Overview

Riemannian spaces are prescribed by non-orthogonal curvilinear coordinates. In this chapter, I generalize one-way wavefield extrapolation to semi-orthogonal Riemannian coordinate systems, that include, but are not limited to, ray coordinate systems. I obtain a one-way wavefield extrapolation method which can be used for waves propagating in arbitrary directions, in contrast with downward continuation which is used for waves propagating mainly in the vertical direction. Ray coordinate systems can be initiated either from point sources, or from plane waves incident at various angles. Since wavefield propagation happens mostly along the extrapolation direction, this method enables us to use inexpensive finite-difference or mixed-domain extrapolators to achieve high angle accuracy. The main applications of this method include imaging of steeply dipping or overturning reflections.