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Reconstruction of Three-Dimensional Aquifer Heterogeneity from Two-Dimensional Geophysical Data

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Abstract

Suitable training images (TIs) for multiple-point statistics (MPS) are difficult to identify in real-case three-dimensional applications, posing challenges for modelers trying to develop realistic subsurface models. This study demonstrates that two-dimensional geophysical images, when employed as training and conditioning data, can provide sufficient information for three-dimensional MPS simulations. The advantage of such a data-driven approach is that it does not rely on any external (possibly inappropriate) TI. The disadvantage is that three-dimensional MPS simulations must be carried out based on two-dimensional information. Three different approaches (two existing, one new) are tested to overcome this problem. The two existing approaches rely on three-dimensional reconstruction of incomplete datasets and on sequential two-dimensional simulations, respectively. The third approach is a newly proposed combination of the two former approaches. The three approaches are applied to model the three-dimensional facies structure of an alluvial aquifer based on high-resolution ground-penetrating radar cross-sections. The quality of each simulation outcome is evaluated based on the similarity of its multiple-point histogram (MPH) to reference MPHs derived from geophysical images. This evaluation reveals that the first approach (three-dimensional reconstruction) performs well close to conditioning data, but farther away from the data the simulation results deteriorate. Quite conversely, the second approach (sequential two-dimensional) performs well when only few conditioning data exist, but with increasing simulation sequence the quality decreases. The newly proposed third approach integrates the benefits of both approaches and is found to reproduce the reference MPHs significantly better than either of the two other approaches alone.

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Acknowledgements

This work was supported in part by the TERrestrial ENvironmental Observatories (TERENO) and in part by the Transregional Collaborative Research Centre 32 (TR32) Patterns in Soil–Vegetation–Atmosphere Systems: Monitoring, Modelling, and Data Assimilation. The authors wish to thank Philippe Renard, Julien Straubhaar, and Gregoire Mariethoz for fruitful discussions and for providing the MPS algorithms impala and direct sampling. We also wish to thank two anonymous reviewers for their valuable suggestions.

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Authors and Affiliations

  1. Agrosphere (IBG-3), Institute of Bio- and Geosciences, Forschungszentrum Jülich, Jülich, Germany

    Nils Gueting & Jan Vanderborght

  2. Geological Sciences, Stanford University, Stanford, CA, USA

    Jef Caers

  3. Dipartimento di Scienze della Terra, Universita degli Studi di Milano, Milan, Italy

    Alessandro Comunian

  4. Earth Sciences, Ruhr-University Bochum, Bochum, Germany

    Andreas Englert

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  1. Nils Gueting
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  2. Jef Caers
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  3. Alessandro Comunian
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  4. Jan Vanderborght
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  5. Andreas Englert
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Correspondence to Nils Gueting.

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Gueting, N., Caers, J., Comunian, A. et al. Reconstruction of Three-Dimensional Aquifer Heterogeneity from Two-Dimensional Geophysical Data. Math Geosci 50, 53–75 (2018). https://doi.org/10.1007/s11004-017-9694-x

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  • DOI: https://doi.org/10.1007/s11004-017-9694-x

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