Two migration methods based on paraxial equations in a 3D heterogeneous medium

We review recent work on paraxial equation based migration methods for 3D heterogeneous media. Two different methods are presented: one deals directly with the classical paraxial equations, by solving a linear system at each step in depth. The other method derives new paraxial equations that lend themselves to splitting in the lateral variables, without losing either accuracy or isotropy. We also show how to incorporate Berenger's perfectly matched layers in this framework. We detail the discretization schemes, both for the full paraxial equations, and for the newly derived equations.