Conclusion and Future Work

We have shown a theoretically attractive formulation of downward extrapolation in $\omega$-$\mathbf{k}$ domain capable of handling arbitrary spatial velocity variations. The initial algorithm can be easily modified to make its cost quadratic in the spatial dimensions. This may be appropriate for 2D data or for post-stack 3D data but is certainly not good enough for prestack 3D data. By sacrificing some accuracy, yet to be quantified, we may be able to arrive to a competitive algorithm that is much easier to implement and whose accuracy can be improved at run time.

We need to research the issues of wavefield subsampling and the extent to which wavefield traces influence one another.