Model-Based Correction of Temperature-Dependent Measurement Errors in Frequency Domain Electromagnetic Induction (FDEMI) Systems

Abstract

Data measured using electromagnetic induction (EMI) systems are known to be susceptible to measurement influences associated with time-varying external ambient factors. Temperature variation is one of the most prominent factors causing drift in EMI data, leading to non-reproducible measurement results. Typical approaches to mitigate drift effects in EMI instruments rely on a temperature drift calibration, where the instrument is heated up to specific temperatures in a controlled environment and the observed drift is determined to derive a static thermal apparent electrical conductivity (ECa) drift correction. In this study, a novel correction method is presented that models the dynamic characteristics of drift using a low-pass filter (LPF) and uses it for correction. The method is developed and tested using a customized EMI device with an intercoil spacing of 1.2 m, optimized for low drift and equipped with ten temperature sensors that simultaneously measure the internal ambient temperature across the device. The device is used to perform outdoor calibration measurements over a period of 16 days for a wide range of temperatures. The measured temperature-dependent ECa drift of the system without corrections is approximately 2.27 mSm−1K−1, with a standard deviation (std) of only 30 μSm−1K−1 for a temperature variation of around 30 K. The use of the novel correction method reduces the overall root mean square error (RMSE) for all datasets from 15.7 mSm−1 to a value of only 0.48 mSm−1. In comparison, a method using a purely static characterization of drift could only reduce the error to an RMSE of 1.97 mSm−1. The results show that modeling the dynamic thermal characteristics of the drift helps to improve the accuracy by a factor of four compared to a purely static characterization. It is concluded that the modeling of the dynamic thermal characteristics of EMI systems is relevant for improved drift correction.

Low-Pass Filters for a Temperature Drift Correction Method for Electromagnetic Induction Systems

“…It is based on the system developed by Mester et al [25] and described by Tan X. [23] as well as Tazifor et al [24]. The system was developed for studying modular and scalable system concepts and for investigating interference effects, e.g., system drifts.…”

“…For each measurement, the device was raised 0.7 m above the ground using wooden supports, and data was acquired in the VCP configuration to further minimize soil effects. Tazifor et al [24] demonstrated that for a measurement at a height of 0.7 m and an inter-coil spacing of 1.2 m, the expected ECa change due to soil temperature changes is about 0.07 mSm −1 K −1 (worst-case). This is low compared with expected system drifts larger than 1 mSm −1 K. For effective temperature drift analysis, only temperature data with a range of at least 10 K were considered (15 out of 21 datasets).…”

“…The drift model is based on the infinite impulse response (IIR) filter function described in detail by Tazifor et al [24]. The inputs for the drift model are pre-selected measured temperatures T ms , which are transformed into a delayed response T mod using the time constant parameter τ and the T mod of the previous time step:…”

“…An NL value different from 1 will result in a non-linear temperature-phase relationship. By using LuT and cubic spline interpolation, the modelled temperatures T mod1 and T mod2 for the two LPFs are converted into the modeled phases Φ mod1 and Φ mod2 respectively, as already described by Tazifor et al [24]. The corrected phase Φ c was then calculated from Φ mod1 and Φ mod2 as…”

“…To eliminate the effects of drifts due to fast, uniform temperature variations, Tazifor et al [24] proposed a dynamic approach that uses information from temperature sensors and a thermal drift model based on a low-pass filter to model and correct delayed drift effects of hardware components. They concluded that such a dynamic thermal characterization of the drift effects improved the overall accuracy compared with pure static characterization, which is solely based on using a simple look-up table for drift correction.…”