Claerbout (1987) introduces count(x,s,t) for velocity analysis as a count of times that a point located on the mesh at (x,t) will be added into slowness s. For the purposes of this section count(t,x) is introduced as a count of times that a point located on the mesh at (x,t) will be added into velocity stack, so that we can write
(19) |
(20) |
d(t,x)=1 | (21) |
Count for a CMP gather is shown in Figure . We can see that the line t=x/v_{min} is the line of the maximum count. Count on each trace is equal to the sum of NMO counts of this trace for each velocity involved in velocity analysis (Appendix B and C). This is apparent from Figure c.
Velocity analysis was done for fifty velocities. From Figure c we can see that in most of the gather below the line t=x/v_{vmin} count does not differ much from 50. This implies that count(x,s,t) does not differ much from 1 in this part of the gather. This result corresponds to NMO, where the same result holds tru truee.
The area above the line t=x/v_{max} is not covered by any hyperbola, so that this part of the gather cannot be restored. It contributes to the singularity of the operator .