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Stochastic Distance Based Geological Boundary Modeling with Curvilinear Features

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Abstract

Obtaining accurate geological boundaries and assessing the uncertainty in these limits are critical for effective ore resource and reserve estimation. The uncertainty in the extent of an ore body can be the largest source of uncertainty in ore resource estimation when drilling is sparse. These limits are traditionally interpreted deterministically and it can be difficult to quantify uncertainty in the boundary and its impact on ore tonnage. The proposed methodology is to consider stochastic modeling of the ore boundary with a distance function recoding of the available data. This technique is modified to incorporate non-stationarities in the form of a locally varying anisotropy field used in kriging and sequential Gaussian simulation. Implementing locally varying anisotropy kriging retains the geologically realistic features of a deterministic model while allowing for a stochastic assessment of uncertainty. A case study of a gold deposit in Northern Canada is used to demonstrate the methodology. The proposed technique generates realistic, curvilinear geological boundary models and allows for an assessment of the uncertainty in the model.

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References

  • Aug C, Chilès J, Courrioux G, Lajaunie C (2004) 3D geological modeling and uncertainty: the potential field method. In: Leuangthong O, Deutsch C (eds) Seventh international geostatistics congress, Banff, Canada, pp 145–155

  • Banerjee S, Gelfand A (2006) Bayesian wombling. J Am Stat Assoc 101:1487–1501

    Article  Google Scholar 

  • Boisvert JB, Deutsch CV (2010) Programs for kriging and sequential Gaussian simulation with locally varying anisotropy using non-Euclidean distances. Comput Geosci 37:495–510

    Google Scholar 

  • Boisvert JB, Deutsch CV (2011) Modeling locally varying anisotropy of CO2 emissions in the united states. Stoch Environ Res Risk Assess. doi:10.1007/s00477-011-0483-7

    Google Scholar 

  • Calcagno P, Chilès J, Courrioux G, Guillen A (2008) Geological modelling from field data and geological knowledge. Part I. Modelling method coupling 3D potential-field interpolation and geological rules. Phys Earth Planet Inter 171:147–157

    Article  Google Scholar 

  • Carpenter RL, Sherlock RL, Quang C, Kleespies P, McLeod R (2003) Geology of the Doris north gold deposits, northern hope bay volcanic belt, slave structural province. Nunavut Geological Survey of Canada Current Research 2003-C6. 12 pp

  • Cherpeau N, Caumon G, Levy B (2010) Stochastic simulations of fault networks in 3D structural modeling. C R Geosci 342(9):687–694

    Article  Google Scholar 

  • Chilès J, Aug C, Guillen A, Lees T (2004) Modelling the geometry of geological units and its uncertainty in 3D from structural data: the potential-field method. In: Dimitrakopoulos R, Ramazan S (eds) Orebody modelling and strategic mine planning. Perth, WA, pp. 313–320

  • Cressie N (1993) Statistics for spatial data revised edn. Wiley, New York, p 900

    Google Scholar 

  • Dijkstra E (1959) A note on two problems in connection with graphs. Numer Math 1(1):269–271

    Article  Google Scholar 

  • Fraser JA (1964) Geological notes on the northeastern district of MacKenzie Northwest territories. Geological Survey of Canada. 20 pp

  • Frondel C, Baum J (1974) Structure and mineralogy of the Franklin zinc-iron-manganese deposit. Econ Geol 69(2):157–180

    Article  Google Scholar 

  • Gabriel E, Allard D, Bacro J (2011) Estimating and testing zones of abrupt change for spatial data. Stat Comput 21:107–120

    Article  Google Scholar 

  • Gerbert J (1993) Geology and mineral potential of the Archean Hope Bay and Elu Inlet volcanic belts, northeastern Slave structural province, District of MacKenzie. Northern Affairs Program, Northwestern Territories Geology Division. 103 pp

  • Henrion V, Caumon G, Cherpeau N (2010) ODSIM: an object-distance simulation method for conditioning complex natural structures. Math Geosci 42(8):911–924

