Figure 1 illustrates the generalization of the
migration operator from a Kirchhoff viewpoint. Simple geometric
relations allow us to derive the kinematics of the generalized
migration operator. If we migrate an impulse recorded at time
*t*_{D}, midpoint *m*_{D} and surface offset *h*_{D}, the migration
impulse response can be expressed as follows:

(1) | ||

(2) | ||

(3) |

(4) |

imp-resp
Geometry used for evaluating the impulse response of
integral migration, generalized to produce a prestack image
function of the subsurface offset .Figure 1 |

The expression for the generalized impulse response of prestack anisotropic migration leads to the analytical evaluation of the offset dip () and midpoint dip () along the planes tangent to the impulse response. When we adopt the Kirchhoff viewpoint, the group aperture angles can then be related to the offset dips in the image, and the group dip angles can be similarly related to the midpoint dips in the image.

4/6/2006