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
Count for a CMP gather is shown in Figure . We can see that the line t=x/vmin 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/vvmin 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/vmax is not covered by any hyperbola, so that this part of the gather cannot be restored. It contributes to the singularity of the operator .