These examples indicate that the procedure developed in this paper can generate coordinate systems from potential function solutions of Laplace's equation. Tests were conducted on surfaces exhibiting moderate-to-rough topography; hence, coordinate surfaces developed for smoother surfaces (e.g., deviated VSP wells) should be subject to less focusing than these examples. Thus, I assert that PF-derived smooth coordinate systems should be good for use in RWE.

However, as the 2D rugged topography example indicates, coordinate systems under rough topography generated by this approach probably are less well-suited for RWE. In particular, the 2D example probably reveals that coordinate system generated through the conformal mapping approach of Shragge and Sava (2004a) are probably better suited for RWE. This is because wavefield extrapolation on severely focused coordinate systems requires high extrapolation operator accuracy. However, the real test of whether coordinate systems generated by the above approach are appropriate for RWE ultimately lies in accurcy of resulting extrapolated wavefields and corresponding images.

5/3/2005