AMO is derived by chaining a 3D prestack imaging operator with its corresponding 3D prestack modeling operator. In principle, any 3D prestack imaging operator can be used for the definition of AMO. However, the characteristics of the resulting AMO operator, mainly computational efficiency and degree of required knowledge of the velocity model, depend on the 3D prestack operator used for its definition. An accurate AMO operator can be derived from 3D prestack migration; however, that would require a detailed knowledge of the velocity function, and it would be very difficult to derive its analytical representation, which could lead to a potentially expensive implementation. Recently, Goldin 1994 and Hubral et al. 1996 presented a general methodology for cascading 3D imaging operators. The implementation of their theory, however, requires expensive numerical evaluation of the cascaded operator.
Originally, we defined AMO from the cascade of dip moveout (DMO) and inverse DMO Biondi and Chemingui (1994). To derive an accurate expression for the spatial aperture of AMO, we used full 3D prestack constant velocity migration Biondi et al. (1998). The two derivations yield to an equivalent, velocity-independent, definition for the kinematics of AMO. Similar to DMO processing Deregowski and Rocca (1981); Hale (1984), the first-order effects of velocity variation are removed by applying a normal moveout correction (NMO) to the data prior to AMO.
As a partial imaging operator, AMO moves events across midpoints according to their dip. It therefore preserves all the dips in the data during partial stacking. The transformation is thoroughly defined in the midpoint-offset domain by the kinematics, the amplitude weights and the spatial extent (aperture) of the AMO impulse response.