INTEGRAL IMPLEMENTATION OF AMO

One of the main advantages of AMO is that it is a narrow operator and that consequently its application to a full 3-D prestack data set is much less costly than the application of full 3-D prestack migration. However, designing an accurate and efficient implementation of the AMO operator is not straightforward. Therefore, in this section we discuss the issues relevant to an effective implementation of the AMO process, as defined in the previous sections. The main challenge is to devise an efficient method that avoids operator aliasing and simultaneously takes advantage of the opportunity for saving computation, by properly limiting the spatial extent of the numerical integration.

The AMO integration surface has the shape of a saddle. The exact shape of the saddle depends on the azimuth rotation and offset continuation that are applied to the input data. When the azimuth rotation is small, the saddle has a strong curvature. Conventional anti-aliasing methods Bevc and Claerbout (1992); Gray (1992) are based on an adaptive low-pass filtering of the data as a function of the operator local dips. When there is a strong curvature, the dips change too quickly for a simple low-pass filter of the input trace to both suppress the aliased dips and preserve the non-aliased dips. To address this problem we perform the spatial integration in a transformed coordinate system. In this new coordinate system, the AMO surface is well behaved, and its shape is invariant with respect to the amount of azimuth rotation and offset continuation.