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

Abstract

S U M M A R YStacks 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. Key words:Time series analysis; Interferometry; Body waves; Surface waves and free oscillations. I N T RO D U C T I O NGreen's functions can be extracted from seismic noise crosscorrelations as theoretically shown with different approaches by , Derode et al. (2003)

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“…3). PCC does not need the pre-processing and does not show the sensitivity to outlying amplitude events (SCHIMMEL et al 2011) as it can be seen from the waveforms and the small variability in the convergence diagram. Our CC and PCC results are similar when there are no outlying amplitude events in the data.…”

“…The instantaneous phases are obtained from the analytic signals of u 1 and u 2 . This approach is amplitude unbiased and does not need time-and frequency domain normalized data (SCHIMMEL et al 2011). In fact, these normalizations deteriorate the noise waveforms which lead to poorer results with PCC.…”

“…In addition, we use the PCC (Eq. 2) by SCHIMMEL (1999) which has been introduced to noise studies in SCHIMMEL et al (2011).…”

“…The main processing steps are common and consisted in (1) pre-processing, (2) cross-correlation and (3) cross-correlogram stacking (e.g., BENSEN et al 2007;SCHIMMEL et al 2011). In order to improve the convergence of the noise correlation function, this processing is performed in a selected frequency band (ROUX et al 2005).…”

“…PCC is based on the instantaneous phase coherence concept used in the phase weighted stacks (SCHIMMEL and PAULSSEN 1997). The PCC is amplitude unbiased and has been introduced to noise correlation studies in SCHIMMEL et al (2011). They demonstrated that PCC due to its phase sensitivity is more efficient when there are large amplitude variations which could hide waveform similarities when using the classical cross-correlation.…”