In 2-D, two angles define the geometry of the problem:
the dip of the interface, , and the aperture
of the reflection, .In 3-D, the reflector is not only defined by its dip ,
but also by its azimuth .Further, in the full 3-D geometry, the rays are not necessarily
coplanar during downward-continuation.
As a consequence, the reflection may have a different azimuth
than the azimuth of the survey.
We call the reflection azimuth.
When the correct migration velocity is used, the two rays
focus correctly in one point. Near this image point the two rays
define defines one plane.
The most general configuration considers an incorrect migration
velocity.
Because the velocity is incorrect, the rays do not focus in one point.
Instead, they stop as two different points with the same depth when
using downward continuation. The distance between the two points is the
offset at constant *z*. The middle of the segment is the image point
in the offset domain domain at constant *z* (zODCIG).
In such configuration, the rays are not necessarily coplanar.
We introduce a new angle, ,accounting for the non-coplanarity of the rays.
To make the link with the 2-D case, we seek an apparent
propagation plane containing all the information about the actual
geometry.
In all cases, the image point in the angle domain moves along the
normal to the apparent interface by an amount dependent on the
migration velocity used, and on the aperture angle.
The image point in the angle domain is obtained by
transforming of the image point in the offset-domain.
We use the post-migration transformation in the Fourier domain
introduced in Sava and Fomel (2000) for the 2-D geometry, and
its 3-D extensions by Tisserant and Biondi (2003) for the
3-D full prestack migration.
Our approach in the next two sections is based on a ray construction.
Later, we will present in the third section another approach
based on plane-waves.

10/14/2003