher frequency components of the input data are removed from the migrated image as output dip increases. Instead of migrating data the conventional way, we apply a wavelet transform over the time axis of the data and then apply Kirchhoff migration to the wavelet coefficients of each wavelet scale separately. We reconstruct the full-bandwidth image from the multi-scale images with an iterative wavelet reconstruction without any anti-aliasing protection. The frequency components of the data that would be aliased by the migration operator are found in the smaller scale or higher frequency/wavenumber bands. The frequency or wavenumber dependent aliased energy is automatically reduced during wavelet reconstruction because it is not consistent across wavelet scales. Using a field data example, we demonstrate that this method produces better resolution and signal-to-noise than conventionally-antialised Kirchhoff migration regardless of the dips of the summation trajectories and the frequency content of the input data.