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

Abstract

We analyse random errors (variances) in cross-correlations of ambient seismic noise in the frequency domain, which differ from 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 variances with the variance of each complex spectrum value. Analysis of synthetic stationary ambient noise is used to estimate the confidence interval of stacked cross-spectrum obtained with different length of noise data corresponding to different number of evenly spaced windows of the same duration. 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. Based on synthetic ambient noise data, we also compare the probability distributions, causal part amplitude and SNR of stacked cross-spectrum function using one-bit normalization or pre-whitening with those obtained without these pre-processing steps. Natural continuous noise records contain both ambient noise and small earthquakes that are inseparable from the noise with the existing pre-processing steps. Using probability distributions of random cross-spectrum values based on the theoretical results providesmore » an effective way to exclude such small earthquakes, and additional data segments (outliers) contaminated by signals of different statistics (e.g. rain, cultural noise), from continuous noise waveforms. This technique is applied to constrain values and uncertainties of amplitude and phase velocity of stacked noise cross-spectrum at different frequencies, using data from southern California at both regional scale (~35 km) and dense linear array (~20 m) across the plate-boundary faults. A block bootstrap resampling method is used to account for temporal correlation of noise cross-spectrum at low frequencies (0.05–0.2 Hz) near the ocean microseismic peaks.« less

Authors:

Liu, Xin ^[1]; Ben-Zion, Yehuda ^[1]; Zigone, Dimitri ^[1]

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+ Show Author Affiliations

1. Univ. of Southern California, Los Angeles, CA (United States)

Publication Date:

Sun Sep 25 00:00:00 EDT 2016

Research Org.:

Univ. of Southern California, Los Angeles, CA (United States)

Sponsoring Org.:

USDOE Office of Science (SC)

OSTI Identifier:

1535644

Grant/Contract Number:  

SC0016520

Resource Type:

Accepted Manuscript

Journal Name:

Geophysical Journal International

Additional Journal Information:

Journal Volume: 207; Journal Issue: 3; Journal ID: ISSN 0956-540X

Publisher:

Oxford University Press

Country of Publication:

United States

Language:

English

Subject:

58 GEOSCIENCES; Geochemistry & Geophysics