The velocity transform and its preconditioning
, by Jon F. Claerbout

The problem is posed of finding a transformation to velocity space
that is close to unitary. A preliminary attempt via Kirchhoff-type algorithms
leads to moderate degradations after about 4 iterations in and out of velocity space.
Results show clearly that summing only one point per trace leads severe degradation where data steps out fast
whereas using more points per trace avoids such noise. A preliminary theory
to make the velocity transform more unitary is based on pre and post operative diagonal scaling.