Analytical expression for cross-spectrum of ambient-noise surface waves in distributed acoustic sensing with multiple or winding cables

SUMMARY In recent years, distributed acoustic sensing (DAS) has enabled the observation of strain over tens of kilometres at metre-level intervals by using optical fibre as a sensor. This study presents an analytical solution for the cross-spectrum of ambient noise with DAS data acquired from arbitrarily shaped and/or multiple fibre-optic cables, with the aim of estimating subsurface S-wave velocity structures using the spatial autocorrelation (SPAC) method. Our formulation accounts for both isotropic and anisotropic wave incidence. The analytical cross-spectrum depends on the angles between the horizontal direction connecting the two measurement points and the axial strain directions at the two points. This study demonstrates that both Rayleigh and Love waves contribute to the cross-spectrum, and that their contributions vary in a complex manner depending on the cable geometry, seismic velocity structure, interstation distance between observation points and source amplitudes. By using this analytical solution, an integrated analysis combining the SPAC method and the ambient noise tomography method is applicable to DAS data acquired from arbitrarily shaped and/or multiple cables. In addition, the analytical expression considering anisotropic wave incidence will be useful for correcting traveltime anomalies caused by source heterogeneity. The application of our formulation to DAS data from winding or multiple cables will facilitate high-resolution and precise imaging of the 3-D structure.