Using instantaneous phase coherence for signal extraction from ambient noise data at a local to a global scale

Stacks of ambient noise cross-correlations are more and more routinely used to extract empirical Green's functions between station pairs. The success of the cross-correlations is due to waves which are recorded by both stations and that constructively sum at lag times which equal their propagation time between the station pair. Stacking cross-correlograms corresponding to different time spans improves the azimuthal noise coverage and further enhances the signals. Here we show how the instantaneous phase coherence can be used for a more efficient signal extraction from ambient noise cross-correlations. The instantaneous phase coherence is obtained by analytic signal processing and can be employed through the phase cross-correlation and/or through the time-frequency domain phase-weighted stack. The phase cross-correlation is more sensitive to waveform similarity but less sensitive to strong amplitude features than the conventional cross-correlation. The time-frequency domain phase-weighted stack cleans the ambient noise cross-correlograms by attenuating incoherent noise and permits an improved signal identification. We show that both approaches are powerful tools in the recovery of signals from ambient noise data and show examples where they improve the extraction of P and Rayleigh waves by considering local and global scale applications.