Articles | Volume 25, issue 5
https://doi.org/10.5194/hess-25-2759-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/hess-25-2759-2021
© Author(s) 2021. This work is distributed under
the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Research article
| 
25 May 2021
Research article |
| 25 May 2021
| 25 May 2021
3D multiple-point geostatistical simulation of joint subsurface redox and geological architectures
Groundwater and Quaternary Geology Mapping, Geological Survey of Denmark and Greenland, Aarhus, 8000, Denmark
Hyojin Kim
Groundwater and Quaternary Geology Mapping, Geological Survey of Denmark and Greenland, Aarhus, 8000, Denmark
Anders Juhl Kallesøe
Groundwater and Quaternary Geology Mapping, Geological Survey of Denmark and Greenland, Aarhus, 8000, Denmark
Peter B. E. Sandersen
Groundwater and Quaternary Geology Mapping, Geological Survey of Denmark and Greenland, Aarhus, 8000, Denmark
Troels Norvin Vilhelmsen
Department of Geoscience, Aarhus University, Aarhus, 8000, Denmark
Thomas Mejer Hansen
Department of Geoscience, Aarhus University, Aarhus, 8000, Denmark
Anders Vest Christiansen
Department of Geoscience, Aarhus University, Aarhus, 8000, Denmark
Ingelise Møller
Groundwater and Quaternary Geology Mapping, Geological Survey of Denmark and Greenland, Aarhus, 8000, Denmark
Birgitte Hansen
Groundwater and Quaternary Geology Mapping, Geological Survey of Denmark and Greenland, Aarhus, 8000, Denmark
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Cited articles
Abbaspour, K. C., Yang, J., Maximov, I., Siber, R., Bogner, K., Mieleitner, J., Zobrist, J., and Srinivasan, R.: Modelling hydrology and water quality in the pre-alpine/alpine Thur watershed using SWAT, J. Hydrol., 333, 413–430, https://doi.org/10.1016/j.jhydrol.2006.09.014, 2007.
Alcalde, J., Bond, C. E., Johnson, G., Butler, R. W. H., Cooper, M. A., and Ellis, J. F.: The importance of structural model availability on seismic interpretation, J. Struct. Geol., 97, 161–171, https://doi.org/10.1016/j.jsg.2017.03.003, 2017.
Auken, E., Christiansen, A. V., Westergaard, J. H., Kirkegaard, C., Foged, N., and Viezzoli, A.: An integrated processing scheme for high-resolution airborne electromagnetic surveys, the SkyTEM system, Explor. Geophys., 40, 184–192, https://doi.org/10.1071/EG08128, 2009.
Auken, E., Christiansen, A. V., Kirkegaard, C., Fiandaca, G., Schamper, C., Behroozmand, A. A., Binley, A., Nielsen, E., Effersø, F., Christensen, N. B., Sørensen, K. I., Foged, N., and Vignoli, G.: An overview of a highly versatile forward and stable inverse algorithm for airborne, ground-based and borehole electromagnetic and electric data, Explor. Geophys., 46, 223–235, https://doi.org/10.1071/EG13097, 2015.
Auken, E., Foged, N., Larsen, J. J., Lassen, K. V. T., Maurya, P. K., Dath, S. M., and Eiskjær, T. T.: tTEM – A towed transient electromagnetic system for detailed 3D imaging of the top 70 m of the subsurface, Geophysics, 84, E13–E22, https://doi.org/10.1190/geo2018-0355.1, 2019.
Barfod, A. S., Møller, I., and Christiansen, A. V.: Compiling a national resistivity atlas of Denmark based on airborne and ground-based transient electromagnetic data, J. Appl. Geophys., 134, 199–209, https://doi.org/10.1016/j.jappgeo.2016.09.017, 2016.
Barfod, A. A. S., Vilhelmsen, T. N., Jørgensen, F., Christiansen, A. V., Høyer, A.-S., Straubhaar, J., and Møller, I.: Contributions to uncertainty related to hydrostratigraphic modeling using multiple-point statistics, Hydrol. Earth Syst. Sci., 22, 5485–5508, https://doi.org/10.5194/hess-22-5485-2018, 2018.
