## Estimating amplitude uncertainty for normalized ambient seismic noise cross-correlation with examples from southern California

Xin Liu, Gregory C. Beroza, & Yehuda Ben-ZionSubmitted August 8, 2016, SCEC Contribution #6561, 2016 SCEC Annual Meeting Poster #188

We estimate the frequency-dependent amplitude error of ambient noise cross-correlations based on the method of Liu et al. (2016) for different normalizations. We compute the stacked cross spectrum of noise recorded at station pairs in southern California by averaging the cross spectrum of evenly spaced windows of the same length, but offset in time. Windows with signals (e.g. earthquakes) contaminating the ambient seismic noise are removed as statistical outliers. Standard errors of the real and imaginary parts of the stacked cross-spectrum are estimated assuming each window is independent. The autocorrelation of the sequence of cross-spectrum values at a given frequency obtained from different windows are used to test the independence of cross-spectrum values in neighboring time windows. For frequencies below 0.2 Hz, we find temporal correlation in the noise data. We account for temporal correlation in computation of errors using a block bootstrap resampling method. The stacked cross-spectrum and associated amplitude are computed under different normalization methods including deconvolution and whitening applied before or after ensemble average of cross-spectrum values. We estimate the amplitude errors based on error propagation from errors of stacked cross-spectrum and verified by bootstrap method. We propose to use this characterization of amplitude uncertainty to constrain uncertainties in ground motion predictions based on ambient-field observations.

**Citation**

Liu, X., Beroza, G. C., & Ben-Zion, Y. (2016, 08). Estimating amplitude uncertainty for normalized ambient seismic noise cross-correlation with examples from southern California. Poster Presentation at 2016 SCEC Annual Meeting.

**Related Projects & Working Groups**

Seismology