Frequency-dependent directivity of distributed acoustic sensing in ocean acoustics

Distributed acoustic sensing (DAS) turns fiber-optic cables into distributed, passive sensors suited for continuous, spatially extended ocean monitoring. Specifically, an optoelectronic interrogator injects laser pulses into the fiber and measures the phase modulation of Rayleigh backscattered light, which is caused by external acoustic wavefields inducing elastic strain over a gauge length. A DAS sensor (channel) is commonly considered a point sensor for signal processing, i.e., introduces no spatial coherence to the measured signal. However, DAS sensors have a non-negligible spatial extent due to the transfer function between the measured optical signal and the external acoustic field. The transfer function between optical and acoustic quantities is factorized into four terms, describing the filtering effect of the acquisition gauge window and the spatial averaging window, and of the acoustic wavenumber and direction of arrival. The resulting sensitivity as a function of frequency and angular direction of individual DAS sensors is related to the sensor’s equivalent spatial aperture. The spatial shape of an individual DAS sensor is derived theoretically, and is quantified in common array signal processing terms, such as equivalent spatial aperture, directivity, and beampattern. The shape of the spatial aperture determines the spatial coherence of DAS measurements in a diffuse acoustic wavefield, as demonstrated on publicly available data. The corresponding spatial coherence predicts the statistical characteristics of the speckle pattern in DAS.