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Amplitude and kinematic corrections of migrated images for nonunitary imaging operators

Obtaining migrated images with meaningful amplitudes is a challenging problem when the migration operator is not unitary. One possible solution to this problem is iterative inversion. However, inversion is an expensive process that can be rather difficult to apply, especially with 3D data. In this paper, I propose estimating migrated images similar to the least-squares inverse images by approximating the inverse Hessian, thus avoiding the need for iterative inversion. The inverse Hessian is approximated with a bank of nonstationary matching filters. These filters are not exact impulse responses and are limited in their ability to mimic the full effects of least-squares inversion. Tests on two data sets show that this filtering approach gives results similar to iterative least-squares inversion at a lower cost. This technique is flexible enough to be applied to images migrated from zero-offset or angle-domain common-image-point gathers.