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Bootstrapping shear-wave splitting errors

New Mexico State University Department of Physics, Las Cruces, New Mexico 88003

Abstract

We have developed a bootstrap method to estimate errors associated with inverting SKS waveforms for shear-wave splitting parameters. Although presented for shear-wave splitting inversions, this method is suitable for any waveform inversion procedure. The bootstrap error estimation method consists of multiple inversions of simulated data that imitate the original data with differing noise sequences. The results of the bootstrap inversions are used to directly calculate variances and covariances for all model parameters. We employ a bootstrap error estimation technique to nonlinear inversion for shear-wave splitting parameters. Since seismic data have correlated errors, the bootstrap method was modified for stationary bandlimited time series. This modified bootstrap method was applied to shear-wave splitting measurements from over 60 pairs of horizontal seismograms. The method is stable under a large range of noise conditions. By using this bootstrap method, we can distinguish among data with no apparent splitting, data with splitting, and noisy data.

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