If the velocity were known and the only task were to migrate, then there would be no fundamental reason why the downward continuation could not be done in (S,G)-space. But the velocity really isn't well known. The sensitivity of migration to velocity error increases rapidly with angle, and angle accuracy is the presumed advantage of (S,G)-space. Furthermore, the finite extent of the recording cable and the tendency to spatial aliasing create the same problems with (S,G)-space migration as are experienced with Snell stacks. I see no fundamental reason why (S,G)-space migration should be any better than CMP slant stacks, and the aliasing and truncation situations seem likely to be worse. Less ambitious and more practical approaches to the wide-angle migration problem are found later in this chapter.
On the other hand, lateral velocity variation (if known) could demand that migration be done in (s,g)-space.
Still another reason to enter shot-geophone space would be that the shots were far from one another. Then the data would be aliased in both midpoint space and offset space.