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:
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:
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.