f Filtering of numerical artifacts for paraxial wave equation migration operators

The paraxial wave equation is one of the most accurate pre-stack imaging tools for seismic data. It has been shown that pre-stack paraxial wave equation migration correctly images seismic data even for very complex velocity models (e.g., such as those containing caustics [1]). Furthermore, since the paraxial approximation gives rise to a one-way wave equation it is ideal for migration and imaging since, in principle, it does not generate reflections as do the acoustic and elastic wave equations. Nevertheless, the formulation and implementation of the paraxial wave equation give rise to some undesirable numerical artifacts.