On the Use of Smooth Velocities in Ray-based Stacking and Time-migration

We revisit ray-based approaches to stacking and time migration of seismic data, and investigate the role of the smooth-velocity condition normally attached to such techniques. It is demonstrated that the smooth velocity field plays the role of a replacement medium which ideally should have the following characteristic: the one-way analogues of the stacking and time-migration operators can be approximated in a paraxial sense by means of its impulse responses. In order to link the intrinsic properties of this smooth medium to the data-driven velocities, an incremental ray propagator system has been introduced. Based on this system, it is shown how stacking and time-migration velocities can be regarded as paraxial quantities which can be mapped to intrinsic properties representing information sampled along the central or mapping ray of the paraxial impulse responses considered.