Constructive optimization of electrode locations for target-focused resistivity monitoring

Wagner, F.; Günther, Thomas; Schmidt‐Hattenberger, Cornelia; Maurer, Hansruedi

doi:10.1190/geo2014-0214.1

Cited by 27 publications

(16 citation statements)

References 36 publications

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“…Therefore, it is crucial to select a small set of measurements from all possible measurement configurations which can still optimally resolve the underground structure. Successively augmenting a base set of measurements (Wilkinson et al 2006;Stummer et al 2004;Loke et al 2014;Wagner et al 2015;Uhlemann et al 2018), we can employ the iterative update formulae in Eqs. (50) to (52) to quickly compute the model resolution and covariance matrices of the augmented data set.…”

Section: Survey Designmentioning

confidence: 99%

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Ren

Kalscheuer

2019

Surv Geophys

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A meaningful solution to an inversion problem should be composed of the preferred inversion model and its uncertainty and resolution estimates. The model uncertainty estimate describes an equivalent model domain in which each model generates responses which fit the observed data to within a threshold value. The model resolution matrix measures to what extent the unknown true solution maps into the preferred solution. However, most current geophysical electromagnetic (also gravity, magnetic and seismic) inversion studies only offer the preferred inversion model and ignore model uncertainty and resolution estimates, which makes the reliability of the preferred inversion model questionable. This may be caused by the fact that the computation and analysis of an inversion model depend on multiple factors, such as the misfit or objective function, the accuracy of the forward solvers, data coverage and noise, values of trade-off parameters, the initial model, the reference model and the model constraints. Depending on the particular method selected, large computational costs ensue. In this review, we first try to cover linearised model analysis tools such as the sensitivity matrix, the model resolution matrix and the model covariance matrix also providing a partially nonlinear description of the equivalent model domain based on pseudo-hyperellipsoids. Linearised model analysis tools can offer quantitative measures. In particular, the model resolution and covariance matrices measure how far the preferred inversion model is from the true model and how uncertainty in the measurements maps into model uncertainty. We also cover nonlinear model analysis tools including changes to the preferred inversion model (nonlinear sensitivity tests), modifications of the data set (using bootstrap re-sampling and generalised cross-validation), modifications of data uncertainty, variations of model constraints (including changes to the trade-off parameter, reference model and matrix regularisation operator), the edgehog method, mostsquares inversion and global searching algorithms. These nonlinear model analysis tools try to explore larger parts of the model domain than linearised model analysis and, hence, may assemble a more comprehensive equivalent model domain. Then, to overcome the bottleneck of computational cost in model analysis, we present several practical algorithms to accelerate the computation. Here, we emphasise linearised model analysis, as efficient computation of nonlinear model uncertainty and resolution estimates is mainly determined by fast forward and inversion solvers. In the last part of our review, we present applications of model analysis to models computed from individual and joint inversions of electromagnetic data; we also describe optimal survey design and inversion grid design as important Extended author information available on the last page of the article applications of model analysis. The currently available model uncertainty and resolution analyses are mainly for 1D and 2D problems due to the limitation...

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Section: Survey Designmentioning

confidence: 99%

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Ren

Kalscheuer

2019

Surv Geophys

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“…While this has been achieved already for studies involving two-electrode capacitance measurements (e.g., Cseresnyés et al 2016) and four-electrode SIP/EIS measurements (e.g., Postic and Doussan 2016), it is challenging for tomographic, broadband four-electrode impedance measurements given the data acquisition and processing demands. Spatial resolution of computed sEIT images might be increased by optimizing electrode locations in relation to the known or expected position of root systems, or specific regions of interest (e.g., Wagner et al 2015), as well as by employing optimized measurement configurations (e.g., Stummer et al 2004;Wilkinson et al 2006;al Hagrey and Petersen 2011).…”

Section: Methodological Considerations For Future Experimental Studiesmentioning

confidence: 99%

Imaging and functional characterization of crop root systems using spectroscopic electrical impedance measurements

