A Data-based Error Analysis for Cross-Correlations of Ambient Seismic Noise in Frequency Domain

Abstract:

We analyze errors in cross-correlations of ambient seismic noise with a different approach than previous time domain methods. Extending theoretical results on ensemble averaged cross-spectrum (Liu & Ben-Zion, 2013), we estimate confidence interval for each frequency value using non-overlapping windows with fixed length. The extended theory also connects amplitude and phase errors with error of each spectrum value. Analysis of synthetic stationary ambient noise is used to estimate the confidence intervals for different length of noise data and different frequency content. This method allows estimating Signal-to-Noise Ratio (SNR) of noise cross-correlation in frequency domain, without specifying bandwidth, filter parameters or signal/noise windows that are needed for time domain SNR estimations. Synthetic tests are also used to compare the probability distributions and SNR of one-bit normalization or pre-whitening with those obtained by skipping these preprocessing steps. Natural continuous noise records contain both ambient noise and small earthquakes that are inseparable from noise with the existing preprocessing steps. Using probability distributions based on the theoretical results can exclude such small earthquakes (outliers) from continuous noise waveform. We apply this technique to constrain amplitude decay of noise cross-spectra and temporal variations of phase velocity derived from ambient noise cross-correlations, using data from southern California at both regional scale (~ 30 km) and dense linear arrays (~ 20 m) across the San Jacinto Fault Zone.