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 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 or by using splitting and
implicit methods, similarly with the techniques used for Cartesian
extrapolation.
2008-12-02