Numerical modelling of the effect of the borehole environment on seismic amplitudes measured by fibre-optic distributed acoustic sensors

Recent studies use seismic strain amplitudes recorded by distributed fibre-optic acoustic sensors (DAS) to estimate elastic properties of the formation (the stiffer the formation, the smaller the strain). However, borehole DAS response can be affected by borehole environment. We model this effect numerically with 1.5D full wave reflectivity method implemented in OASES software (3D wave propagation in a 1D model). In these simulations, cement, casing and wellbore are represented by infinite vertical layers. For a P-wave with a dominant frequency of 40 Hz propagating parallel to a 10-cm-thick cement layer, the vertical strain amplitude in the cement (with or without a 1 cm thick steel casing) differs from the amplitude away from the well by no more than 5%. The (small) effect of the cement layer extends some 200 m into the formation. The vertical strain in a liquid-filled borehole (modelled by a 10 cm thick liquid layer) is comparable to that in the formation (but can be larger or smaller, depending on the source configuration). However, DAS is not measuring strain in the fluid; it measures strain in an optical fibre or cable immersed in the fluid. Modelling of an optical cable by a 1 cm-thick elastic layer shows that the strain amplitude in that layer is of the same order as (but lower than) both in the formation and in the fluid, and appears to scale with the Poisson's ratio of the `cable'. The strain in the cable is zero both when `cable' Poisson's ratio is zero, and when the borehole fluid is replaced with air. The results are consistent with recent laboratory and field studies, and confirm the feasibility of borehole DAS measurements with fibre-optic cables suspended in a borehole liquid (but not gas!) provided the cable has a relatively high Poisson's ratio.