Velocity picking

Conventional velocity analysis is done in two steps. The first step is to compute the semblances from CMP gathers. The second step is to pick a velocity model that maximizes the semblances. It is clear that if equation (1) is replaced by the Dix equation

$$\hat{t}^2 = t^2+{\hat{x}^2 \over v^2_{RMS}},$$ (14)

then the algorithm described earlier can be used for velocity analysis. The constraint required in this problem is a smooth RMS velocity function. Figure a shows a CMP gather from the Gulf of Mexico. The semblance computed from this gather is displayed in Figure b. I overlay the semblance with the picked velocity functions. The stars indicates the picks when unconstrained optimization is used. These picks form a rough and unrealistic velocity function. By using a weak smoothness constraint, I get a velocity function plotted with the dashed curve. Now the result becomes more acceptable. But still, the algorithm picks the peak around 2.3 second, that is known to be caused by a dipping bed. I further increase the smoothness constraint and obtain the final picks plotted with a solid curve in Figure b. This result is reasonably good.

 

halevel
Figure 7 Velocity picking: (a) a common midpoint gather; (b) semblance overlain with the results of velocity picking. The stars show the locations of the maximum of semblance for each time samples. The dashed curve shows the velocity picking with a weak constraint. The final result is shown by the solid curve.