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Inversion of Multiconfiguration Complex EMI Data with Minimum Gradient Support Regularization: A Case Study

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Abstract

Frequency-domain electromagnetic instruments allow the collection of data in different configurations, that is, varying the intercoil spacing, the frequency, and the height above the ground. Their handy size makes these tools very practical for near-surface characterization in many fields of applications, for example, precision agriculture, pollution assessments, and shallow geological investigations. To this end, the inversion of either the real (in-phase) or the imaginary (quadrature) component of the signal has already been studied. Furthermore, in many situations, a regularization scheme retrieving smooth solutions is blindly applied, without taking into account the prior available knowledge. The present work discusses an algorithm for the inversion of the complex signal in its entirety, as well as a regularization method that promotes the sparsity of the reconstructed electrical conductivity distribution. This regularization strategy incorporates a minimum gradient support stabilizer into a truncated generalized singular value decomposition scheme. The results of the implementation of this sparsity-enhancing regularization at each step of a damped Gauss–Newton inversion algorithm (based on a nonlinear forward model) are compared with the solutions obtained via a standard smooth stabilizer. An approach for estimating the depth of investigation, that is, the maximum depth that can be investigated by a chosen instrument configuration in a particular experimental setting, is also discussed. The effectiveness and limitations of the whole inversion algorithm are demonstrated on synthetic and real data sets.

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Acknowledgements

The authors wish to thank the reviewers for their comments, which led to improvements in the presentation. This research was supported in part by the Fondazione di Sardegna 2017 research project “Algorithms for Approximation with Applications [Acube]”, the INdAM-GNCS research project “Metodi numerici per problemi mal posti”, the INdAM-GNCS research project “Discretizzazione di misure, approssimazione di operatori integrali ed applicazioni”, the Regione Autonoma della Sardegna research project “Algorithms and Models for Imaging Science [AMIS]” (RASSR57257, intervento finanziato con risorse FSC 2014-2020 - Patto per lo Sviluppo della Regione Sardegna), the Visiting Scientist Programme 2015/2016 (University of Cagliari), and an RAS/FBS Grant (Grant No. F71/17000190002).

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Authors and Affiliations

  1. Department of Civil and Environmental Engineering and Architecture, University of Cagliari, via Ospedale 72, 09124, Cagliari, Italy

    Gian Piero Deidda & Giulio Vignoli

  2. Department of Mathematics and Computer Science, University of Cagliari, via Ospedale 72, 09124, Cagliari, Italy

    Patricia Díaz de Alba & Giuseppe Rodriguez

  3. Groundwater and Quaternary Geology Mapping Department, Geological Survey of Denmark and Greenland (GEUS), C.F. Møllers Allé 8, 8000, Aarhus C, Denmark

    Giulio Vignoli

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  1. Gian Piero Deidda
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  2. Patricia Díaz de Alba
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  3. Giuseppe Rodriguez
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  4. Giulio Vignoli
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Correspondence to Patricia Díaz de Alba.

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Deidda, G.P., Díaz de Alba, P., Rodriguez, G. et al. Inversion of Multiconfiguration Complex EMI Data with Minimum Gradient Support Regularization: A Case Study. Math Geosci 52, 945–970 (2020). https://doi.org/10.1007/s11004-020-09855-4

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