Velocity continuation and the anatomy of residual prestack time migration

Velocity continuation is an imaginary continuous process of seismic image transformation in the postmigration domain. It generalizes the concepts of residual and cascaded migrations. Understanding the laws of velocity continuation is crucially important for a successful application of time-migration velocity analysis. These laws predict the changes in the geometry and intensity of reflection events on migrated images with the change of the migration velocity. In this paper, I derive kinematic and dynamic laws for the case of prestack residual migration from simple geometric principles. The main theoretical result is a decomposition of prestack velocity continuation into three different components corresponding to residual normal moveout, residual dip moveout, and residual zero-offset migration. I analyze the contribution and properties of each of the three components separately. This theory forms the basis for constructing efficient finite-difference and spectral algorithms for time-migration velocity analysis.