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Ideally, every seismic data set should be imaged by use of 3D prestack migration. In practice, the computational cost of such migration limits its applications. Often, one can apply less expensive methods that yield satisfactory results in less time and with fewer resources.

However, computational complexity is not the only consideration. Prestack migration is very sensitive to the choice of velocity function and to irregular sampling of the data. This chapter introduces approximation methods for imaging prestack data — methods that are less expensive and often are more robust than full prestack migration. Therefore, approximate prestack-imaging operators can be applied successfully when full prestack migration might fail. Furthermore, prestack-imaging operators might be used to precondition (e.g., to regularize or to perform partial stacks of) the data before application of full prestack migration and before an accurate knowledge of the velocity model is gained.

The simplest of such partial-prestack-migration methods is based on the normal moveout (NMO) operator, which approximately transforms prestack data into equivalent zero-offset data. As one of the most basic seismic-processing operators, NMO is a simple stretching of the seismic traces. In the presence of dipping reflectors, NMO is not sufficiently accurate, and a more complex operator, dip moveout (DMO), becomes necessary to transform prestack data into equivalent zero-offset data. The DMO operator moves energy across the midpoint axes, partially focusing (migrating) the data. Therefore, it belongs to a family of partial-prestack-migration operators.

Another partial-prestack-migration operator that can be applied to reduce the computational cost of prestack migration

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