Baveye, P. C., Otten, W., Kravchenko, A., Balseiro-Romero, M., Beckers, É., Chalhoub, M., Darnault, C., Eickhorst, T., Garnier, P., Hapca, S., Kiranyaz, S., Monga, O., Mueller, C. W., Nunan, N., Pot, V., Schlüter, S., Schmidt, H., and Vogel, H. J.: Emergent properties of microbial activity in heterogeneous soil microenvironments: Different research approaches are slowly converging, yet major challenges remain, Front. Microbiol., 9, 1–48, https://doi.org/10.3389/fmicb.2018.01929, 2018.
Blicher-Mathiesen, G., Holm, H., Houlborg, T., Rolighed, J., Andersen, H. E.,
Carstensen, M. V., Jensen, P. G., Wienke, J., Hansen, B., and Thorling, L.:
Landovervågningsoplande 2018, NOVANA, Aarhus Universitet, DCE – Nationalt
Center for Miljø og Energi, Videnskabelig rapport nr. 352, 241 pp., 2019 (in Danish).
Bond, C. E.: Uncertainty in structural interpretation: Lessons to be learnt, J. Struct. Geol., 74, 185–200, https://doi.org/10.1016/j.jsg.2015.03.003, 2015.
Buried Valleys: available at: https://buriedvalleys.dk/, last access: 25 May 2020.
Chilès, J.-P. and Delfiner, P.: Geostatistics, 2nd edn., John Wiley and Sons, Inc., Hoboken, NJ, USA, 2012.
Christiansen, A. V., Foged, N., and Auken, E.: A concept for calculating accumulated clay thickness from borehole lithological logs and resistivity models for nitrate vulnerability assessment, J. Appl. Geophys., 108, 69–77, https://doi.org/10.1016/j.jappgeo.2014.06.010, 2014.
Claerbout, J. F. and Abma, R.: Earth soundings analysis: Processing versus inversion. Vol. 6. London: Blackwell Scientific Publications, 1992.
Close, M. E., Abraham, P., Humphries, B., Lilburne, L., Cuthill, T., and Wilson, S. R.: Predicting groundwater redox status on a regional scale using linear discriminant analysis, J. Contam. Hydrol., 191, 19–32, https://doi.org/10.1016/j.jconhyd.2016.04.006, 2016.
Curtis, A.: The science of subjectivity, Geology, 40, 95–96, https://doi.org/10.1130/focus012012.1, 2012.
Dalgaard, T., Hansen, B., Hasler, B., Hertel, O., Hutchings, N. J., Jacobsen, B. H., Stoumann Jensen, L., Kronvang, B., Olesen, J. E., Schjørring, J. K., Sillebak Kristensen, I., Graversgaard, M., Termansen, M., and Vejre, H.: Policies for agricultural nitrogen management – trends, challenges and prospects for improved efficiency in Denmark, Environ. Res. Lett., 9, 115002, https://doi.org/10.1088/1748-9326/9/11/115002, 2014.
Danielsen, J. E., Auken, E., Jørgensen, F., Søndergaard, V. H., and Sørensen, K. I.: The application of the transient electromagnetic method in hydrogeophysical surveys, J. Appl. Geophys., 53, 181–198, https://doi.org/10.1016/j.jappgeo.2003.08.004, 2003.
de Vries, L. M., Carrera, J., Falivene, O., Gratacós, O., and Slooten, L. J.: Application of multiple point geostatistics to non-stationary images, Math. Geosci., 41, 29–42, https://doi.org/10.1007/s11004-008-9188-y, 2009.
Ephesia consult: DeeSse software, available at: https://www.ephesia-consult.com/portfolio/deesse/, last access: 18 May 2021.
Ernstsen, V. and von Platen, F.: GEUS Rapport 2014/20: Opdatering af det
nationale redoxkort fra 2006, GEUS, report, Copenhagen, Denmark, 2014.
Ernstsen, V., von Platen, F., and Jakobsen, P. R.: GEUS Rapport 2008/30: Nitratreduktionsklasser for kystnære arealer (“hvide områder”) – data og metode, Supplement til GEUS rapport 2006/93, GEUS, Copenhagen, Denmark,
2008.
European Commission: Report from the Commission to the Council and the
European Parliament on the implementation of Council Directive 91/676/EEC
concerning the protection of waters against pollution caused by nitrates from
agricultural sources based on Member State reports fo,
available at:
https://eur-lex.europa.eu/legal-content/EN/TXT/PDF/?uri=CELEX:52018DC0257&from=en (last access: 15 May 2021),
2018.
