For the case when prestack depth migration has been performed with inaccurate velocities, it can be shown that second-order approximations can be used to predict the residual depth moveout of common-image and angle-domain common-image gathers. Corrections may be made in terms of offset and common-reflection angles that can be estimated from the migrated data using moveout analysis schemes. The residual moveout determined can be used to improve the signal-to-noise ratio of the migrated data and to determine the variation of parameters of well-known formation-dependent velocity laws away from borehole positions. Although the method is developed for small offsets, reflection angles, and velocity differences, realistic examples may be used to demonstrate that satisfactory approximations to the residual moveout curve can be obtained over a relatively wide range of offsets or reflection angles and for moderate velocity differences. A zero-offset inversion was applied to the estimated residual radii of curvature. This inversion was performed layerwise. For each layer, the velocity was assumed to vary according to a known depth-varying and a laterally varying component to be determined. Iterative applications of the suggested approach have rendered satisfactory results for several representative velocity models. For each application, appropriate initial models were provided. Applications to initial models with large velocity differences and to seismic data with large offsets have to be investigated.

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