Discussion

Figure presents the geometry of the problem throughout an example.

 

multi_incorrect_v_2 Figure 3 Ray-tracing with the incorrect velocity function V(z)=1.41+.47z km/s. Because the velocity is too slow, the rays end at too shallow of a depth.

It has been built considering the same events as in Figure but by using an incorrect velocity. Because the velocity is too low, the rays stop at too shallow of a depth, where they are not coplanar. The gap between the source and the receiver endpoints is the horizontal offset (zODCIG, z for constant z). The middle of the horizontal offset is the image point in the zODCIG domain. One can measure on Figure the azimuth of the source-receiver end points segment. We call it $\beta'$.$\beta'$ can be decomposed into two components: one, $\beta$, is the azimuth due to ray-bending, the other, $\xi$,accounts for the non-coplanarity due to the use of an incorrect migration velocity. If the migration velocity is too slow, the rays stop too early, yielding to an underestimated reflection azimuth. Conversely, if the migration velocity is too high, the rays stop too late, yielding to a overestimated reflection azimuth. When the velocity is exact, the rays are coplanar and the rotation of the reflection azimuth is only due to ray-bending and dips.