PS-AMO

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 (). Our PS-AMO operator is a cascade operation of PS-DMO and inverse PS-DMO.

The 2D PS-DMO smile (, , ) 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:  

 69#69 (31)

where,  

 70#70 (32)

71#71 (33)

and

72#72

Here, 73#73 is the midpoint position vector, 74#74 is the offset vector and 44#44 ratio. The PS-AMO operator, a cascade operator of PS-DMO and inverse PS-DMO, takes the form of:

75#75 (34)

where This operator reduces to the traditional expression of PP-AMO () for 77#77 (i.e. 65#65).

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 78#78 ratio. We assume that the velocity of the new trace position is the same as in the previous position.