Foged, N., Marker, P. A., Christansen, A. V., Bauer-Gottwein, P., Jørgensen, F., Høyer, A.-S., and Auken, E.: Large-scale 3-D modeling by integration of resistivity models and borehole data through inversion, Hydrol. Earth Syst. Sci., 18, 4349–4362, https://doi.org/10.5194/hess-18-4349-2014, 2014.
GERDA, GEUS: National geophysical database, available at: https://eng.geus.dk/products-services-facilities/data-and-maps/national-geophysical-database-gerda, last access: 18 May 2021.
Goovaerts, P., AvRuskin, G., Meliker, J., Slotnick, M., Jacquez, G., and Nriagu, J.: Geostatistical modeling of the spatial variability of arsenic in groundwater of southeast Michigan, Water Resour. Res., 41, 1–19, https://doi.org/10.1029/2004WR003705, 2005.
Gravesen, P. and Fredericia, J.: ZEUS-geodatabase system, Borearkivet,
Databeskrivelse, kodesystem og sideregistre, 1984 (in Danish).
Gravey, M. and Mariethoz, G.: QuickSampling v1.0: a robust and
simplified pixel-based multiple-point simulation approach, Geosci. Model Dev.,
13, 2611–2630, https://doi.org/10.5194/gmd-13-2611-2020, 2020.
Grenthe, I., Stumm, W., Laaksuharju, M., Nilsson, A. C., and Wikberg, P.: Redox potentials and redox reactions in deep groundwater systems, Chem. Geol., 98, 131–150, https://doi.org/10.1016/0009-2541(92)90095-M, 1992.
Groffman, P. M., Butterbach-Bahl, K., Fulweiler, R. W., Gold, A. J., Morse, J. L., Stander, E. K., Tague, C., Tonitto, C., and Vidon, P.: Challenges to incorporating spatially and temporally explicit phenomena (hotspots and hot moments) in denitrification models, Biogeochemistry, 93, 49–77, https://doi.org/10.1007/s10533-008-9277-5, 2009.
Guardiano, F. B. and Srivastava, R. M.: Multivariate Geostatistics: Beyond Bivariate Moments, in: Geostatistics Tróia '92. Quantitative Geology and Geostatistics, edited by: Soares, A., Springer, Dordrecht, 133–144, 1993.
Gulbrandsen, M. L., Cordua, K. S., Bach, T., and Hansen, T. M.: Smart Interpretation – automatic geological interpretations based on supervised statistical models, Comput. Geosci., 21, 427–440, https://doi.org/10.1007/s10596-017-9621-8, 2017.
Gunnink, J. L. and Siemon, B.: Applying airborne electromagnetics in 3D stochastic geohydrological modelling for determining groundwater protection, Near Surf. Geophys., 13, 45–60, https://doi.org/10.3997/1873-0604.2014044, 2015.
Hansen, A. L., Christensen, B. S. B., Ernstsen, V., He, X., and Refsgaard, J. C.: A concept for estimating depth of the redox interface for catchment-scale nitrate modelling in a till area in Denmark, Hydrogeol. J., 22, 1639–1655, https://doi.org/10.1007/s10040-014-1152-y, 2014.
Hansen, B., Sonnenborg, T. O., Møller, I., Bernth, J., Høyer, A.-S., Rasmussen, P., Sandersen, P. B. E., and Jørgensen, F.: Nitrate vulnerability assessment of aquifers, Environ. Earth Sci., 75, 999, https://doi.org/10.1007/s12665-016-5767-2, 2016.
Hansen, B., Thorling, L., Schullehner, J., Termansen, M., and Dalgaard, T.: Groundwater nitrate response to sustainable nitrogen management, Sci. Rep.-UK, 7, 8566, 1–12, https://doi.org/10.1038/s41598-017-07147-2, 2017.
Hansen, B., Thorling, L., Kim, H., and Blicher-Mathiesen, G.: Long-term nitrate response in shallow groundwater to agricultural N regulations in Denmark, J. Environ. Manage., 240, 66–74, https://doi.org/10.1016/j.jenvman.2019.03.075, 2019.
Hansen, B., Voutchkova, D. D., Sandersen, P. B. E., Kallesøe, A., Thorling, L., Møller, I., Madsen, R. B., Jakobsen, R., Aamand, J., Maurya, P., and Kim, H.: Assessment of complex subsurface redox structures for sustainable development of agriculture and the environment, Environ. Res. Lett., 16, 025007, https://doi.org/10.1088/1748-9326/abda6d, 2021.
