Abstract
Applications of time-lapse inversion of electrical resistivity tomography allow monitoring variations in the subsurface that play a key role in a variety of contexts. The inversion of time-lapse data provides successive images of the subsurface properties showing the medium evolution. Image quality is highly dependent on the data weighting determined from the data error estimates. However, the quantification of errors in the inversion of time-lapse data has not yet been addressed. We have developed a methodology for the quantification of time-lapse data error based on the analysis of the discrepancy between normal and reciprocal readings acquired at different times. We applied the method to field monitoring data sets collected during the injection of heated water in a shallow aquifer. We tested different error models to indicate that the use of an appropriate time-lapse data error estimate yielded significant improvements in terms of imaging. An adapted inversion weighting for time-lapse data implies that the procedure does not allow an over-fitting of the data, so the presence of artifacts in the resulting images is greatly reduced. Our results determined that a proper estimate of time-lapse data error is mandatory for weighting optimally the inversion to obtain images that best reflect the evolution of medium properties over time.
Highlights
Time-lapse electrical resistivity tomography (ERT) has become a widely used method to characterize hydrogeologic processes
We performed a detailed analysis of time-lapse ERT measurements using reciprocal readings
We proposed a methodology for the error model estimation to describe the data error present in the data differences between the baseline and time-lapse measurements
Summary
Time-lapse electrical resistivity tomography (ERT) has become a widely used method to characterize hydrogeologic processes. The method has been used to study water and snowmelt infiltration in soil and in the vadose zone (e.g., Daily et al, 1992; LaBrecque et al, 2002; French and Binley, 2004; Oberdörster et al, 2010; Slater et al, 2010; Travelletti et al, 2012), groundwater flow (e.g., Coscia et al, 2011; Doetsch et al, 2012), solute transport (e.g., Kemna et al, 2002; Koestel et al, 2008; Ogilvy et al, 2009; Robert et al, 2012; Rucker 2014), changes in the thermal state of permafrostaffected rocks (e.g., Krautblatter et al, 2010), heat conduction and transport (e.g., Hermans et al, 2015), and many others It is well-known that ERT suffers from loss of resolution with increasing distance to the electrodes (e.g., Nguyen et al, 2009; Perri et al, 2012), which can be analyzed using sensitivity and uncertainty analyses (see, e.g., Hermans et al, 2012b; Robert et al, 2012). Such regularization constrains the inversion to a Manuscript received by the Editor 11 January 2017; revised manuscript received 18 May 2017; published ahead of production 13 July 2017; published online 26 August 2017; corrected version published online 10 October 2017
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