In our quest for quality, we will also recall various approximations as we go. Now is the time to see how the use of approximations degrades results, and to discover how to improve those results. Five specific problems will be considered:

- 1
- The frequency dispersion that results from the approximation of differential operators by difference operators
- 2
- The anisotropy distortion of phase and group velocity that results from square-root approximations
- 3
- The effect of truncation at the end of the survey line
- 4
- Dips greater than ninety degrees
- 5
- Wraparound problems of Fourier transformation
- 6
- The effect of
*v*(*z*) upon the Stolt method and how to improve the result by stretching

Following study of these approximations, is a penetrating study of causality, which covers much ground including how Fourier domain migration can simulate the causality intrinsic to time domain migrations and a grand summary of techniques. A single program is presented that can simulate diffraction hyperbolas from many different migration methods. This facilitates comparison of techniques and optimization of parameters. Figure 1 and many of the other figures in this chapter were produced with this program, so you should be able to reproduce them.

10/31/1997