Optimal stacking of noise cross-correlation functions

Abstract

Summary Cross-correlations of ambient seismic noise are widely used for seismic velocity imaging, monitoring, and ground motion analyses. A typical 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, including arithmetic mean or linear stacking, robust stacking, selective stacking, cluster stacking, phase-weighted stacking, time-frequency phase-weighted stacking, Nth-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 images, convergence rate, temporal changes in the ballistic and coda waves, relative amplitude decays with distance, and computational time. We show that robust stacking is the best choice for all applications (velocity tomography, monitoring, and attenuation studies) using Raw NCFs. For applications using One-bit NCFs, all methods but phase-weighted and Nth-root stacking are good choices for seismic velocity tomography. Linear, robust, and selective stacking methods are all equally appropriate choices when using One-bit NCFs for monitoring applications. For applications relying on accurate relative amplitudes, the linear, robust, selective, and cluster stacking methods all perform well with 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 accompanying open-source software, which can be used for general purposes in time-series stacking.

The Seismic Signature of California's Earthquakes, Droughts, and Floods

“…We finally cross-correlate the East-North (EN), East-vertical (EZ), and North-vertical (NZ) components in the frequency domain before transforming them back to the time domain. We stack all cross-correlations within each day using a robust stack algo- rithm (Pavlis & Vernon, 2010;Yang et al, 2022). To increase convergence of the cross-correlation functions, we also linearly stack cross-correlations for the previous 90 days.…”

Monitoring Velocity Change Over 20 Years at Parkfield

“…The purpose of this threshold is to exclude the CFs that show a large discrepancy to the reference stack due to the perturbation of the noise sources so that the measurement of dv/v is assumed to be implausible. The comparison of the performance for the selective stacking to the other stacking methods can be found in Yang et al (2022). In our case, 70% of monthly stacks are not affected by the selective stack, that is, the linear stack is applied.…”

“…The comparison of the performance for the selective stacking to the other stacking methods can be found in Yang et al. (2022). In our case, 70% of monthly stacks are not affected by the selective stack, that is, the linear stack is applied.…”

Shear Velocity Evidence of Upper Crustal Magma Storage Beneath Valles Caldera

“…The data were down‐sampled to 10 Hz, bandpass filtered from 0.02 to 2 Hz, normalized in the time domain using a running absolute mean, and then whitened before cross‐correlation. Correlations were computed for 4‐hr half‐overlapping time windows throughout the continuous data (e.g., Seats et al., 2012) and then all correlations for each station pair were linearly stacked to preserve phase (Yang et al., 2023). We focus on the vertical‐vertical (ZZ) component cross‐correlations which show clear fundamental mode Rayleigh waves on the positive and negative lag portions of the symmetric cross‐correlations (Figure 1b).…”