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Evaluating the impact of data quantity, distribution and algorithm selection on the accuracy of 3D subsurface models using synthetic grid models of varying complexity

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Abstract

Testing the accuracy of 3D modelling algorithms used for geological applications is extremely difficult as model results cannot be easily validated. This paper presents a new approach to evaluate the effectiveness of common interpolation algorithms used in 3D subsurface modelling, utilizing four synthetic grids to represent subsurface environments of varying geological complexity. The four grids are modelled with Inverse Distance Weighting and Ordinary Kriging, using data extracted from the synthetic grids in different spatial distribution patterns (regular, random, clustered and sparse), and with different numbers of data points (100, 256, 676 and 1,600). Utilizing synthetic grids for this evaluation allows quantitative statistical assessment of the accuracy of both interpolation algorithms in a variety of sampling conditions. Data distribution proved to be an important factor; as in many geological situations, relatively small numbers of randomly distributed data points can generate more accurate 3D models than larger amounts of clustered data. This study provides insight for optimizing the quantity and distribution of data required to accurately and cost-effectively interpolate subsurface units of varying complexity.

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References

  • Bond CE, Gibbs AD, Shipton ZK, Jones S (2007) What do you think this is? “Conceptual uncertainty” in geoscience interpretation. GSA Today 17(11):4–10. doi:10.1002/(SICI)1099-095X(199601)7:1<1:AID-ENV157>3.0.CO;2-Y

    Article  Google Scholar 

  • Brus DJ, De Gruijter JJ, Marsman BA, Visschers R, Bregt KA, Breeuwsma A, Bouma J (1996) The performance of spatial interpolation methods and choropleth maps to estimate properties at points: a soil survey case study. Environmetrics 7(1):1–16. doi:10.1002/(SICI)1099-095X(199601)7:1<1:AID-ENV157>3.0.CO;2-Y

    Article  Google Scholar 

  • Burrough PA (2001) GIS and geostatistics: essential partners for spatial analysis. Environ Ecol Stat 8(4):361–377. doi:10.1023/A:1012734519752

    Article  Google Scholar 

  • Burt A (2007) Three-dimensional geological modelling of thick quaternary deposits in the Barrie-Oro area, central Ontario: new modelling techniques. In: Summary of field work and other activities 2007. Ontario geological survey open file report 6145:35-1–35-5

  • Davis JC (2002) Statistics and data analysis and geology. Wiley, New York

    Google Scholar 

  • de Kemp EA (2006) 3-D interpretive mapping: an extension of GIS technologies for the geoscientist. In: Harris JR (ed) GAC special paper 44: GIS for the earth sciences. GAC, Canada

    Google Scholar 

  • Dille JA, Milner M, Groeteke JJ, Moretensen DA, Williams MM (2003) How good is your weed map? A comparison of spatial interpolators. Weed Sci 51(1):44–55. doi:10.1614/0043-1745(2002)051[0044:HGIYWM]2.0.CO;2

    Article  Google Scholar 

  • Heuvelink GBM (1998) Error propagation in environmental modelling with GIS. Taylor and Francis, London

    Google Scholar 

  • Isaaks EH, Srivastava RM (1989) An introduction to applied geostatistics. Oxford University Press, New York

    Google Scholar 

  • Jackson I (2007) So where do we go from here? Three-dimensional geologic mapping for groundwater applications. Minnesota geological survey open file report 07-4:19–22

    Google Scholar 

  • Jones NL, Davis RJ, Sabbah W (2003) A comparison of three-dimensional interpolation techniques for plume characterization. Groundwater 41(4):411–419. doi:10.1111/j.1745-6584.2003.tb02375.x

    Article  Google Scholar 

  • Kaufmann O, Martin T (2008) 3D geological modeling from boreholes, cross-sections and geological maps, application over former natural gas storage in coal mines. Comput Geosci 34(3):278–290. doi:10.1016/j.cageo.2007.09.005

    Article  Google Scholar 

  • Keefer DA (2007) A framework and methods for characterizing uncertainty in geologic maps. In: Thorleifson LH, Berg RC, Russell HAJ (eds) Three-dimensional geologic mapping for groundwater applications. Minnesota Geological Survey, Open-File Report 07-4. pp 23–26

  • Kessler H, Lelliott M, Bridge D, Ford F, Sibusch HG, Mathers S, Simon Price S, Merritt J, Royse K (2005) 3D geosciences models and their delivery to customers. Three-dimensional geologic mapping for groundwater applications. Geological survey of Canada, open file 5048:39-42

  • Krajewski SA, Gibbs BL (1996) Understanding contouring. Gibbs Associates, Colorado

    Google Scholar 

  • Kravchenko AN (2003) Influence of spatial structure on accuracy of interpolation methods. Soil Sci Soc Am J 67(5):1564–1571. doi:10.2136/sssaj2003.1564

    Article  Google Scholar 

  • Lapen DR, Hayhoe HN (2003) Spatial analysis of seasonal and annual temperature and precipitation normals in southern Ontario, Canada. J Gt Lakes Res 29(4):529–544. doi:10.1016/S0380-1330(03)70457-2

    Article  Google Scholar 

  • Logan C, Russel HAJ, Sharpe DR, Kenny FM (2006) The role of GIS and expert knowledge in 3-D modelling, Oak Ridges Moraine, southern Ontario. In Harris JR (ed) GAC special paper 44: GIS for the earth sciences, geological association of Canada, St. John’s, pp 519–542

