Rosales and Biondi (2002a) introduce the converted-wave azimuth moveout operator. This operator transforms data from a given offset and azimuth to data with a different offset and azimuth. This operator is a sequential application of converted-wave dip moveout and its inverse. PS-AMO reduces to the known expression of AMO for the extreme case when the P velocity is the same as the S velocity. Moreover, PS-AMO preserves the resolution of dipping events and internally applies a correction for the lateral shift between the common midpoint and the common reflection/conversion point. An implementation of PS-AMO in the log-stretch frequency-wavenumber domain is computationally efficient.

For migration efficiency, we want to use a four-dimensional data
cube instead of a full five-dimensional data cube.
The crossline offset axis is reduced to only one element (*h*_{y}=0). The
traditional process uses Normal Moveout and stacking along the
crossline direction to transform the data from an
irregular grid to a regular grid with four axes; however, this
technique does not consider the dip and the variations
along the inline and crossline directions.
In this paper, we use the PS-AMO operator
to map the data into a regular 4-D mesh.
We follow the method described first in Clapp (2006)
and extended for PS data by Rosales and Clapp (2006).

Figure 1

We use the nearest-neighbor interpolation operator ()to map the data from an irregular mesh into a regular mesh.
The PS-AMO operator (diagramed in Figure 1)
allows the transformation between various
vector offsets. We use PS-AMO to transform data from to
*h*_{y}=0. We can think of it in terms of an operator which is a sumation over *h*_{y}. We allow for some mixing
between *h*_{x} by expanding our sumation to form *h*_{x}=*a* *h*_{y}=0,
by summing over all *h*_{y} and

(1) |

We can combine these two operators to estimate a 4-D model () from a 5-D irregular dataset () through,

(2) |

(3) |

(4) |

(5) |

1/16/2007