# REFERENCES

• Claerbout, J. C., 1985, Imaging the Earth's Interior: Blackwell Scientific Publications.

• Deregowski, S. M., and Rocca, F., 1981, Geometrical optics and wave theory of constant-offset sections in layered media: Geophysical Prospecting, 29, 374-406.

• Gazdag, J., 1978, Wave equation migration with the phase shift method: Geophysics, 43, 1342-1351.

• Hale, I. D., 1983, Dip-moveout by Fourier transform: Ph.D. thesis, Stanford University.

• Hale, I. D., 1988, Dip-moveout processing: Course notes from SEG continuing education course, SEG.

• Popovici, A. M., 1990, Prestack partial migration analysis: SEP-65, 17-28.

• Popovici, A. M., 1992, Dip-Moveout processing: A Tutorial. DMO basics and DMO by Fourier transform: SEP-75, 407-425.

• Stolt, R.H., 1978, Migration by Fourier transform: Geophysics, 43, 23-48.

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## APPENDIX A

In equation (1) the values of the constant kz, given by equation (2), have to be real. Imaginary values of kz do not satisfy the downward continuation ordinary differential equation

and have to be excluded. Real values of kz from equation (2) require the conditions:

which can be reduced to the condition
 (16)
After the change of variable from to in equation (5)

we want to express function of and determine the integration boundaries for .We start with the expression for :
 (17)
and after reducing

and grouping

we have
 (18)
The discriminant is

From the conditions on kz, is always positive and therefore is always real within the limits.

The integration limits for are found by starting with the limits for :

and after we square both sides

and replacing in the equation for we have
 (19)
The integration in is done from and from . After changing the order of integration from to kh, the integration boundaries for kh become
 (20)