Hansen, M. and Pjetursson, B.: Free, online Danish shallow geological data, Geol. Surv. Den. Greenl., 23, 53–56, https://doi.org/10.34194/geusb.v23.4842, 2011.
Hansen, T. M.: Entropy and Information Content of Geostatistical Models, Math. Geosci., 53, 163–184, https://doi.org/10.1007/s11004-020-09876-z, 2021.
Hansen, T. M., Cordua, K. S., Jacobsen, B. H., and Mosegaard, K.: Accounting for imperfect forward modeling in geophysical inverse problems – Exemplified for crosshole tomography, Geophysics, 79, H1–H21, https://doi.org/10.1190/GEO2013-0215.1, 2014.
Hansen, T. M., Vu, L. T., and Bach, T.: MPSLIB: A C
Hansen, T. M., Vu, L. T., Mosegaard, K., and Cordua, K. S.: Multiple point statistical simulation using uncertain (soft) conditional data, Comput. Geosci., 114, 1–10, https://doi.org/10.1016/j.cageo.2018.01.017, 2018.
He, X., Koch, J., Sonnenborg, T. O., Jørgensen, F., Schamper, C., and Christian Refsgaard, J.: Transition probability-based stochastic geological modeling using airborne geophysical data and borehole data, Water Resour. Res., 50, 3147–3169, https://doi.org/10.1002/2013WR014593, 2014.
He, X., Højberg, A. L., Jørgensen, F., and Refsgaard, J. C.: Assessing hydrological model predictive uncertainty using stochastically generated geological models, Hydrol. Process., 29, 4293–4311, https://doi.org/10.1002/hyp.10488, 2015.
He, X. L., Sonnenborg, T. O., Jørgensen, F., and Jensen, K. H.: The effect of training image and secondary data integration with multiple-point geostatistics in groundwater modelling, Hydrol. Earth Syst. Sci., 18, 2943–2954, https://doi.org/10.5194/hess-18-2943-2014, 2014.
Hoffimann, J., Scheidt, C., Barfod, A. S., and Caers, J.: Stochastic simulation by image quilting of process-based geological models, Comput. Geosci., 106, 18–32, https://doi.org/10.1016/j.cageo.2017.05.012, 2017.
Høyer, A.-S., Jørgensen, F., Sandersen, P. B. E., Viezzoli, A., and Møller, I.: 3D geological modelling of a complex buried-valley network delineated from borehole and AEM data, J. Appl. Geophys., 122, 94–102, https://doi.org/10.1016/j.jappgeo.2015.09.004, 2015.
Høyer, A.-S., Vignoli, G., Hansen, T. M., Vu, L. T., Keefer, D. A., and Jørgensen, F.: Multiple-point statistical simulation for hydrogeological models: 3-D training image development and conditioning strategies, Hydrol. Earth Syst. Sci., 21, 6069–6089, https://doi.org/10.5194/hess-21-6069-2017, 2017.
GEUS: GEUS Maps of Denmark, available at:
https://eng.geus.dk/products-services-facilities/data-and-maps/maps-of-denmark/,
last access: 25 May 2020.
Jakobsen, P. R. and Tougaard, L.: Danmarks digitale jordartskort 1:25 000
Version 5.0, GEUS, Copenhagen, Denmark,
2020 (in Danish).
Jessell, M. W., Aillères, L., and de Kemp, E. A.: Towards an integrated inversion of geoscientific data: What price of geology?, Tectonophysics, 490, 294–306, https://doi.org/10.1016/j.tecto.2010.05.020, 2010.
Jørgensen, F. and Sandersen, P. B. E.: Buried and open tunnel valleys in Denmark-erosion beneath multiple ice sheets, Quaternary. Sci. Rev., 25, 1339–1363, https://doi.org/10.1016/j.quascirev.2005.11.006, 2006.
Jørgensen, F., Møller, R. R., Nebel, L., Jensen, N. P., Christiansen, A. V., and Sandersen, P. B. E.: A method for cognitive 3D geological voxel modelling of AEM data, B. Eng. Geol. Environ., 72, 421–432, https://doi.org/10.1007/s10064-013-0487-2, 2013.
