Offset-to-angle transformation.

The apparent propagation plane plays another interesting role during the offset-to-angle transformation: despite the non-coplanarity of the rays, the energy moves only in the apparent propagation plane. Figure illustrates this property. Two offset-domain image points are displayed. points in the offset domain to the image point in the angle domain along a direction orthogonal to the direction of the offset. All the possible directions define a plane. The two orthogonal planes are displayed on Figure . The intersection of the two planes with the normal gives the position of the image point in the angle domain. More specifically, the energy moves at the intersection between the orthogonal plane and the apparent propagation plane. To sum up, when an incorrect migration velocity is used, the rays are not coplanar. There is however a preferential plane, the apparent propagation plane, which allows one to cast the 3-D problem into a 2-D one.

 

gamma_planes_2 Figure 6 Geometric construction of the image point in the angle domain from the image points in the offset domain.

 

gamma_planes Figure 7 Geometric construction of the image point in the angle domain from the source and receiver rays end points.