Using path-integrated strain in Distributed Acoustic Sensing

Distributed Acoustic Sensing (DAS) is becoming 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 appear similar to particle motion (displacement, velocity, acceleration) waveforms, not all of 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 differs from conventional particle motion sensors, and DAS experiences an increased sensitivity to slow waves, often composed of highly scattered waves that are challenging to analyze. To address these issues, several strategies have been already proposed to convert strain rate measurements to particle velocity.

Based on a previously proposed mathematical formalism, we stress some fundamental differences between path-integrated strain and conventional displacement measurements. DAS inherently records arc length variation of the cable which is a relative motion measurement along a curvilinear path. We show that if the geometry of the DAS deployment is adapted to the wavefield of interest, path-integrated strain can be used to closely approximate the displacement wavefield without the need of additional instruments. We validate this theoretical result using collocated seismometers, discuss the limitations of this approach, and show two benefits: enhancing direct P-wave arrivals and simplifying the magnitude estimation of seismic events. While using path integrated strain is in some aspects more challenging, it achieves flat (hence lower) noise levels both in frequency and wavenumber. It also provides better sensitivity to high velocity phases, and permits the direct application of conventional seismological tools that are less effective when applied to the original strain data.