Optimal Stacking of Noise Cross-Correlation Functions
• +3
• Xiaotao Yang,
• Jared Bryan,
• Kurama Okubo,
• Chengxin Jiang,
• Timothy Clements,
• Marine Denolle
Xiaotao Yang
Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, Department of Earth, Atmospheric, and Planetary Sciences, Purdue University, Department of Earth, Atmospheric, and Planetary Sciences, Purdue University

Corresponding Author:xtyang@purdue.edu

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Jared Bryan
Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology, Department of Earth, Atmospheric, and Planetary Sciences, Massachusetts Institute of Technology
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Kurama Okubo
Department of Earth and Planetary Sciences, Harvard University, Department of Earth and Planetary Sciences, Harvard University, Department of Earth and Planetary Sciences, Harvard University
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Chengxin Jiang
Department of Earth and Planetary Sciences, Harvard University, Department of Earth and Planetary Sciences, Harvard University, Department of Earth and Planetary Sciences, Harvard University
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Timothy Clements
Department of Earth and Planetary Sciences, Harvard University, Department of Earth and Planetary Sciences, Harvard University, Department of Earth and Planetary Sciences, Harvard University
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Marine Denolle
Department of Earth and Planetary Sciences, Harvard University, Department of Earth and Planetary Sciences, Harvard University, Department of Earth and Planetary Sciences, Harvard University
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Abstract

Cross-correlations of ambient seismic noise are widely used for seismic velocity imaging, monitoring, and ground motion analyses. A common step in analyzing Noise Cross-correlation Functions (NCFs) is stacking short-term NCFs over longer time periods to increase the signal quality. Spurious NCFs could contaminate the stack, degrade its quality, and limit its use. Many methods have been developed to improve the stacking of coherent waveforms, including earthquake waveforms, receiver functions, and NCFs. This study systematically evaluates and compares the performance of eight stacking methods: arithmetic mean or linear stacking, robust stacking, selective stacking, cluster stacking, phase-weighted stacking, time-frequency phase-weighted stacking, $N^{th}$-root stacking, and averaging after applying an adaptive covariance filter. Our results demonstrate that, in most cases, all methods can retrieve clear ballistic or first arrivals. However, they yield significant differences in preserving the phase and amplitude information. This study provides a practical guide for choosing the optimal stacking method for specific research applications in ambient noise seismology. We evaluate the performance using multiple onshore and offshore seismic arrays in the Pacific Northwest region. We compare these stacking methods for NCFs calculated from raw ambient noise (referred to as Raw NCFs) and from ambient noise normalized using a one-bit clipping time normalization method (referred to as One-bit NCFs). We evaluate six metrics, including signal-to-noise ratios, phase dispersion at individual station pairs, convergence rate, temporal changes in the ballistic and coda waves, relative amplitude decays with distance, and computational time. For seismic velocity tomography, we show that robust stacking is the best for imaging using Raw NCFs, that all methods but phase-weighted and $N^{th}$-root stacking perform equally well for One-bit NCFs. For monitoring applications, robust stacking is the best when using Raw NCFs while linear, robust, and selective stacking methods are all equally appropriate choices when using One-bit NCFs. For applications relying on accurate relative amplitudes, robust stacking should be used for Raw NCFs while both the robust and cluster stacking methods both perform well for One-bit NCFs. The evaluations in this study can be generalized to a broad range of time-series analysis that utilizes data coherence to perform ensemble stacking. Another contribution of this study is the accompanied open-source software, which can be used for general purposes.