A Robust Borehole Optical Fiber Areal Strainmeter: Design, Calibration, and a Four-Year Comparison with a Gladwin Tensor Strainmeter

Borehole strainmeters can measure deformation too small for GNSS and too slow for seismometers, but their precision transducers are complex, and this has limited them to specialized applications as either isolated instruments or sparse arrays. We developed a passive borehole areal strainmeter built with simple machining, no moving parts, and no downhole electronics to address these limitations. The sensing element is 265 m of optical fiber wound on a compliant aluminum mandrel, read as one arm of a Michelson interferometer. The Areal Optical Fiber Strainmeter (AOFS) was grouted in limestone at 28 m depth in the North Avant Field, Oklahoma, 15 m from a Gladwin Tensor Strainmeter (GTSM), and the two instruments were recorded side by side for 1579 days. Both records were calibrated against the theoretical areal strain tide with a generalized least-squares estimator that fits areal and shear couplings and a barometric admittance. The AOFS calibration is 0.2958±0.0007 nε per radian of optical phase, stationary to 0.6% over four years, with a shear leakage of 5% of the areal sensitivity. The tidally calibrated instruments agree to 1% at M2 and 2% at O1; their amplitude spectra coincide at the tidal lines and across the microseism band, where their cross spectrum has unit gain and zero phase; and with the barometric pressure removed, the GTSM spectrum lies 1.3 to 3 times above the AOFS between 1 × 10−6 and 1 × 10−2 Hz. Above 1 Hz, the AOFS noise floor is 3 to 10 times lower than the GTSM digitizer floor, and the AOFS records a local M2.4 earthquake with 14 times lower background noise than the GTSM. The AOFS is 2.5 to 2.8 times less sensitive to barometric pressure, and its record of a 23-day water injection into a reservoir 500 m below is essentially identical to that of the GTSM. The new instrument matches the GTSM at the tides, in the microseism band, and in the injection test and has a lower noise floor above 1 Hz; it is simple to build and robust to operate, which enables a new generation of applications for borehole strainmeters.