Automation of shear-wave splitting measurements using cluster analysis

The propagation of two orthogonally polarized shear waves, or shear-wave splitting, is arguably the most robust indication of seismic anisotropy in the Earth. This splitting can be parameterized in terms of the polarization of the fast shear-wave phi and the lag time between fast and slow components deltat. These two parameters provide constraints on the mechanism causing the anisotropy. All methods of calculating splitting require a shear-wave analysis window to be selected. Then the phi and deltat that best account for the splitting in that window are calculated. Conventionally the shear-wave analysis window is picked manually. However, manual window selection is laborious and also very subjective; in many cases different windows give very different results. We present a method for automating the selection of the window. First, the splitting analysis is performed for a range of window lengths. Then a cluster analysis is applied in order to find those measurements that are stable over many different windows. Once clusters of stable results have been found, the final choice of shear-wave analysis window corresponds to the measurement with the lowest error in the cluster with the lowest variance. Resulting estimates of phi and deltat are objective, and very large datasets can be analyzed easily. The success of the technique is illustrated with application to a microseismic dataset of 324 events, which confirms previously published results using manually selected analysis windows.