Determination of borehole tiltmeter orientation using earth tides

Accurate orientation of geodetic instruments is fundamental for understanding deformation processes within the Earth's interior. Misalignment can lead to significant errors in data interpretation, affecting various geophysical applications. However, accurate alignment of standalone instruments like seismometers, strainmeters and tiltmeters remains a challenge in field geodesy. While numerous seismic-wave-based orientation methods have been successfully applied to seismometers, they are often inapplicable to tiltmeters due to their high-frequency filtering behavior and the requirement for a neighboring, pre-oriented instrument. In response to these challenges, we propose a novel orientation calibration method for borehole tiltmeters based on maximizing the correlation between recorded tilt data and theoretical tides by adjusting azimuthal angles. Our study encompasses two kinds of borehole tiltmeters and four datasets from three different field sites. Using solid and ocean tides modeling together with local topography and cavity disturbances, we obtain coefficient correlations ranging between 0.831 and 0.963, and 95% confidence intervals of azimuthal angles below 3.3 degrees. The correlation-based method demonstrates robustness across various tidal-signal extraction techniques, including different averaging window sizes and band-pass filters. Moreover, it yields azimuthal results in agreement with direct compass measurements for known orientations, while exhibiting a moderate sensitivity to factors such as ocean tides and site-specific topography for the studied cases. This method appears to be advantageous when direct measurements are either unavailable or challenging, and emerges as an accurate tool for determining borehole tiltmeter orientation. Its potential applicability may extend beyond tiltmeters to other instruments that can also record tidal phenomena, such as strainmeters and broadband seismometers. Additionally, its utility could be extended to environments like the seafloor, in order to refine the precision of azimuthal angle estimation and simplify methods for azimuthal angle determination.