Effect of the number of velocities

The velocity-push transformation is affected by the number of velocities used. As stated earlier the computation cost does not depend on the number of velocity bins. This means that as the number of bins is increased, the number of data points contributing to each bin decreases and signal quality is reduced. On the other hand, too few bins reduces velocity resolution.

 

Figure 2: Semblance as a function of number of velocities. Same data as in Figure 1. Too few velocities reduce resolution. Too many reduce signal-to-noise. Resampling due to hardcopy plotting distorts these results somewhat.

The experiments displayed in Figure 2 bear this out. Bins increase by powers-of-two from less than the number of data offsets (48) to many more. The two smaller cases are under-resolved while the last one is low in signal.

Figure 3 graphs kurtosis as a function of number of velocity bins. Curiously there is a minima at near the visual optimum number of velocities viewed in Figure 2.