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From now on for simplicity I will use the variables
In equation (8), the values of the constant *k*_{z}
have to be real. Imaginary values of *k*_{z} do not
satisfy the downward continuation ordinary differential
equation:
| |
(12) |

and have to be excluded. Real values of *k*_{z}
from equation (9) require both of the following
conditions to be satisfied:
which can be reduced to the condition
| |
(13) |

Therefore, equation (8) should be written

| |
(14) |

For each value of *v*_{y} the integration in is done
in two regions: under the value
and
over the value
as displayed in Figure .
**khkyomega
**

Figure 2 Regions of integration.

Before substituting the new variable in the prestack
migration equation let us analyze the limits of integration for
the new variable .From Appendix A, the expression of is

| |
(15) |

and the boundary values for corresponding
to the limits for in equation (13):

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Stanford Exploration Project

11/17/1997