Definition of the 3-D problem

The 3-D construction in Figure generalizes the 2-D construction presented in Biondi and Symes (2003).

 

3D_coplan Figure 1 3-D geometry of coplanar source and receiver rays when using too slow a velocity. Due to the incorrect velocity, source and receiver rays do not end up meeting at the true image point I. They stop instead in S0 and R0. Iz is the image point of a Horizontal Offset Common Image Gather (at constant z). Ig is the image point in Angle Domain Common Image Gather.

If the migration velocity is not correct, the source and receiver rays may not be coplanar at the image point. We limit ourselves, though, to the case where the two rays are coplanar. An incorrect migration velocity introduces also a premature focusing of the energy if the velocity is too slow, or a late focusing if the velocity is too fast. Given this geometry, and considering only the constant z Horizontal Offset Common Image Gather, we examine how to transform an offset gather into an angle gather.