In the context of structural imaging of geological settings the determination of the subsurface velocity model is the most crucial step. For this determination, the results of prestack depth migration of seismic data can be used. However, in case of important lateral velocity variations in the subsurface, the image quality obtained by prestack depth migration is not sufficient for interpretation (used for a subsequent update of the velocity model) and for checking the correctness of the velocity model. We propose to substitute prestack depth migration by Prestack Imaging by Coupled Linearized Inversion (PICLI). This approach yields improved images without altering the important kinematic information contained in prestack migrated images. The PICLI method is computationally more expensive than prestack depth migration and contains notably the solution of a huge size linear system, on which ordinary conjugate gradient methods are ineffective. An adequate change of the scalar product in model space leads to a preconditioned conjugate gradient algorithm which gives in a few iterations the solution of this huge inverse problem.
"Prestack imaging by coupled linearized inversion", Proc. SPIE 2033, Mathematical Methods in Geophysical Imaging, (1 December 1993); doi: 10.1117/12.164847; https://doi.org/10.1117/12.164847