Improved characterisation and modelling of measurement errors in electrical resistivity tomography (ERT) surveys

• Published in: Journal of applied geophysics Vol. 146; pp. 103 - 119
• Main Authors: Tso, Chak-Hau Michael, Kuras, Oliver, Wilkinson, Paul B., Uhlemann, Sebastian, Chambers, Jonathan E., Meldrum, Philip I., Graham, James, Sherlock, Emma F., Binley, Andrew
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.11.2017
• Subjects: ERT; Inversion; Linear mixed effects; Measurement errors; Resistivity; Uncertainty; Linear mixed effects; Measurement errors; Inversion; Uncertainty; ERT; Resistivity
• ISSN: 0926-9851; 1879-1859
• DOI: 10.1016/j.jappgeo.2017.09.009

Measurement errors can play a pivotal role in geophysical inversion. Most inverse models require users to prescribe or assume a statistical model of data errors before inversion. Wrongly prescribed errors can lead to over- or under-fitting of data; however, the derivation of models of data errors is often neglected. With the heightening interest in uncertainty estimation within hydrogeophysics, better characterisation and treatment of measurement errors is needed to provide improved image appraisal. Here we focus on the role of measurement errors in electrical resistivity tomography (ERT). We have analysed two time-lapse ERT datasets: one contains 96 sets of direct and reciprocal data collected from a surface ERT line within a 24h timeframe; the other is a two-year-long cross-borehole survey at a UK nuclear site with 246 sets of over 50,000 measurements. Our study includes the characterisation of the spatial and temporal behaviour of measurement errors using autocorrelation and correlation coefficient analysis. We find that, in addition to well-known proportionality effects, ERT measurements can also be sensitive to the combination of electrodes used, i.e. errors may not be uncorrelated as often assumed. Based on these findings, we develop a new error model that allows grouping based on electrode number in addition to fitting a linear model to transfer resistance. The new model explains the observed measurement errors better and shows superior inversion results and uncertainty estimates in synthetic examples. It is robust, because it groups errors together based on the electrodes used to make the measurements. The new model can be readily applied to the diagonal data weighting matrix widely used in common inversion methods, as well as to the data covariance matrix in a Bayesian inversion framework. We demonstrate its application using extensive ERT monitoring datasets from the two aforementioned sites. Probability density functions (PDF) of different ERT errors for 24h of surface ERT data collected at a wetland site in the UK. The mean repeatability errors generally increase with the period of time considered. Reciprocal errors generally agree with short-term repeatability errors. The PDF of stacking errors shows much lower mean and variance. Using stacking errors as a measure of measurement errors may lead to overfitting of data during inversion and underestimation of uncertainty. [Display omitted] •Stacking, reciprocal and repeatability errors are compared using statistical analysis.•Having common electrodes increases correlation between measurements.•A new error model based on grouping the electrodes used is developed.•The new model yields better inversion results and uncertainty estimates.