Riemannian spaces are described by nonorthogonal curvilinear coordinates. We generalize one-way wavefield extrapolation to semiorthogonal Riemannian coordinate systems that include, but are not limited to, ray coordinate systems. We obtain a one-way wavefield extrapolation method that can be used for waves propagating in arbitrary directions, in contrast to downward continuation, which is used for waves propagating mainly in the vertical direction. Ray coordinate systems can be initiated in many different ways; for example, from point sources or from plane waves incident at various angles. Since wavefield propagation happens mostly along the extrapolation direction, we can use inexpensive finite-difference or mixed-domain extrapolators to achieve high angle accuracy. The main applications of our method include imaging of steeply dipping or overturning reflections.

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