For smooth vertical inhomogeneities, the AMO operator has a shape and size similar to its homogeneous medium counterpart; a general skewed saddle shape. This is especially the case when the AMO operator includes only azimuth corrections. In fact, such an operator is also free of triplications, which will ease its use in practice. AMO operators that include offset correction, often show triplications. In general, AMO operators that correct only the azimuth are much simpler than those that also correct the offset. Therefore, using such operators in Kirchhoff-type implementation, should be straightforward.
The residual operators, derived by cascading a forward homogeneous-medium AMO and an inverse v(z) AMO, confirm the small difference in AMO between the two media. In fact, for the linear and low-velocity zone examples the vertical size of the operator is less than 10 ms. This is not the case for the complicated high-velocity layer model, where the residual AMO operator has almost the size of the full AMO operator.
The computational efficiency of a Kirchhoff-type AMO implementation depends largely on the size of the AMO operator. We have shown that for smooth v(z) media, as for homogeneous media, the AMO operator is generally small.