The azimuth moveout (AMO) correction is a valuable tool for processing 3-D data. Most prestack imaging algorithms (i.e., dip moveout and prestack migration) are theoretically designed to work for data acquired along a single source-receiver azimuth. Yet, in 3-D surveys, data are seldom acquired along a single azimuth. Azimuth variation is often ignored and seismic traces are binned, after normal-moveout (NMO) correction, into a regularly sampled data set in offset and Common midpoint (CMP). Though, for isotropic homogeneous media, such binning has no bearing on reflections from horizontal events, ignoring the azimuth variation can harm reflections from dipping events Biondi et al. (1998), resulting in the attenuation of such reflections when partial stacking is applied to reduce the volume of the data set Hanson and Witney (1995). Thus, the multi-azimuth nature of seismic data acquired using 3-D marine or land surveys, and the desire of processors to preserve energy from dipping events, made the AMO correction an important tool in processing.

Like the DMO operator, the AMO operator is applied after NMO correction.
Because the AMO operator is small in size compared with the DMO operator,
Alkhalifah and Biondi (1998) showed that
smooth vertical velocity variation has an overall small influence on the operator shape. Strong
vertical velocity variation was needed to considerably alter the shape of the homogeneous operator. The size of the residual
AMO operator, which was smaller than the full AMO operator by a factor of 10, further demonstrated the fact that
smooth *v*(*z*) variations can some what be ignored in AMO correction.

Alkhalifah (1997c) showed that anisotropy can highly impact the 3-D DMO operator. In fact, for homogeneous media, the presence of anisotropy will give the DMO operator a 3-D shape. This is a big change from the 2-D operator associated with the isotropic DMO in homogeneous media. The presence of anisotropy also results in triplications in the DMO operator even for homogeneous media, where the DMO operator for the isotropic case has a simple ellipse shape. AMO consists of a cascade of a forward and inverse DMO. The inverse DMO is applied after rotating the axes by an angle equal to the desired azimuth correction. Thus, some of the features Alkhalifah (1997c) described for the DMO operator should apply to AMO operators, as well.

In this paper, I will investigate the impact that anisotropy has on AMO operators, specifically as it relates to the operator size and shape. The AMO operator for isotropic media will be used as a reference operator to judge the influence of anisotropy. Later, I will add vertical velocity variation to the mix, since the combination of velocity increase with depth and anisotropy is very common.

8/21/1998