Jørgensen, F., Høyer, A.-S., Sandersen, P. B. E., He, X., and Foged, N.: Combining 3D geological modelling techniques to address variations in geology, data type and density – An example from Southern Denmark, Comput. Geosci., 81, 53–63, https://doi.org/10.1016/j.cageo.2015.04.010, 2015.
Journel, A. and Zhang, T.: The necessity of a multiple-point prior model, Math. Geol., 38, 591–610, https://doi.org/10.1007/s11004-006-9031-2, 2006.
Journel, A. G. and Huijbregts, C. J.: Mining Geostatistics, 1st edn., Academic Press, Inc., London, 1978.
Juda, P., Renard, P., and Straubhaar, J.: A Framework for the Cross-Validation of Categorical Geostatistical Simulations, Earth Space Sci., 7, 1–17, https://doi.org/10.1029/2020EA001152, 2020.
Jupiter, GEUS: National geophysical database, available at: https://eng.geus.dk/products-services-facilities/data-and-maps/national-well-database-jupiter, last access: 18 May 2021.
Kallis, G. and Butler, D.: The EU water framework directive: Measures and implications, Water Policy, 3, 125–142, https://doi.org/10.1016/S1366-7017(01)00007-1, 2001.
Keaton, J. R. and Degraff, J. V.: Surface observation and geologic mapping,
Spec. Rep. – Natl. Res. Counc. Transp. Res. Board, 247 (January 1996), National academy Press, Washington D.C., USA, 178–230, 1996.
Keefer, D. A.: A Framework and Methods for Characterizing Uncertainty in
Geologic Maps, edited by: Thorleifson, L. H.,
Berg, R. C., and Russel, H., Three
Dimens. Geol. Mapp. Groundw. Appl. Minnesota Geol. Surv. Open File Rep., Minnesota Geological Survey, Minnesota, USA,
07–4, 2007.
Kim, H., Høyer, A.-S., Jakobsen, R., Thorling, L., Aamand, J., Maurya, P. K., Christiansen, A. V., and Hansen, B.: 3D characterization of the subsurface redox architecture in complex geological settings, Sci. Total Environ., 693, https://doi.org/10.1016/j.scitotenv.2019.133583, 2019.
Koch, J., Stisen, S., Refsgaard, J. C., Ernstsen, V., Jakobsen, P. R., and Højberg, A. L.: Modeling Depth of the Redox Interface at High Resolution at National Scale Using Random Forest and Residual Gaussian Simulation, Water Resour. Res., 55, 1451–1469, https://doi.org/10.1029/2018WR023939, 2019.
Lee, J., Jang, C., Wang, S., Liang, C., and Liu, C.: Delineation of spatial redox zones using discriminant analysis and geochemical modelling in arsenic-affected alluvial aquifers, Hydrol. Process., 22, 3029–3041, https://doi.org/10.1002/hyp.6884, 2008.
Lin, Y. P.: Simulating Spatial Distributions, Variability and Uncertainty of Soil Arsenic by Geostatistical Simulations in Geographic Information Systems, Open Environ. Sci., 2, 26–33, https://doi.org/10.2174/1876325100802010026, 2008.
Lindsay, M. D., Aillères, L., Jessell, M. W., de Kemp, E. A., and Betts, P. G.: Locating and quantifying geological uncertainty in three-dimensional models: Analysis of the Gippsland Basin, southeastern Australia, Tectonophysics, 546–547, 10–27, https://doi.org/10.1016/j.tecto.2012.04.007, 2012.
Loke, M. H., Chambers, J. E., Rucker, D. F., Kuras, O., and Wilkinson, P. B.: Recent developments in the direct-current geoelectrical imaging method, J. Appl. Geophys., 95, 135–156, https://doi.org/10.1016/j.jappgeo.2013.02.017, 2013.
Madsen, R. B: Replication Data for: Running MPS simulations of geology and redox in LOOP3 catchment area, Denmark, GEUS Dataverse, V1, https://doi.org/10.22008/FK2/XBQURH, 2021.
Madsen, R. B. and Hansen, T. M.: Estimation and accounting for the modeling error in probabilistic linearized AVO inversion, Geophysics, 83, N15–N30, https://doi.org/10.1190/geo2017-0404.1, 2018.
Madsen, R. B., Nørmark, E., and Hansen, T. M.: Accounting for Processing
Errors in AVO/AVA Data, in: 80th EAGE Conference and Exhibition Proceedings,
EAGE, 11-14 June, Copenhagen, Denmark, 5, 2018.
