We introduce a new partial prestack-migration operator, named Azimuth MoveOut (AMO), that rotates the azimuth and modifies the offset of 3-D prestack data. AMO can improve the accuracy and reduce the computational cost of 3-D prestack imaging. We have successfully applied AMO to the partial stacking of a 3-D marine data set over a range of offsets and azimuths. Our results show that when AMO is included in the processing flow, the high-frequency steeply-dipping energy is better preserved during partial stacking than when conventional partial-stacking methodologies are used. Because the test data set requires 3-D prestack depth migration to handle strong lateral variations in velocity, the results of our tests support the applicability of AMO to prestack depth-imaging problems.
AMO is defined as the cascade of a 3-D prestack imaging operator with the corresponding 3-D prestack modeling. To derive analytical expressions for the AMO impulse response, we used both constant-velocity DMO and its inverse, as well as constant-velocity prestack migration and modeling. Because 3-D prestack data is typically irregularly sampled in the surface coordinates, AMO is naturally applied as an integral operator in the time-space domain. The AMO impulse response is a skewed saddle surface in the time-midpoint space. Its shape depends on the amount of azimuth rotation and offset continuation to be applied to the data, but it is velocity independent. The AMO spatial aperture, on the contrary, does depend on the minimum velocity. When the azimuth rotation is small (), the AMO impulse response is compact and its application as an integral operator is inexpensive. Implementing AMO as an integral operator is not straightforward because the AMO saddle may have a strong curvature when it is expressed in the usual midpoint coordinates. To regularize the AMO saddle, we introduce an appropriate transformation of the midpoint axes that leads to an effective implementation.