Weigand

Kemna

2018

Plant Soil

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Background and aims Non-or minimally invasive methods are urgently needed to characterize and monitor crop root systems to foster progress in phenotyping and general system understanding. Electrical methods have come into focus due to their unique sensitivity to various structural and functional root characteristics. The aim of this study is to highlight imaging capabilities of these methods with regard to crop root systems and to investigate changes in electrical signals caused by physiological reactions. Methods Spectral electrical impedance tomography (sEIT) and electrical impedance spectroscopy (EIS) were used in three laboratory experiments to characterize oilseed root systems embedded in nutrient solution. Two experiments imaged the root extension with sEIT, including one experiment monitoring a nutrient stress situation. In the third experiment Responsible Editor: W Richard Whalley. Electronic supplementary materialThe online version of this article (https://doi.electrical signatures were observed over the diurnal cycle using EIS.Results Root system extension was imaged using sEIT under static conditions. During continuous nutrient deprivation, electrical polarization signals decreased steadily. Systematic changes were observed over the diurnal cycle, indicating further sensitivity to associated physiological processes. Spectral parameters suggest polarization processes at the μm scale. Conclusions Electrical imaging methods are able to non-invasively characterize crop root systems in controlled laboratory conditions, thereby offering links to root structure and function. The methods have the potential to be upscaled to the field scale.

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“…Yaramanci (2007, 2008) introduce a resolution analysis based on singular value decomposition that allows for calculating resolution-optimized data sets. Further approaches for efficient data sets have been recently presented for ERT measurement by Wagner et al (2015), who optimize electrode positions based on resolution analysis -a scheme that could possibly be adapted for Torus-NMR. Once the target aquifer is identified by a borehole or a conventional surface NMR with high resolution, an optimized q-distribution for the Torus-NMR measurements can be determined that focuses the further investigation on a specific depth range.…”

Section: Discussionmentioning

confidence: 99%

Torus-nuclear magnetic resonance: Quasicontinuous airborne magnetic resonance profiling by using a helium-filled balloon

et al. 2016

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The application of surface nuclear magnetic resonance (NMR) measurements, although proven to be valuable for various hydrogeological issues, is in practice often limited to single 1D surveys because measurement progress is slow. First, large stacking rates are necessary to overcome the low signal-to-noise ratio and, second, time and effort are required to move the equipment and to place the measurement loops in the field. We have evaluated a novel approach to cope with the latter. We have assessed and tested a data acquisition scheme based on a torus-shaped helium-filled balloon carrying the loop and moving it rapidly from one to the next measurement position along the profile lines. We have referred to this system as Torus-NMR. We have showed the feasibility of the system to deliver reliable results using common processing and inversion. Surface NMR field data are acquired at successively overlapping positions along a test profile using the Torus-NMR system. To take advantage of the faster loop setup, the overall measurement time of the single NMR soundings is reduced by reducing the number of stacks, whereas the number of soundings is increased to obtain highly overlapping coverage. Regarding a single measurement position, a significant loss of vertical resolution must be accepted that can, however, be compensated to some extent by inverting the complete profile data set simultaneously using a laterally constrained inversion. We have found that for simple subsurface models, e.g., a layered earth with up to three layers, the proposed scheme provided reasonable results, which were demonstrated using synthetic and real field data. We do not expect the Torus-NMR concept to replace 2D data acquisition schemes if high spatial resolution is required. However, we expect fields of application that aim at rapid lateral overview of how specific hydrogeological parameters of shallow aquifers are distributed over large catchment-scale areas.

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Constructive optimization of electrode locations for target-focused resistivity monitoring

Cited by 27 publications

References 36 publications

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Uncertainty and Resolution Analysis of 2D and 3D Inversion Models Computed from Geophysical Electromagnetic Data

Imaging and functional characterization of crop root systems using spectroscopic electrical impedance measurements

Torus-nuclear magnetic resonance: Quasicontinuous airborne magnetic resonance profiling by using a helium-filled balloon

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