A Kirchhoff migration analog to least-squares slant stacking is summarized in Figure . Since we are using time-invariant transforms, a separate least-squares problem is set up for each frequency. In the slant stack case, this problem involved transformation to a one-dimensional space (ray parameter p), since only one parameter is needed to describe a linear moveout trajectory, its slope.
In the migration case, two parameters are needed to describe a migration hyperbola: the position beneath which the apex of the hyperbola lies (x), and another parameter that describes the curvature of the hyperbola. If we fix velocity, this second parameter can be called t0. For a given constant velocity, the hyperbola will have greater curvature for an early t0, and less for a later one. The transform space, then, contains two parameters (x and t0) instead of one in the slant stack case.
This means that the least-squares problem is likely to be larger than in the slant-stack case, and is typically underdetermined. But in principle there is nothing wrong with the transform space having an extra dimension.