Array Signal Processing on Distributed Acoustic Sensing Data: Directivity Effects in Slowness Space

• Published in: Journal of geophysical research. Solid earth Vol. 127; no. 2
• Main Authors: Näsholm, Sven Peter, Iranpour, Kamran, Wuestefeld, Andreas, Dando, Ben D. E., Baird, Alan F., Oye, Volker
• Format: Journal Article
• Language: English
• Published: 01.02.2022
• Subjects: array design; array signal processing; beamforming; distributed fiber‐optic acoustic sensing; steered response
• ISSN: 2169-9313; 2169-9356
• DOI: 10.1029/2021JB023587

Distributed Acoustic Sensing (DAS) involves the transmission of laser pulses along a fiber‐optic cable. These pulses are backscattered at fiber inhomogeneities and again detected by the same interrogator unit that emits the pulses. Elastic deformation along the fiber causes phase shifts in the backscattered laser pulses which are converted to spatially averaged strain measurements, typically at regular fiber intervals. DAS systems provide the potential to employ array processing algorithms. However, there are certain differences between DAS and conventional sensors. While seismic sensors typically record the directional particle displacement, velocity, or acceleration, the DAS axial strain is inherently proportional to the spatial gradient of the axial cable displacement. DAS is therefore insensitive to broadside displacement, for example, broadside P‐waves. In classical delay‐and‐sum beamforming, the array response function is the far‐field response on a horizontal slowness (or wavenumber) grid. However, for geometrically non‐linear DAS layouts, the angle between wavefront and cable varies, requiring the analysis of a steered response that varies with the direction of arrival. This contrasts with the traditional array response function which is given in terms of slowness difference between arrival and steering. This paper provides a framework for DAS steered response estimation accounting also for cable directivity and gauge‐length averaging – hereby demonstrating the applicability of DAS in array seismology and to assess DAS design aspects. It bridges a gap between DAS and array theory frameworks and communities, facilitating increased employment of DAS as a seismic array, while providing building blocks for the development of DAS array design tools. Plain Language Summary This study considers optical fiber sensors to probe seismic waves. Laser light is emitted into the cable. Processing the signals encoded in the light returning back to the transmitter, we can resolve the effect of seismic waves on the cable. However, the optical cable is insensitive to waves arriving from broadside to the cable and the sensitivity is reduced for waves not arriving along the cable axis. Hence, there is a directional sensitivity to consider in the signal processing and in assessing the wavefield probing capability. This sensitivity depends on the cable layout geometry. In classical array processing with conventional sensors, the directivity is typically equal for all sensors. Here, the array response – a function of the array sensor layout – can be utilized to estimate the array's capability to resolve the direction of arrival of seismic waves. We demonstrate how to take this cable directivity into account when assessing the distributed optical sensing system direction of arrival resolution. Our tools can be applied when assessing cable layouts. In this work, we bridge the gap between classical array signal processing and the emerging field of distributed acoustical sensing system signal processing, allowing well‐established processing tools to be applied. Key Points We model directional sensitivity and gauge length effects on distributed acoustic sensing systems using array signal processing theory We provide closed‐form expressions to estimate the steered response in slowness or wavenumber space for a given gauge length setting The frameworks can also be used to in some extent compensate for the directivity which varies along a geometrically non‐linear cable layout