Difficulty arises first on the widest-offset trace. Too large an interval in velocity will leave a gap between the hyperbolic scans. With the new method there is no chance of missing a point on the wide-offset trace. Also, the inner trace enters only once. The new method also makes many old interpolation issues irrelevant.
New questions arise, however.
A disadvantage is that some points in -space may happen to get no input data, especially if we refine v too much. The result of the new velocity transformation is shown in Figure 3 . To exhibit all the artifacts as clearly as possible, I changed all signal values to their signed square roots before plotting brightness. This has the effect of making the plots look noisier than they really are. I also chose to be unrealistically large to enable you to see each point.