Effective filtering of artifacts for implicit finite-difference paraxial wave equation migration1

Implicit finite-difference implementations of the paraxial wave equation are widely used in industrial prestack and post-stack migration programs for imaging and velocity analysis. This type of implementation gives rise to numerical artifacts which, in general, do not degrade image quality but which do impede effective velocity analysis. This paper reviews the artifacts generated by the paraxial approximation and a post-extrapolation, spatially varying filtering scheme is described which completely eliminates these artifacts. The method is illustrated with numerous examples.