Retrieval and precise phase-velocity estimation of Rayleigh waves by the spatial autocorrelation method between distributed acoustic sensing and seismometer data

In distributed acoustic sensing (DAS), optical fibre is used as sensors, which enables us to observe strain over tens of kilometres at intervals of several metres. S-wave velocity (Vs) structures of shallow sediments of high resolution have been obtained from surface wave dispersion curves by applying seismic interferometry to DAS data both onshore and offshore. However, it is known that there is a disadvantage to DAS seismic interferometry. In addition to Rayleigh waves, Love waves are also included. Consequently, the accuracy of the estimated phase velocities for Rayleigh waves is reduced due to the contamination of Love waves. To address this shortcoming, we suggest a spatial autocorrelation (SPAC) method between DAS and the vertical component of seismometer data. The SPAC method is equivalent to seismic interferometry and is useful for obtaining phase-velocity dispersion curves of surface waves from the cross-correlation functions (CCFs) between the records of two receivers. The CCFs obtained from a combination of DAS and vertical seismometer data should contain only Rayleigh waves because Love waves have no vertical component. CCFs between DAS and vertical seismometer data are therefore expected to give more accurate phase velocities of Rayleigh waves than CCFs with DAS data only. In this study, we first formulated analytical expressions of cross-spectra for DAS and three-component seismometer data because seismic observation is generally carried out using a three-component seismometer. A new SPAC method is presented in the form of analytical expressions. We showed that our formulation only includes Rayleigh and not Love waves in the cross-spectra with DAS and the vertical-component seismometer data. We applied our SPAC method to actual DAS and vertical seismometer data recorded on the seafloor. Then, we compared our new SPAC method for DAS and vertical seismometer data with a conventional SPAC method for only DAS data. The results reveal that our new SPAC method can estimate the phase velocities of Rayleigh waves more accurately than the conventional method. In addition, the analytical formulations of the cross-spectrum between DAS and three-component seismometer data, which we obtained in this study, are expected to be useful for the estimation of accurate 3-D structures in the future, although this is not available at the moment due to the lack of an applicable data set.