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 tD, midpoint mD and surface offset hD, the migration impulse response can be expressed as follows:
Figure 1 Geometry used for evaluating the impulse response of integral migration, generalized to produce a prestack image function of the subsurface offset .
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.