Assessment of resolution and accuracy of the Moving Window Cross Spectral technique for monitoring crustal temporal variations using ambient seismic noise

Temporal variations in the elastic behaviour of the Earth's crust can be monitored through the analysis of the Earth's seismic response and its evolution with time. This kind of analysis is particularly interesting when combined with the reconstruction of seismic Green's functions from the cross-correlation of ambient seismic noise, which circumvents the limitations imposed by a dependence on the occurrence of seismic events. In fact, because seismic noise is recorded continuously and does not depend on earthquake sources, these cross-correlation functions can be considered analogously to records from continuously repeating doublet sources placed at each station, and can be used to extract observations of variations in seismic velocities. These variations, however, are typically very small: of the order of 0.1 per cent. Such accuracy can be only achieved through the analysis of the full reconstructed waveforms, including later scattered arrivals. We focus on the method known as Moving-Window Cross-Spectral Analysis that has the advantage of operating in the frequency domain, where the bandwidth of coherent signal in the correlation function can be clearly defined. We investigate the sensitivity of this method by applying it to microseismic noise cross-correlations which have been perturbed by small synthetic velocity variations and which have been randomly contaminated. We propose threshold signal-to-noise ratios above which these perturbations can be reliably observed. Such values are a proxy for cross-correlation convergence, and so can be used as a guideline when determining the length of microseismic noise records that are required before they can be used for monitoring with the moving-window cross-spectral technique.