    Article  Google Scholar 

  • Holden L, Mostad P, Nielsen B, Gjerde J, Townsend C, Ottesen S (2003) Stochastic structural modeling. Math Geol 35(8):899–914

    Article  Google Scholar 

  • Isaaks E, Davis B (1999) The kriging oxymoron: conditionally unbiased and accurate prediction. In: SME annual meeting, Denver, CO

  • Isaaks E, Srivastava R (1989) An introduction to applied geostatistics. Oxford University Press, New York. 561 pp

    Google Scholar 

  • Jones M, Baerentzen J, Sramek M (2006) 3D distance fields: a survey of techniques and applications. IEEE Trans Visual Computing Comput Graph 12(4):581–599

    Article  Google Scholar 

  • Journel A, Kyriakidis P (2004) Evaluation of mineral reserves: a simulation approach. Oxford University Press, New York. 232 pp

    Google Scholar 

  • Krige D (1996) A practical analysis of the effects of spatial structure and data available and used. In: on conditional biases in ordinary kriging. In: 5th international geostatistics congress, Wollongong, Australia

  • Krige D, Assibey-Bonsu W (1999) Practical problems in the estimation of recoverable reserves when using kriging or simulation techniques. In: International symposium on geostatistical simulation in mining, Perth, Australia

  • Lajaunie C, Courrioux G, Manuel L (1997) Foliction fields and 3D cartography in geology: principles of a method based on potential interpolation. Math Geol 29:571–584

    Article  Google Scholar 

  • Lecour M, Cognot R, Duvinage I, Thore P, Dulac J (2001) Modelling of stochastic faults and fault networks in a structural uncertainty study. Pet Geosci 7:31–42

    Article  Google Scholar 

  • Lorensen W, Cline H (1987) Marching cubes: a high resolution 3D surface construction algorithm. Comput Graph 21:163–169

    Article  Google Scholar 

  • Mallet J (2002) Geomodeling. Oxford University Press, New York. 624 pp

    Google Scholar 

  • Mallet J (2004) Space–time mathematical framework for sedimentary geology. Math Geol 36:1–32

    Article  Google Scholar 

  • McLennan J (2008) The decision of stationarity. PhD dissertation, University of Alberta, Canada. 191 pp

  • Sherlock RL, Carpenter RL, Bardoux M, Flkood E, Kleespies P (2002) Volcanic relationships and gold mineralization in the Wolverine–Madrid corridor, hope bay volcanic belt. Nunavut Geological Survey of Canada Current Research 2002-C9. 11 pp

  • Stroet C, Snepvangers J (2005) Mapping curvilinear structures with local anisotropy kriging. Math Geol 37:635–649

    Article  Google Scholar 

  • Womble W (1951) Differential systematics. Science 114:315–322

    Article  Google Scholar 

  • Xu W (1996) Conditional curvilinear stochastic simulation using pixel-based algorithms. Math Geol 28:937–949

    Article  Google Scholar 

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Acknowledgements

The author would like to thank Newmont for providing the data set. Specifically, thanks are extended to Bruce Perry and Larry Allen for their assistance throughout the course of the work in both data preparation and helpful comments.

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Authors and Affiliations

  1. Centre for Computational Geostatistics, Department of Civil and Environmental Engineering, 3-133 Markin/CNRL Natural Resources Facility, University of Alberta, Edmonton, AB, Canada, T6G 2W2

    Maksuda Lillah & Jeff B. Boisvert

  2. Centre for Computational Geostatistics, Department of Civil and Environmental Engineering, 3-133 Markin/CNRL Natural Resources Facility, University of Alberta, Edmonton, AB, Canada, T6G 2G4

    Jeff B. Boisvert

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  1. Maksuda Lillah
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  2. Jeff B. Boisvert
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Correspondence to Jeff B. Boisvert.

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Lillah, M., Boisvert, J.B. Stochastic Distance Based Geological Boundary Modeling with Curvilinear Features. Math Geosci 45, 651–665 (2013). https://doi.org/10.1007/s11004-012-9426-1

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