Optimal stacking of noise cross-correlation functions

Cross-correlations of ambient seismic noise are widely used for seismic velocity imaging, monitoring and ground motion analyses. A typical step in analysing 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 package, StackMaster, which can be used for general purposes of time-series stacking.