We define an acoustic wave-equation for semi-orthogonal Riemannian coordinates, from which we derive a one-way wavefield extrapolation equation. We use ray coordinates initiated either from a point source, or from an incident plane wave at the surface. Many other types of coordinates are acceptable, as long as they fulfill the semi-orthogonal condition of our acoustic wave equation.

Since wavefield propagation happens mostly along the extrapolation direction, we can use cheap finite-difference or mixed-domain extrapolators to achieve high angle accuracy. If the ray coordinate system overturns, our method can be used to image overturning waves with one-way wavefield extrapolation.

A special case of extrapolation corresponds to coordinates initiated by a plane wave at the surface propagating initially in the vertical direction. Since our extrapolation is done as a function of one-way traveltime, this case resembles imaging in vertical traveltime, although it is more physically correct, since it allows lateral movement of energy, which is not the case for vertical imaging.

Two main applications of our method are imaging of steeply dipping or overturning reflections.

10/14/2003