From strain to displacement: using deformation to enhance distributed acoustic sensing applications

Over a period of less than a decade, distributed acoustic sensing (DAS) has become a well-established technology in seismology. For historical and practical reasons, DAS manufacturers usually provide instruments that natively record strain (rate) as the principal measurement. While at first glance strain recordings seem related to ground motion waveforms (displacement, velocity and acceleration), not all the seismological tools developed over the past century (e.g. magnitude estimation, seismic beamforming, etc.) can be readily applied to strain data. Notably, the directional sensitivity of DAS is more limited than conventional particle motion sensors, and DAS experiences an increased sensitivity to slow waves, often highly scattered by the subsurface structure and challenging to analyse. To address these issues, several strategies have been already proposed to convert strain rate measurements to particle motion. In this study, we focus on strategies based on a quantity we refer to as 'deformation'. Deformation is defined as the change in length of the cable and is closely related to displacement, yet both quantities differ from one another: deformation is a relative displacement measurement along a curvilinear path. We show that if the geometry of the DAS deployment is made of sufficiently long rectilinear sections, deformation can be used to recover the displacement without the need of additional instruments. We validate this theoretical result using full-waveform simulations and by comparing, on a real data set, the seismic velocity recovered from DAS with that recorded by collocated seismometers. The limitations of this approach are discussed, and two applications are shown: enhancing direct P-wave arrivals and simplifying the magnitude estimation of seismic events. Converted displacement provides better sensitivity to high velocity phases, improves broadside response and permits the direct application of conventional seismological tools that are less effective when applied to strain (rate) data.