Tidal calibration of plate boundary observatory borehole strainmeters

[1] The Plate Boundary Observatory, the geodetic component of the EarthScope program, includes 74 borehole strainmeters installed in the western United States and on Vancouver Island, Canada. In this study, we calibrate 45 of the instruments by comparing the observed M2 and O1 Earth tides with those predicted using Earth tide models. For each strainmeter, we invert for a coupling matrix that relates the gauge measurements to the regional strain field assuming only that the measured strains are linear combinations of the regional areal and shear strains. We compare these matrices to those found when constraints are imposed which require the coupling coefficients to lie within expected ranges for this strainmeter design. Similar unconstrained and constrained coupling matrices suggest the instrument is functioning as expected as no other coupling matrix can be found that better reduces the misfit between observed and predicted tides when the inversion is unconstrained. Differences imply a coupling matrix with coefficients outside typical ranges gives a better fit between the observed and predicted tides. We find that 22 of the strainmeters examined have coupling matrices for which there is little difference between the constrained and unconstrained inversions. If we allow a greater divergence in the shear coupling coefficients and consider the possibility that one gauge may not function as expected, the discrepancies between the unconstrained and constrained coupling matrices are resolved for a subset of the remaining strainmeters. Our results also indicate that most of the strainmeters are less sensitive to areal strain than expected from theory.