Model space weighting operators can be applied to an image after it has been produced by an imaging operator. One familiar operator used to help bring up amplitudes in seismic images is automatic gain control (AGC). However, AGC does not make use of the information we have about the subsurface and, therefore, the illumination. Since most imaging operators use a velocity model, why not use that velocity model to help design a smarter weighting operator that will do a better job of compensating for illumination? Rickett (2001) suggested using the velocity model and a downward continuation operator to approximate the Hessian, giving us an appropriate weighting operator.
In this paper, I will first review the method proposed by Rickett (2001) for the construction of a model space weighting operator. I will then apply this weighting operator to a complex synthetic model with clear illumination problems. Finally, I will compare the model space weighted results with the more expensive regularized inversion methods used by Prucha and Biondi (2002b).