Model versus data normalization

 Illumination problems caused by finite-recording aperture and lateral velocity lensing can lead to amplitude fluctuations in migrated images. I calculate both model and data-space weighting functions that compensate for these illumination problems in finite-frequency depth migration results. These weighting functions can either be applied directly with migration to mitigate the effects of poor subsurface illumination, or used as preconditioning operators in iterative least-squares (L2) migrations. Computational shortcuts allow the weighting functions to be computed at about the cost of a single migration. Results indicate that model-space normalization can significantly reduce amplitude fluctuations due to illumination problems. However, for the examples presented here, data-space normalization proved susceptible to coherent noise contamination.