Higher Order Paraxial Wave Equation Approximations in Heterogeneous Media

Abstract

A new family of paraxial wave equation approximations is derived. These approximations are of higher order accuracy than the parabolic approximation and they can be applied to the same computational problems, e.g., in seismology, underwater acoustics and as artificial boundary conditions. The equations are written as systems which simplify computations. The support and singular support are studied; energy estimates are given which prove the well-posedness. The reflection and transmission are shown to be continuously dependent on material interfaces in heterogeneous media.