Generalized sampling and "beyond Nyquist" imaging

Peter W. Cary

We routinely image seismic data beyond the usual Nyquist sampling limits when we stack into limited-offset stacks either before or after migration. Binning or stacking a number of aliased common-offset gathers approximately dealiases the data because of the staggered common-midpoint sampling between common-offset gathers. The interleaved subsurface sampling of individual subsets of the full prestack data allows unaliased poststack images to be obtained from aliased prestack data. The highest recoverable wavenumber in the migrated image is not determined by the smallest sample rate of the input wavefield, as simple sampling theory dictates, but by the average subsurface sample interval, which follows from a more general form of sampling theory. Prestack migration of individual aliased subsets of the data should allow the migration operator to alias in order to recover all frequencies in the stack.