Madsen, R. B., Møller, I., and Hansen, T. M.: Choosing between Gaussian and MPS simulation: the role of data information content – a case study using uncertain interpretation data points, Stoch. Env. Res. Risk A., 2, https://doi.org/10.1007/s00477-020-01954-2, 2021.
Malinverno, A. and Briggs, V. A.: Expanded uncertainty quantification in inverse problems: Hierarchical Bayes and empirical Bayes, Geophysics, 69, 1005–1016, https://doi.org/10.1190/1.1778243, 2004.
Maps of Denmark, GEUS: Maps of Denmark, available at: https://eng.geus.dk/products-services-facilities/data-and-maps/maps-of-denmark/pricelist, last access: 18 May 2021).
Mariethoz, G. and Caers, J.: Multiple-point geostatistics: Stochastic modeling
with training images, 1st edn., John Wiley and Sons, Chichester, UK, 2015.
Mariethoz, G., Renard, P., and Straubhaar, J.: The direct sampling method to perform multiple-point geostatistical simulations, Water Resour. Res., 46, 1–14, https://doi.org/10.1029/2008WR007621, 2010.
Mariethoz, G., Straubhaar, J., Renard, P., Chugunova, T., and Biver, P.: Constraining distance-based multipoint simulations to proportions and trends, Environ. Model. Softw., 72, 184–197, https://doi.org/10.1016/j.envsoft.2015.07.007, 2015.
Møller, I., Søndergaard, V. H., and Jørgensen, F.: Geophysical methods and data administration in Danish groundwater mapping, Geol. Surv. Den. Greenl., 17, 41–44, https://doi.org/10.34194/geusb.v17.5010, 2009.
Nolan, B. T., Fienen, M. N., and Lorenz, D. L.: A statistical learning framework for groundwater nitrate models of the Central Valley, California, USA, J. Hydrol., 531, 902–911, https://doi.org/10.1016/j.jhydrol.2015.10.025, 2015.
Pyrcz, M. J., Boisvert, J. B., and Deutsch, C. V.: A library of training images for fluvial and deepwater reservoirs and associated code, Comput. Geosci., 34, 542–560, https://doi.org/10.1016/j.cageo.2007.05.015, 2008.
Randle, C. H., Bond, C. E., Lark, R. M., and Monaghan, A. A.: Uncertainty in geological interpretations: Effectiveness of expert elicitations, Geosphere, 15, 108–118, https://doi.org/10.1130/GES01586.1, 2019.
Ransom, K. M., Nolan, B. T., A. Traum, J., Faunt, C. C., Bell, A. M., Gronberg, J. A. M., Wheeler, D. C., Z. Rosecrans, C., Jurgens, B., Schwarz, G. E., Belitz, K., M. Eberts, S., Kourakos, G., and Harter, T.: A hybrid machine learning model to predict and visualize nitrate concentration throughout the Central Valley aquifer, California, USA, Sci. Total Environ., 601–602, 1160–1172, https://doi.org/10.1016/j.scitotenv.2017.05.192, 2017.
Rosecrans, C. Z., Nolan, B. T., and Gronberg, J. A. M.: Prediction and visualization of redox conditions in the groundwater of Central Valley, California, J. Hydrol., 546, 341–356, https://doi.org/10.1016/j.jhydrol.2017.01.014, 2017.
Sandersen, P. B. E.: Uncertainty assessment of geological models – A
qualitative approach, in: Calibration and Reliability in Groundwater
Modelling: Credibility of Modelling, edited by: Refsgaard, J. C., Kovar, K.,
Haarder, E., and Nygaard, E., IAHS Redbook ModelCARE 2007, Copenhagen, Denmark, 345–349,
2008.
Sandersen, P. B. E. and Jørgensen, F.: Kortlægning af begravede dale i
Danmark [Mapping of Buried Valleys in Denmark], Opdatering 2015 (Update 2015),
Vol. 1 and 2, GEUS Special Publication, Copenhagen, Denmark,
2016 (in Danish).
Sandersen, P. B. E., and Jørgensen, F.: Buried tunnel valleys in Denmark and their impact on the geological architecture of the subsurface, Geol. Surv. Den. Greenl., 38, 13–16, https://doi.org/10.34194/geusb.v38.4388, 2017.
