CMP SEPARATIONS OF THE DOUBLE SQUARE ROOT EQUATION
, by Jon F. Claerbout and Ozdogan Yilmaz

The double square root (DSR) operator in common midpoint (CMP) space can be approximately separated into two
terms, one involving only migration effects, the other involving only moveout correction. This separation
provides an analysis of conventional processing. Estimation of errors in the separation yields an equation
that suggests a "devilishly" clever procedure for pre-migration of wide offset data to bring it to zero offset
before conventional velocity analysis, stack and final migration. Incorporation of lateral velocity variation
exhibits a large, unfamiliar term proportional to the product of the first powers of offset, dip, and lateral
velocity gradient.