Data Assimilation for Resource Model Updating

Part of the SpringerBriefs in Applied Sciences and Technology book series (BRIEFSAPPLSCIENCES)


One of the two core constituents of Closed-Loop Management for Mineral Resources is data assimilation for resource and grade control model updating. Similar to weather forecast models, the aim is to update the knowledge and forecast ability of the ROM ore as soon as new data from production monitoring become available. This chapter provides a formal description of the geostatistical foundations, a practical workflow and outlines one particular solution for updating. The theory is underpinned by three industrial-scale case studies and a discussion about practical aspects for operational implementation in Chap.  4.


  1. M. Abzalov, Applied Mining Geology. Springer International Publishing (2016). Scholar
  2. T.W. Anderson, An Introduction to Multivariate Statistical Analysis. (John Wiley & Sons, Inc., New York, 1984), 675 pGoogle Scholar
  3. D. Beal, P. Brasseur, J.M. Brankart, Y. Ourmieres, J. Verron, Characterization of mixing errors in a coupled physical biogeochemical model of the north Atlantic: implications for nonlinear estimation using gaussian anamorphosis. Ocean Sci. 6, 247–262 (2010)CrossRefGoogle Scholar
  4. J. Benndorf, Making use of online production data: sequential updating of mineral resource models. Math. Geosci. 47(5), 547–563 (2015)zbMATHCrossRefGoogle Scholar
  5. J. Benndorf, R. Dimitrakopoulos, New efficient methods for conditional simulations of large Orebodies. In: Advances in Applied Strategic Mine Planning (pp. 353–369). Springer, Cham (2018)CrossRefGoogle Scholar
  6. L. Bertino, G. Evensen, H. Wackernagel, Combining geostatistics and Kalman filtering for data assimilation in an estuarine system. Inverse Prob. 18, 1–23 (2002)zbMATHCrossRefGoogle Scholar
  7. A. Boucher, R. Dimitrakopoulos, Multivariate block-support simulation of the Yandi iron ore deposit Western Australia. Math. Geosci. 44(4), 449–468 (2012)CrossRefGoogle Scholar
  8. G. Burgers, P. Jan van Leeuwen, G. Evensen, Analysis scheme in the ensemble Kalman filter. Mon. Weather Rev. 126, 1719–1724 (1998)CrossRefGoogle Scholar
  9. J.P. Chiles, P. Delfiner, Geostatistics, Modelling Spatial Uncertainty, 2nd edn. (Wiley, New York, 2012)zbMATHCrossRefGoogle Scholar
  10. M.D. Davis, Production of conditional simulations via the LU triangular decomposition of the covariance matrix. Math. Geol. 19(2), 91–98 (1987)Google Scholar
  11. R. Tolosana-Delgado, U. Mueller, K.G. van den Boogaart, Geostatistics for compositional data: an overview. Math. Geosci. 51(4), 485–526 (2019)MathSciNetzbMATHCrossRefGoogle Scholar
  12. A. Desbarats, R. Dimitrakopoulos, Geostatistical simulation of regionalized pore-size distributions using min/max autocorrelation factors. Math. Geol. 32(8), 919–942 (2000)CrossRefGoogle Scholar
  13. C. Deutsch, A. Journel, GSLIB Geostatistical Software Library and User’s Guide (Oxford University Press, Oxford, 1992)Google Scholar
  14. C.R. Dietrich, Computationally efficient generation of Gaussian conditional simulation over regular sample grids. Math. Geol. 25(1), 439–452 (1993)MathSciNetzbMATHCrossRefGoogle Scholar
  15. R. Dimitrakopoulos, X. Luo, Generalised sequential Gaussian simulation on group size ν and screen—effect approximations for large field simulations. Math. Geol. 36(5), 567–591 (2004)MathSciNetzbMATHCrossRefGoogle Scholar
  16. G. Evensen, Advanced data assimilation for strongly nonlinear dynamics. Mon. Weather Rev. 125, 1342–1354 (1997)CrossRefGoogle Scholar
  17. G. Evensen, The ensemble Kalman filter: theoretical formulation and practical implementation. Ocean Dyn. 53, 343–367 (2003)CrossRefGoogle Scholar
  18. M. Godoy, A risk analysis based framework for strategic mine planning and design—method and application. In: Advances in Applied Strategic Mine Planning (pp. 75–90). Springer, Cham (2018)CrossRefGoogle Scholar
  19. J.J. Gómez-Hernández, A.G. Journel, Joint Sequential Simulation of Multigaussian Fields. In: Geostatistics Troia’92. (Springer, Dordrecht 1993), pp. 85–94Google Scholar
  20. P. Goovaerts, Geostatistics for Natural Resources Evaluation. Applied Geostatistics Series. (Oxford University Press, New York 1997)Google Scholar
  21. L. Heidari, V. Gervais, M. Le Ravalec, H. Wackernagel, History matching of reservoir models by ensemble Kalman filtering: The state of the art and a sensitivity study. Uncertainty Analysis and Reservoir Modeling: AAPG Memoir 96, 249–264 (2011)Google Scholar
  22. H.J. Hendricks Franssen, H.P. Kaiser, U. Kuhlmann, G. Bauser, F. Stauffer, R. Müller, W. Kinzelbach, Operational real‐time modeling with ensemble Kalman filter of variably saturated subsurface flow including stream‐aquifer interaction and parameter updating. Water Resour. Res. 47(2) (2011)Google Scholar
  23. A. Horta, A. Soares, Direct sequential co-simulation with joint probability distributions. Math. Geosci. 42(3), 269–292 (2010)zbMATHCrossRefGoogle Scholar
