Removal of temperature drift from tiltmeter recordings

MEMS Tiltmeters are an effective tool in high-precision monitoring of ground and infrastructure but their sensitivity to temperature variations remains a challenge. This can be a prohibiting factor for their application in field monitoring of natural processes, despite the fact that tiltmeters are likely one of the very few technologies that can provide information on minute movements in real-time and at relatively low cost. Temperature drift, if not removed effectively, can completely mask small tilts or lead to wrong interpretations of the monitored process. Up until very recently, the tiltmeter response to temperature change was assumed to be instantaneous, but previous work by the authors has shown that there is a delay of varying duration between the two over time. We present a weighted least square (WLS) - based method that takes this dynamic change of time-lags into consideration. The time-series data is divided into a number of time-windows based on time-lag values, wherein windows with identical lags are grouped together. Time windows longer than a specified duration are subdivided based on an optimal window length. We describe a method for selecting the optimal window size applicable to different monitoring scenarios. Finally, an iteratively WLS is applied to produce values that best represent the temperature drift over time within each time window. To examine the impact of varying window sizes on results, a sensitivity analysis is performed using the Monte Carlo method, enabling the calculation of prediction intervals. Our approach provides a reliable framework for the removal of temperature drift from tiltmeter recordings, enabling the use of tiltmeters for the monitoring of subtle ground movements. This can be crucial for applications such as early warning systems for landslides and monitoring of the ground surface response to hydrological processes at depth.