A graph approach for fast dense array inter-station phase delay interpretation

Abstract

SUMMARY We present a phase-delay detection procedure adapted for seismic arrays composed of a large number of stations. We use graph formalism to introduce a direct method to compute station phase delays starting from inter-station phase differences deduced from noise cross-correlation functions. We focus this study on surface wave main arrival as phase-difference evaluation at each station requires high coherence level. Then, we perform numerical experiments with synthetic data computed as a realistic and dense network of 79 stations in a 400 by $400\, \mathrm{km^2}$ square box. For one of the 79 stations, we simulate a phase difference of 15 per cent of the signal period. Further, we evaluate the accuracy and precision of phase-delay estimation at each station with regard to the quality of the cross-correlation functions (i.e. the signal-to-noise ratio). When the inter-station coherence levels are larger than 0.6 (i.e. a high-quality signal), we show good agreement between the phase-delay estimation and its expected value of 15 per cent of the signal period. We introduce a coherence-weighted estimate of phase delay and show that applying this weighting allows us to be less vulnerable to phase-delay underestimation for intermediate-quality signals. Then, the method is applied to experimental data recorded by a high density nodal array with 923 vertical geophones with 19 d of continuous records, centred on the 600 by $600\, \mathrm{m^2}$ damage zone of the Clark branch of the San Jacinto Fault Zone, Southern California (USA). We verify that the San Jacinto network is well synchronized, as most of the estimated phase delays are less than 2 per cent of the central period of the signal, and they are associated with high levels of inter-station coherence. More surprisingly, the spatial features of the estimated phase delays show deterministic geographical patterns that are related to topography and that exhibit similarities with phase velocity maps at $4.5\, \mathrm{Hz}$ from previous 3-D velocity inversions. This suggests that the topographic effect may be accounted for to estimate accurate phase delays. Also, we note that the temporal variability of the estimated phase delays in the case of the San Jacinto data set are related to atmospheric forcing. Our direct method for estimating phase delays is applicable to structure-oriented monitoring studies, and it opens perspectives in the monitoring of seismic velocity variations.