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

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 24 h 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