Robust Illumination Compensation for Shot-Profile Migration

For shot-profile migration, illumination compensation can be achieved if the imaging condition incorporates a deconvolution (division in the frequency domain) of the up-going wavefield by the down-going wavefield. To avoid division by zero, the deconvolution requires the selection of a damping parameter that turns out to be quite difficult to select. Consequently, a cross-correlation of the two wavefields is often selected. Alternatively, the zeros in the spectrum of the down-going wavefield can be filled with an average of the neighboring points. Therefore, instead of dividing by the wavefield, we can divide by a smoothed version of it. Smoothing is robust and easy to parameterize. It also corrects illumination problems in the migrated images.