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## Integration limits

From now on for simplicity I will use the variables

In equation (8), the values of the constant kz have to be real. Imaginary values of kz do not satisfy the downward continuation ordinary differential equation:
 (12)
and have to be excluded. Real values of kz 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 vy 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):

Next: Integration order Up: Introduction Previous: Second definition: MZO extracted
Stanford Exploration Project
11/17/1997