Sandersen, P. B. E., Jørgensen, F., Larsen, N. K., Westergaard, J. H., and Auken, E.: Rapid tunnel-valley formation beneath the receding Late Weichselian ice sheet in Vendsyssel, Denmark, Boreas, 38, 834–851, https://doi.org/10.1111/j.1502-3885.2009.00105.x, 2009.
Schaaf, A. and Bond, C. E.: Quantification of uncertainty in 3-D seismic interpretation: implications for deterministic and stochastic geomodeling and machine learning, Solid Earth, 10, 1049–1061, https://doi.org/10.5194/se-10-1049-2019, 2019.
Schamper, C., Jørgensen, F., Auken, E., and Effersø, F.: Assessment of near-surface mapping capabilities by airborne transient electromagnetic data – An extensive comparison to conventional borehole data, Geophysics, 79, B187–B199, https://doi.org/10.1190/geo2013-0256.1, 2014.
Schullehner, J. and Hansen, B.: Nitrate exposure from drinking water in Denmark over the last 35 years, Environ. Res. Lett., 9, 095001, https://doi.org/10.1088/1748-9326/9/9/095001, 2014.
Schullehner, J., Hansen, B., Thygesen, M., Pedersen, C. B., and Sigsgaard, T.: Nitrate in drinking water and colorectal cancer risk: A nationwide population-based cohort study, Int. J. Cancer, 143, 73–79, https://doi.org/10.1002/ijc.31306, 2018.
SDFE: The Danish Map Supply, available at: https://kortforsyningen.dk/indhold/english, last access: 18 May 2021.
Sexstone, A. J., Revsbech, N. P., Parkin, T. B., and Tiedje, J. M.: Direct Measurement of Oxygen Profiles and Denitrification Rates in Soil Aggregates, Soil Sci. Soc. Am. J., 49, 645–651, https://doi.org/10.2136/sssaj1985.03615995004900030024x, 1985.
Shannon, C. E.: A Mathematical Theory of Communication, Bell Syst. Tech. J., 27, 623–656, https://doi.org/10.1002/j.1538-7305.1948.tb00917.x, 1948.
Sørensen, K. I. and Auken, E.: SkyTEM – a new high-resolution helicopter transient electromagnetic system, Explor. Geophys., 35, 194–202, https://doi.org/10.1071/EG04194, 2004.
Straubhaar, J.: DeeSse User's Guide, The Centre for Hydrogeology and Geothermics (CHYN), University of Neuchatel, Neuchâtel, Switzerland, 2019.
Straubhaar, J., Renard, P., Mariethoz, G., Froidevaux, R., and Besson, O.: An improved parallel multiple-point algorithm using a list approach, Math. Geosci., 43, 305–328, https://doi.org/10.1007/s11004-011-9328-7, 2011.
Strebelle, S.: Conditional Simulation of Complex Geological Structures Using Multiple-Point Statistics, Math. Geol., 34, 1–21, https://doi.org/10.1109/CEC.2011.5949612, 2002.
Strebelle, S.: Multiple-Point Geostatistics: from Theory to Practice, in:
Expanded Abstract Collection from Ninth International Geostatistics Congress, 11–15 June, Oslo, Norway,
1–65, 2012.
Styrelsen for Dataforsyning og Effektivisering: Danmarks Højdemodel,
DHM/Terræn. Data version 2.0 – Januar 2015, available at:
https://www.kortforsyningen.dk/sites/default/files/dk_dhm_terraen_v2_1_aug_2016.pdf (last access: 15 May 2021),
2016 (in Danish).
Tahmasebi, P.: Multiple Point Statistics: A Review, in: Handbook of Mathematical Geosciences, edited by: Daya Sagar, B. S., Cheng, Q., and Agterberg, F., Springer International Publishing, Cham, 613–643, 2018.
Tahmasebi, P., Hezarkhani, A., and Sahimi, M.: Multiple-point geostatistical modeling based on the cross-correlation functions, Comput. Geosci., 16, 779–797, https://doi.org/10.1007/s10596-012-9287-1, 2012.
Tarantola, A.: Inverse problem theory and Methods for Model Parameter Estimation, 1st edn., SIAM, Philadelphia, USA, 2005.
Temkin, A., Evans, S., Manidis, T., Campbell, C., and Naidenko, O. V.: Exposure-based assessment and economic valuation of adverse birth outcomes and cancer risk due to nitrate in United States drinking water, Environ. Res., 176, 1–14, https://doi.org/10.1016/j.envres.2019.04.009, 2019.
