Conclusions

Performing wave-equation migration directly from topographic surfaces is achievable with a minimum of preprocessing in topographic coordinate systems. We show that conformal mapping generates the required topographic coordinate systems, and that the conformal map transform determines the appropriate wavefield extrapolation equations. We also conclude that multiple reference media are likely needed to image under complicated topography, which is consistent with wavefield extrapolation practice in a Cartesian coordinate system.

By extension, we show that upward datuming on a coordinate system generated through conformal mapping transformation could work as a pre-imaging processing step. Moreover, upward datuming could be more effective than downward migration direct from topography, since a constant velocity function would likely improve the range over which the phase-screen approximation is accurate. Standard Cartesian-based migration technology could then be used to downward continue the upward datumed wavefields.