Simulation of mineral grades with hard and soft conditioning data: application to a porphyry copper deposit
This work deals with the geostatistical simulation of mineral grades whose distribution exhibits spatial trends within the ore deposit. It is suggested that these trends can be reproduced by using a stationary random field model and by conditioning the realizations to data that incorporate the avail...
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| Published in | Computational geosciences Vol. 13; no. 1; pp. 79 - 89 |
|---|---|
| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
Dordrecht
Springer Netherlands
01.03.2009
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1420-0597 1573-1499 1573-1499 |
| DOI | 10.1007/s10596-008-9106-x |
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| Abstract | This work deals with the geostatistical simulation of mineral grades whose distribution exhibits spatial trends within the ore deposit. It is suggested that these trends can be reproduced by using a stationary random field model and by conditioning the realizations to data that incorporate the available information on the local grade distribution. These can be hard data (e.g., assays on samples) or soft data (e.g., rock-type information) that account for expert geological knowledge and supply the lack of hard data in scarcely sampled areas. Two algorithms are proposed, depending on the kind of soft data under consideration: interval constraints or local moment constraints. An application to a porphyry copper deposit is presented, in which it is shown that the incorporation of soft conditioning data associated with the prevailing rock type improves the modeling of the uncertainty in the actual copper grades. |
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| AbstractList | This work deals with the geostatistical simulation of mineral grades whose distribution exhibits spatial trends within the ore deposit. It is suggested that these trends can be reproduced by using a stationary random field model and by conditioning the realizations to data that incorporate the available information on the local grade distribution. These can be hard data (e.g., assays on samples) or soft data (e.g., rock-type information) that account for expert geological knowledge and supply the lack of hard data in scarcely sampled areas. Two algorithms are proposed, depending on the kind of soft data under consideration: interval constraints or local moment constraints. An application to a porphyry copper deposit is presented, in which it is shown that the incorporation of soft conditioning data associated with the prevailing rock type improves the modeling of the uncertainty in the actual copper grades. (PUBLICATION ABSTRACT) This work deals with the geostatistical simulation of mineral grades whose distribution exhibits spatial trends within the ore deposit. It is suggested that these trends can be reproduced by using a stationary random field model and by conditioning the realizations to data that incorporate the available information on the local grade distribution. These can be hard data (e.g., assays on samples) or soft data (e.g., rock-type information) that account for expert geological knowledge and supply the lack of hard data in scarcely sampled areas. Two algorithms are proposed, depending on the kind of soft data under consideration: interval constraints or local moment constraints. An application to a porphyry copper deposit is presented, in which it is shown that the incorporation of soft conditioning data associated with the prevailing rock type improves the modeling of the uncertainty in the actual copper grades. |
| Author | Emery, Xavier Robles, Lucía N. |
| Author_xml | – sequence: 1 givenname: Xavier surname: Emery fullname: Emery, Xavier email: xemery@ing.uchile.cl organization: Department of Mining Engineering, University of Chile – sequence: 2 givenname: Lucía N. surname: Robles fullname: Robles, Lucía N. organization: Department of Mining, Metals and Materials Engineering, McGill University |