Tesoriero, A. J., Terziotti, S., and Abrams, D. B.: Predicting Redox Conditions in Groundwater at a Regional Scale, Environ. Sci. Technol., 49, 9657–9664, https://doi.org/10.1021/acs.est.5b01869, 2015.
Thomsen, R., Søndergaard, V. H., and Sørensen, K. I.: Hydrogeological mapping as a basis for establishing site-specific groundwater protection zones in Denmark, Hydrogeol. J., 12, 550–562, https://doi.org/10.1007/s10040-004-0345-1, 2004.
Vest Christiansen, A. and Auken, E.: A global measure for depth of investigation, Geophysics, 77, WB171–WB177, https://doi.org/10.1190/geo2011-0393.1, 2012.
Viezzoli, A., Christiansen, A. V., Auken, E., and Sørensen, K. I.: Quasi-3D modeling of airborne TEM data by spatially constrained inversion, Geophysics, 73, F105–F113, https://doi.org/10.1190/1.2895521, 2008.
Viezzoli, A., Jørgensen, F., and Sørensen, C.: Flawed processing of airborne em data affecting hydrogeological interpretation, Groundwater, 51, 191–202, https://doi.org/10.1111/j.1745-6584.2012.00958.x, 2013.
Vignoli, G., Fiandaca, G., Christiansen, A. V., Kirkegaard, C., and Auken, E.: Sharp spatially constrained inversion with applications to transient electromagnetic data, Geophys. Prospect., 63, 243–255, https://doi.org/10.1111/1365-2478.12185, 2015.
Vilhelmsen, T. N., Auken, E., Christiansen, A. V., Barfod, A. S., Marker, P. A., and Bauer-Gottwein, P.: Combining Clustering Methods With MPS to Estimate Structural Uncertainty for Hydrological Models, Front. Earth Sci., 7, 1–15, https://doi.org/10.3389/feart.2019.00181, 2019.
Wellmann, J. F. and Caumon, G.: 3-D Structural geological models: Concepts, methods, and uncertainties, 1st edn., Elsevier Inc., London, UK,
2018.
Wellmann, J. F., De La Varga, M., Murdie, R. E., Gessner, K., and Jessell, M. W.: Uncertainty estimation for a geological model of the Sandstone greenstone belt, Western Australia – insights from integrated geological and geophysical inversion in a Bayesian inference framework, Geol. Soc. Spec. Publ., 453, 41–56, https://doi.org/10.1144/SP453.12, 2018.
Wilkin, R. T., Barnes, H. L., and Brantley, S. L.: The size distribution of framboidal pyrite in modern sediments, Geochim. Cosmochim. Ac., 60, 3897–3912, 1996.
Wilson, C. G., Bond, C. E., and Shipley, T. F.: How can geologic decision-making under uncertainty be improved?, Solid Earth, 10, 1469–1488, https://doi.org/10.5194/se-10-1469-2019, 2019.
Wilson, S. R., Close, M. E., and Abraham, P.: Applying linear discriminant analysis to predict groundwater redox conditions conducive to denitrification, J. Hydrol., 556, 611–624, https://doi.org/10.1016/j.jhydrol.2017.11.045, 2018.
Wycisk, P., Hubert, T., Gossel, W., and Neumann, C.: High-resolution 3D spatial modelling of complex geological structures for an environmental risk assessment of abundant mining and industrial megasites, Comput. Geosci., 35, 165–182, https://doi.org/10.1016/j.cageo.2007.09.001, 2009.
Yan, S., Liu, Y., Liu, C., Shi, L., Shang, J., Shan, H., Zachara, J., Fredrickson, J., Kennedy, D., Resch, C. T., Thompson, C., and Fansler, S.: Nitrate bioreduction in redox-variable low permeability sediments, Sci. Total Environ., 539, 185–195, https://doi.org/10.1016/j.scitotenv.2015.08.122, 2016.
Short summary
The protection of subsurface aquifers from contamination is an ongoing environmental challenge. Some areas of the underground have a natural capacity for reducing contaminants. In this research these areas are mapped in 3D along with information about, e.g., sand and clay, which indicates whether contaminated water from the surface will travel through these areas. This mapping technique will be fundamental for more reliable risk assessment in water quality protection.
The protection of subsurface aquifers from contamination is an ongoing environmental challenge....
