Another definition of MZO given by Deregowski and Rocca (1981) is based on the decomposition of MZO into prestack migration followed by zero-offset modeling. Following this definition an impulse in a prestack constant-offset section is transformed into a depth model that represents all the possible reflector locations (an ellipse in constant velocity). By modeling the reflector back to zero-offset one obtains a curve that represents the impulse response of the MZO operator. The impulse response curve can be applied to constant-offset data as a Kirchhoff integral operator.

Hale (1983) tries to derive the ray-theoretical DMO from wave-equation principles by decomposing the prestack migration equation (double-square root in )in four major processing steps:

- 1.
- DMO,
- 2.
- NMO,
- 3.
- Stacking,
- 4.
- Zero-offset migration.

- 1.
- Migration to zero-offset (MZO).
- 2.
- Zero-offset migration (ZOM).

I apply the variable velocity MZO to three synthetic models and obtain very good coincidence between the initial zero-offset section and the output of the zero-offset migration. The drawback of the method is that summing over the offset is performed as part of the MZO. Further work is needed to isolate the stacking sequence.

11/17/1997