  24. P. Houtekamer, H. Mitchell, Data assimilation using an ensemble kalman filter technique. Mon. Weather Rev. 126, 796–811 (1998)CrossRefGoogle Scholar
  25. L.Y. Hu, Y. Zhao, Y. Liu, C. Scheepens, A. Bouchard, Updating multipoint simulations using the ensemble Kalman filter. Comput. Geosci. 51, 7–15 (2012)CrossRefGoogle Scholar
  26. E.H. Isaaks, The application of Monte Carlo methods to the analysis of spatially correlated data. Unpubl. PhD dissertation, Department of Applied Earth Sciences, Stanford University, Stanford, California, 213 p (1990)Google Scholar
  27. E. Isaaks, R.M. Srivastava, An Introduction to Applied Geostatistics. (Oxford University Press 1989)Google Scholar
  28. J.D. Jansen, S.D. Douma, D.R. Brouwer, van den P.M.J. Hof, O.H. Bosgra, A.W. Hemink, Closed-Loop Reservoir management. Paper 119098 presented at the SPE Reservoir Simulation Symposium. Woodlands (2009)Google Scholar
  29. A. Jewbali, R. Dimitrakopoulos, Implementation of conditional simulation by successive residuals. Comput. Geosci. 37, 129–142 (2011)CrossRefGoogle Scholar
  30. Joint Ore Reserves Committee (JORC). Australasian Code for Reporting of Exploration Results, Mineral Resources, and Ore Reserves (The JORC Code) (2012)Google Scholar
  31. A.G. Journel, C.J. Huijbregts, Mining Geostatistics (Academic Press, London, 1978), p. 600Google Scholar
  32. R.E. Kalman, A new approach to linear filtering and prediction problems. Trans. ASME J. Basic Eng. 82, 35–45 (1960)MathSciNetCrossRefGoogle Scholar
  33. A.N. Kolmogorov, Foundations of the Theory of Probability: Chelsa. (New York, 1950), 71 pGoogle Scholar
  34. D. E. Myers, Vector conditional simulation. In: Geostatistics. (Springer, Dordrecht 1989), pp. 283–293CrossRefGoogle Scholar
  35. U. Mueller, van den K. G. Boogaart, R. Tolosana-Delgado, A truly multivariate normal score transform based on lagrangian flow. In: Geostatistics Valencia 2016. (Springer, Cham 2017), pp. 107–118CrossRefGoogle Scholar
  36. W. Naworyta, J. Benndorf, Accuracy assessment of geostatistical modelling methods of mineral deposits for the purpose of their future exploitation—based on one lignite deposit. Mineral Resour. Manag. 28(1), 77–101 (2012) (Polish)Google Scholar
  37. NI 43–101. National Instrument 43-101, standards of Disclosure for Mineral Projects (NI 43-101). CIM SV 56—2013, National Instrument 43-101 Standards of Disclosure for Mineral Projects (2011)Google Scholar
  38. V. Pawlowsky-Glahn, A. Buccianti, Compositional Data Analysis. (Wiley 2011)Google Scholar
  39. A. Prior, J. Benndorf, U. Müller, Resource and grade control model updating for underground mining production settings. Math. Geosci. (2020a) (in print)Google Scholar
  40. A. Prior, R. Tolosana-Delgado, van den K.G. Boogaart, J. Benndorf, Resource model updating for compositional geometallurgical variables. Math. Geosci. (2020b). (Accepted)Google Scholar
  41. M. Rosenblatt, Remarks on multivariate transformation. Ann. Math. Stat. 23, 470–472 (1952)Google Scholar
  42. M.E. Rossi, C.V. Deutsch, Mineral Resoure Estimation (DOI, Springer, Dordrecht, 2014). Scholar
  43. P. Switzer, A. Green, (1984). Min/max autocorrelation factors for multivariate spatial imagery. Dept. of Statistics, Stanford University, Tech. Rep. 6 (1984)Google Scholar
  44. K.G. van den Boogaart, U. Mueller, R. Tolosana-Delgado, An affine equivariant multivariate normal score transform for compositional data. Math. Geosci. 49(2), 231–251 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  45. J.A. Vargas-Guzmán, T.C.J. Yeh, Sequential Kriging and co-kriging: two powerful geostatistical approaches. Stoch. Env. Res. Risk Assess. 13, 416–435 (1999)zbMATHCrossRefGoogle Scholar
  46. J.A. Vargas-Guzmán, R. Dimitrakopoulos, Conditional simulation of random fields by successive residuals. Math. Geol. 34, 597–611 (2002)MathSciNetzbMATHCrossRefGoogle Scholar
  47. H. Wackernagel, Multivariate geostatistics: an introduction with applications. (Springer Science & Business Media 2013)Google Scholar
  48. T. Wambeke, J. Benndorf, A simulation-based geostatistical approach to real-time reconciliation of the grade control model. Math. Geosci. 49(1), 1–37 (2017)MathSciNetzbMATHCrossRefGoogle Scholar
  49. T. Wambeke, J. Benndorf, A study of the influence of measurement volume, blending ratios and sensor precision on real-time reconciliation of grade control models. Math. Geosci. 50(7), 801–826 (2018)zbMATHCrossRefGoogle Scholar
  50. A.M. Yaglom, Correlation theory of stationary and related random functions. (Springer, New York, 1987), 235 pGoogle Scholar
  51. H. Zhou, J.J. Gomez-Hernandez, H.J. Hendricks Franssen, L. Li, An approach to handling Non-gaussianity of parameters and state variables in ensemble Kalman. Adv. Water Resour. 34, 844–864 (2011)CrossRefGoogle Scholar

Copyright information

© The Author(s), under exclusive license to Springer Nature Switzerland AG 2020

Authors and Affiliations

  1. 1.Department of Mine Surveying and GeodesyUniversity of Technology Bergakademie FreibergFreibergGermany

Personalised recommendations