Discussion

The 3-D geometry implies that the rays can now have different azimuth and can propagate out of the vertical plane. If the migration velocity is correct, the two rays focus at the same point at zero subsurface offset (Figure ). By assuming the velocity is constant around the image point, all the elements (rays, normal, image points) are contained in one plane: the plane of the propagation. By an appropriate change of coordinates, this 3-D problem with correct migration velocity can be locally transformed in a 2-D problem, and the 2-D theory analyzed by Biondi and Symes (2003) be applied. The offset-to-angle transformation must be adapted though.

 

multi_correct_v_2 Figure 1 The velocity function is V(z)=1.5+.5z km/s. The target has a fixed position, azimuth ($\phi=45$) and dip ($\alpha=60$).