We are developing the theory, numerical algorithm, and prototype implementation of seismic imaging by
Riemannian wavefield extrapolation (RWE). RWE was proposed by Sava and Fomel (2004) for imaging steeply
dipping and overturning reflections in geologically complex exploration areas, such as deep subsalt structures
in the Gulf of Mexico.
RWE belongs to the class of wave-equation extrapolation methods that are known to handle accurately
large-velocity contrasts, multipathing, and band-limited wave propagation effects. Instead of conventional
downward extrapolation, RWE employs a coordinate transformation to extrapolate waves numerically in a direction
close to the preferential direction of natural wave propagation. As a result, one can accurately image large
propagation angles, including overturning salt-flank reflections, using inexpensive extrapolation operators.