  • MacCormack KE, MacLachlan JC, Eyles CH (2005) Viewing the subsurface in three dimensions: initial results of modeling the quaternary sedimentary infill of the Dundas valley, Hamilton, Ontario. Geosphere 1:23–31. doi:10.1130/GES00007.1

    Article  Google Scholar 

  • Moffat AM, Papale D, Reichstein M, Hollinger DY, Richardson AD, Barr AG, Beckstein C, Braswell BH, Churkina G, Desai AR, Falge E, Gove JH, Heimann M, Hui D, Jarvis AJ, Kattge J, Noormets A, Stauch VJ (2007) Comprehensive comparison of gap-filling techniques for eddy covariance net carbon fluxes. Agric For Meteorol 147(3–4):209–232. doi:10.1016/j.agroformet.2007.08.011

    Article  Google Scholar 

  • Mueller TG, Pusuluri PB, Mathias KK, Cornelius PL, Barnhisel RI, Shearer SA (2004) Map quality for ordinary kriging and inverse distance weighted interpolation. Soil Sci Soc Am J 68(6):2042–2047. doi:10.2136/sssaj2004.2042

    Article  Google Scholar 

  • Nalder IA, Wein RW (1998) Spatial interpolation of climatic normals: test of a new method in the Canadian boreal forest. Agric For Meteorol 92(4):211–225. doi:10.1016/S0168-1923(98)OD102-6

    Article  Google Scholar 

  • Paulen RC, McClenaghan MB, Harris JR (2006) Bedrock topography and drift thickness models from the Timmins area, northeastern Ontario: an application of GIS to the timmins overburden drillhole database. In: Harris JR (ed) GAC special paper 44: GIS for the earth sciences, geological association of Canada, St. John’s, pp 413–434

  • RockWare (2006) Version 2006. RockWare, Denver

    Google Scholar 

  • Ross M, Parent M, Lefebvre R (2005) 3D geologic framework models for regional hydrogeology and land-use management: a case study from a quaternary basin of southwestern Quebec, Canada. Hydrogeol J 13(5–6):690–707. doi:10.2136/sssaj2001.652470x

    Article  Google Scholar 

  • Schloeder CA, Zimmerman NE, Jacobs MJ (2001) Comparison of methods for interpolating soil properties using limited data. Soil Sci Soc Am J 65(2):470–479. doi:10.2136/sssaj2001.652470x

    Article  Google Scholar 

  • Tabios GQ, Salas JD (1985) A comparative-analysis of techniques for spatial interpolation of precipitation. Water Resour Bull 21(3):365–380. doi:10.1111/j.1752-1688.1985.tb00147.x

    Article  Google Scholar 

  • Walker DD, Loftis JC (1997) Alternative spatial estimators for ground-water and soil measurements. Groundwater 35(4):593–601. doi:10.1111/j.1745-6584.1997.tb00124.x

    Article  Google Scholar 

  • Weber D, Englund EJ (1992) Evaluation and comparison of spatial interpolators. Math Geol 24(4):381–391. doi:10.1007/BF00891270

    Article  Google Scholar 

  • Weber D, Englund EJ (1994) Evaluation and comparison of spatial interpolators II. Math Geol 26(5):589–603. doi:10.1007/BF02089243

    Article  Google Scholar 

  • Webster R, Oliver MA (1992) Sample adequately to estimate variograms of soil properties. J Soil Sci 43(1):177–192. doi:10.1111/j.1365-2389.1992.tb00128.x

    Article  Google Scholar 

  • Wu Q, Xu H, Zou X (2005) An effective method for 3D geological modeling with multi-source data integration. Comput Geol 31(1):35–43. doi:10.1016/j.cageo.2004.09.005

    Article  Google Scholar 

  • Zimmerman D, Pavlik C, Ruggles A, Armstrong MP (1999) An experimental comparison of ordinary and universal kriging and inverse distance weighting. Math Geol 31(4):375–390. doi:10.1023/A:1007586507433

    Article  Google Scholar 

  • Zwiers WG, Rainsford DRB, Bajc AF (2008) Project unit 06-026: investigation of the dundas buried Bedrock valley. Summary of field work and other activities 2008, Ontario geological survey open file report 6226:33-1–33-7

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Acknowledgments

We would like to thank Dr. Jeff Harris, Dr. Antonio Paez, and the anonymous reviewers for their helpful comments and suggestions pertaining to this research, and Prateek Gupta for his assistance with manuscript preparation.

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Authors and Affiliations

  1. School of Environmental Sciences, University of Guelph, 50 Stone Road East, Guelph, ON, N1G 2W1, Canada

    Kelsey E. MacCormack

  2. School of Geography and Earth Sciences, McMaster University, 1280 Main Street West, Hamilton, ON, L8S 4K1, Canada

    Jason J. Brodeur & Carolyn H. Eyles

Authors
  1. Kelsey E. MacCormack
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  2. Jason J. Brodeur
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  3. Carolyn H. Eyles
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Correspondence to Kelsey E. MacCormack.

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MacCormack, K.E., Brodeur, J.J. & Eyles, C.H. Evaluating the impact of data quantity, distribution and algorithm selection on the accuracy of 3D subsurface models using synthetic grid models of varying complexity. J Geogr Syst 15, 71–88 (2013). https://doi.org/10.1007/s10109-011-0160-x

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  • DOI: https://doi.org/10.1007/s10109-011-0160-x

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