Sensitivity of distributed acoustic sensing to waves in fluids

Distributed acoustic sensing (DAS) is a new, powerful modality of active and passive acoustic sensing of the ocean and atmosphere. The measurand in DAS is a time-resolved variation of phase of the Rayleigh-scattered coherent light propagating in an optical fiber. The optical phase is coupled to mechanical waves in the surrounding fluid through the strains and stresses in the fiber. Despite the exponential proliferation of DAS applications, physics-based understanding of the transfer function between the acoustic field and the DAS measurand is lacking. We partially fill this gap by considering scattering of acoustic waves by unclad and clad fiber suspended in fluid. The fiber is modeled as an infinite, solid circular cylinder, the properties of which may vary with distance from the cylinder axis. The theory is simplified by the fiber diameter being small compared to acoustic wavelength. DAS proves sensitive to acoustic pressure in the incident wave rather than radial or axial particle displacement. DAS sensitivity is found to differ drastically from the one previously predicted for fiber-optic hydrophones assuming uniform pressure field. The angular and frequency dependence of the DAS transfer function are strongly affected by resonance scattering of sound that is associated with an axially symmetric mode of free vibrations of infinite cylinder. Appropriate cladding can shift the resonance scattering from propagating to evanescent acoustic waves and increase the signal-to-noise ratio of DAS measurements. The DAS transfer function derived for acoustic pressure applies also to pressure variations due to gravity waves.