I compute the impulse response of MZO by considering the process as the combination of full prestack migration followed by zero-offset modeling (Deregowski and Rocca, 1981; Deregowski, 1985). I use a fast algorithm to compute the travel-time map necessary for modeling wave propagation in a general 2-D medium (Van Trier and Symes, 1990). I applied the proposed algorithm for computing the kinematics of the impulse response when velocity is constant and for different velocity functions of depth. The impulse response in varying velocity can differ substantially from the constant velocity one (Popovici, 1990). I use the impulse response in a Kirchoff type algorithm applied to a series of synthetic models. As a result there is a better alignment of prestack data migrated to zero-offset than in the case of conventional algorithms, which imply better stacking for a range of different offsets.
The proposed algorithm for computing the impulse response of MZO using finite-difference travel-time maps is based on the principle that MZO is the combination of two processes: full prestack migration and zero-offset modeling. In a constant velocity medium this definition allows for an analytical formulation of the MZO operator which is identical with the DMO after NMO formulation (Popovici and Biondi, 1989). The algorithm used to investigate the MZO operator in variable velocity media follows the definition of the MZO method and can be divided in two parts: