As a condition for further generalization of the migration to zero-offset in variable velocity media, I develop the theory for 2D migration to zero offset (MZO) in constant velocity media, starting from prestack migration in midpoint-offset coordinates. In arrive at an integral formulation for the MZO operator, analytically derived from the double square root (DSR) prestack migration equation. The integral formulation for the MZO is similar in form to the DSR equation, suggesting a generalization to variable velocity media using a phase-shift algorithm.
Alexander Mihai Popovici,
"Migration to zero-offset in variable velocity media", Proc. SPIE 2301, Mathematical Methods in Geophysical Imaging II, (23 September 1994); doi: 10.1117/12.187490; https://doi.org/10.1117/12.187490