Conclusions

Higher-order Riemannian wavefield extrapolation is needed when the coordinate system does not closely conform with the general direction of wavefield propagation. This situation occurs, for example, when the coordinate system is created by ray tracing in a medium that is different from the one used for extrapolation, or when the coordinate system is constructed based on some geometrical properties of the acquisition geometry (e.g. migration from topography). Space-domain and mixed-domain finite-difference solutions to Riemannian wavefield extrapolation improve the angular accuracy. 3D solutions can be addressed with explicit finite-differences, although this remains subject for future research.