Generalized Riemannian wavefield extrapolation

Jeff Shragge

jeff@sep.stanford.edu

ABSTRACT

This paper extends wavefield extrapolation to generalized Riemannian spaces. The key component is the development of a dispersion relationship appropriate for propagating wavefield on generalized non-orthogonal meshes. This wavenumber contains a number of mixed-domain fields in addition to velocity that represent coordinate system geometry. An extended split-step Fourier approximation of the extrapolation wavenumber is developed, which provides accurate results when multiple reference parameters sets are used. Three examples are presented that demonstrate the validity of the theory. An important consequence is that greater emphasis can be placed on generating smoother computational meshes rather than satisfying restrictive semi-orthogonal criteria. This result should lead to more accurate and efficient generalized Riemannian wavefield extrapolation.