Azimuth moveout is a prestack partial migration operator that transforms 3D prestack data with a given offset and azimuth into equivalent data with a different offset and azimuth.

PP-AMO is not a single trace to trace transformation. It is a
partial migration operator that moves events across **midpoints** according
to their dip.
Due to the nature of PS-data, where
multiple coverage is obtained through common conversion point
gathers (CCP), the PS-AMO operator moves events across **common conversion points**
according to their geological dip.

Theoretically, the cascade of any imaging operator with its corresponding forward-modeling operator generates an AMO operator Biondi (2000). Our PS-AMO operator is a cascade operation of PS-DMO and inverse PS-DMO.

The 2D PS-DMO smile Harrison (1990); Rosales (2002); Xu et al. (2001) extends to
3D by replacing the offset and midpoint coordinates for the offset and
midpoint vectors, respectively. The factor *D*, responsible for the
CMP to CCP transformation, also transforms to a vector quantity.
The PS-DMO smile in 3D takes the form of:

(1) |

where,

(2) |

(3) |

and

Here, is the midpoint position vector, is the offset vector and ratio.

The PS-AMO operator, a cascade operator of PS-DMO and inverse PS-DMO, takes the form of:

(4) |

where

This operator reduces to the traditional expression of PP-AMO Biondi et al. (1998) for (i.e. ).

Although the PP-AMO operator is velocity independent, this independence doesn't propagate for the PS-AMO operator. The PS-AMO operator depends on the P velocity and the ratio. We assume that the velocity of the new trace position is the same as in the previous position.

6/7/2002