Heterodyne distributed vibration sensing (hDVS) is one of the techniques for distributed acoustic sensing (DAS) to record seismic data using an optical fibre. The conventional hDVS data processing method suffers from nonlinear response of the hDVS system to strain measurement. To improve the hDVS data processing, we investigate the numerical application of Marchenko redatuming, which retrieves the Green’s response to a virtual source inside the unknown medium from single-sided reflection measurement. We build a forward model for the recorded hDVS signal. It is heterodyned down to the intermediate frequency from the optical frequency, where the laser pulse propagates physically inside the fibre and multiple scattering has strong impacts. We derive the Marchenko equations for the hDVS signal and find that the same causality argument holds. Without knowledge of the fibre medium, we iteratively retrieve the Green’s response to a desired virtual source inside the fibre from the hDVS signal recorded at one end of the fibre. The redatumed Green’s functions have the potential to clean up hDVS raw data, handle multiple scattering, and improve strain estimation.


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