A bootstrap procedure for high-resolution velocity analysis

A method is given for further improving velocity estimates derived from high-resolution velocity analysis. In conventional velocity analysis, a set of tentative velocities is used to apply a normal moveout (NMO) correction to a set of spatio-temporal windows, the coherence measure is evaluated for each velocity and finally, the velocity estimate is retrieved from the peak of the coherence measure. Because analytical expressions for velocity uncertainties are difficult to derive, I propose an intensive statistical procedure, the bootstrap method, to assess the accuracy of the velocity estimate. In the bootstrap method, I create a data sample by randomly drawing seismic traces with replacement from a window of the common midpoint gather (CMP). Next, I calculate the velocity that maximizes the coherence measure for each bootstrap realization. The variation of this velocity provides a means to compute standard errors. I also use the bootstrap method to construct an average coherence measure and a kernel density estimator of the velocity that maximizes the coherence. The average coherence exhibits an important attenuation of spurious events while retaining enough resolution to model reflections properly with similar moveout curves. The latter is illustrated with synthetic and field data examples.