Approximate linearized inversion by optimal scaling of prestack depth migration

Linearized inversion provides one possible sense of image amplitude correctness. An image or bandlimited model perturbation has correct amplitudes if it is an approximate inversion, that is, if linearized modeling (demigration), with the image as input, reproduces the data approximately. The theory of linearized acoustic inverse scattering with slowly varying background or macromodel shows that an approximate inversion may be recovered from the output of prestack depth migration by a combination of scaling and filtering. The necessary filter is completely specified by the theory, and the scale factor may be estimated via filtering, linearized modeling, a second migration, and the solution of a small auxiliary inverse problem.