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Frequency domain analysis of errors in cross-correlations of ambient seismic noise

Xin Liu, Yehuda Ben-Zion, & Dimitri Zigone

Published February 15, 2016, SCEC Contribution #6233

We analyze errors in cross-correlations of ambient seismic noise in the frequency domain, different than previous time domain methods. Extending previous theoretical results on ensemble averaged cross-spectrum, we estimate confidence interval of stacked cross-spectrum of finite amount of data at each frequency using non-overlapping windows with fixed length. The extended theory also connects amplitude and phase errors with error of each complex spectrum value. Analysis of synthetic stationary ambient noise is used to estimate the confidence interval of stacked cross-spectrum for different length of noise data. This method allows estimating Signal/Noise Ratio (SNR) of noise cross-correlation in the frequency domain, without specifying filter bandwidth or signal/noise windows that are needed for time domain SNR estimations. Synthetic tests are also used to compare the probability distributions, causal part amplitude and SNR of one-bit normalization or pre-whitening with those obtained without these preprocessing steps. Natural continuous noise records contain both ambient noise and small earthquakes that are inseparable from the noise with the existing preprocessing steps. Using probability distributions based on the theoretical results can exclude such small earthquakes (outliers) from continuous noise waveform. This technique is applied to constrain amplitude decay of noise cross-spectra and phase velocity derived from ambient noise cross-correlations, using data from southern California at both regional scale (~ 35 km) and dense linear array (~ 20 m) across the plate-boundary faults. A bootstrap resampling method is used to account for temporal correlation of noise cross-spectrum at some frequencies (0.05-0.2 Hz) near the ocean microseismic peaks.

Liu, X., Ben-Zion, Y., & Zigone, D. (2016). Frequency domain analysis of errors in cross-correlations of ambient seismic noise. Geophys. J. Int., 207, 1630-1652.