The PS-AMO operator described above works on
a regular sampled cube, our data is recorded on an irregular mesh.
Following the methodology described in Clapp (2006)
we first map our data to a regular 5-D
mesh. For this problem we chose nearest neighbor interpolation,
designated by the operator .
For migraion efficiency, and because the five-dimensional space
is sparsely populated, we want to reduce the dimensionality
of our dataset. A common goal, and the one we chose to implement,
was to create common azimuth volume orriented along the inline
direction. As a result we want to eliminate the *h*_{y} axis.

Our PS-AMO operator (diagramed in Figure )
allows to transform between various
vector offsets. We use it 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 can 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

(8) |

flow
Diagram flow for the
implementation of the PS-AMO operator.
Figure 1 |

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

(9) |

(10) |

(11) |

(12) |

4/5/2006