Equation (9) applies to downward-going waves. When we do the two-pass and four-pass migration, we apply the exploding reflector concept Claerbout (1985), so we use the equation for upward-coming waves instead of the one for downward-going waves.

When the velocity is slowly variable or independent of *x* and *y*,
the conditions of full separation do apply.
The dispersion relation for upward-coming waves can be written as follows:

(10) |

Using the splitting method, we can separate equation (10) into a thin lens term and a diffraction term as follows:

(11) |

(12) |

The counterpart of equation (12) in the () domain,

(13) |

is the equation we use to derive the differencing star and do migration.

For the *x* and *y* directions, we use *dx*,*dy*, and *dz* / 2 to derive
the six-point implicit finite-differencing star; for the *x*' and *y*' diagonal
directions, we use , and *dz* / 2, assuming *dx*=*dy*.
And to minimize frequency dispersion, we use the one-sixth trick Claerbout (1985).

11/16/1997