paul sava

Riemannian wavefield extrapolationRiemannian spaces are described by nonorthogonal curvilinear coordinates. Oneway wavefield extrapolation can be generalized to semiorthogonal Riemannian coordinate systems, which include, but are not limited to, ray coordinate systems. The result are oneway wavefield extrapolation methods which are not limited to any particular extrapolation direction. Such extrapolation techniques can be used for both wavefield modeling and migration. The pictures below depict wavefronts emerging from a point source in the middle of the model: one frame is computed with oneway Riemannian extrapolation in the frequency domain, and the other frame is computed with timedomain finite differences. The wavefronts are overlain over the velocity model which is smoothed to avoid backscattering at sharp discontinuities. Aside from a slight phase difference, the two wavefields are almost identical. Which frame corresponds to which method?
The Marmousi velocity model depicted in Cartesian coordinates and in
Riemannian coordinates, defined by rays from a point source.

http://www.mines.edu/~psava 