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| Cites_doi | 10.2113/gsecongeo.69.5.673 10.1016/j.cageo.2006.08.003 10.1111/1467-9868.00070 10.1007/978-3-662-05294-5 10.1007/BF00893318 10.2113/gsecongeo.100.5.935 10.1002/9780470316993 10.1007/978-94-011-1739-5_17 10.1007/BF00897191 10.1023/A:1011094131273 10.1007/BF00898032 10.1007/978-3-662-12718-6 10.1007/BF00898189 10.1109/TPAMI.1984.4767596 10.1007/978-3-662-04808-5 10.1007/s00126-002-0264-9 10.1007/978-94-015-8267-4_5 |
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| Keywords | Gibbs sampler Conditional simulation Spatial trends Soft conditioning data Geostatistics |
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| References | LarrondoP.LeuangthongO.DeutschC.V.MagriE.OrtizJ.KnightsP.HenríquezF.VeraM.BarahonaC.Grade estimation in multiple rock types using a linear model of coregionalization for soft boundariesInternational Conference on Mining Innovation Minin 20042004SantiagoGecamin187196 JournelA.G.RossiM.E.When do we need a trend model in kriging?Math. Geol.198921771573910.1007/BF00893318doi:10.1007/BF00893318 JournelA.G.HuijbregtsC.J.Mining Geostatistics1978LondonAcademic Press AlabertF.The practice of fast conditional simulations through the LU decomposition of the covariance matrixMath. Geol.198719536938610.1007/BF00897191doi:10.1007/BF00897191 ArmstrongM.GalliA.Le Loc’hG.GeffroyF.EschardR.Plurigaussian Simulations in Geosciences2003BerlinSpringer SkewesM.A.HolmgrenC.SternC.R.The Donoso copper-rich, tourmaline-bearing breccia pipe in central Chile: petrologic, fluid inclusion and stable isotope evidence for an origin from magmatic fluidsMiner. Depos.200338122110.1007/s00126-002-0264-9doi:10.1007/s00126-002-0264-9 JournelA.G.Constrained interpolation and qualitative information: the soft kriging approachMath. Geol.198618326928610.1007/BF00898032823434doi:10.1007/BF00898032 DeutschC.V.BaafiE.Y.SchofieldN.A.Direct assessment of local accuracy and precisionGeostatistics Wollongong’961997DordrechtKluwer Academic115125 JournelA.G.Geostatistics for conditional simulation of orebodiesEcon. Geol.197469567368710.2113/gsecongeo.69.5.673 FreulonX.de FouquetC.SoaresA.Conditioning a Gaussian model with inequalitiesGeostatistics Tróia’921993DordrechtKluwer Academic201212 WackernagelH.Multivariate Geostatistics: An Introduction with Applications20033BerlinSpringer1015.62128 FreulonX.ArmstrongM.DowdP.A.Conditional simulation of a Gaussian random vector with nonlinear and/or noisy observationsGeostatistical Simulations1994DordrechtKluwer Academic5771 GalliA.GaoH.Rate of convergence of the Gibbs sampler in the Gaussian caseMath. Geol.20013366536771011.8600810.1023/A:10110941312731956389doi:10.1023/A:1011094131273 EmeryX.GonzálezK.E.Incorporating the uncertainty in geological boundaries into mineral resources evaluationJ. Geol. Soc. India.20076912938 FrikkenP.H.CookeD.R.WalsheJ.L.ArchibaldD.SkarmetaJ.SerranoL.Mineralogical and isotopic zonation in the Sur-Sur tourmaline breccia, Río Blanco - Los Bronces Cu-Mo deposit, Chile: implications for ore genesisEcon. Geol.2005100593596110.2113/100.5.935doi:10.2113/100.5.935 Robles, L., Emery, X., Ortiz, J.M.: Geostatistical simulation of mineral grades in the presence of spatial trends. In: Magri, E.J. (ed.) 33rd International Symposium on Applications of Computers and Operations Research in the Mineral Industry APCOM 2007, pp. 87–93. Gecamin, Santiago (2007) LantuéjoulC.Geostatistical Simulation: Models and Algorithms2002BerlinSpringer0990.86007 Serrano, L., Vargas, R., Stambuk, V., Aguilar, C., Galeb, M., Holmgren, C., et al: The late Miocene to early Pliocene Río Blanco-Los Bronces copper deposit, Central Chilean Andes. In: Camus, F., Sillitoe, R.H., Petersen, R. (eds.) Andean Copper Deposits: New Discoveries, Mineralizations, Styles and Metallogeny, pp. 119–130. Society of Economic Geologists, Littleton (1996), Special Publication no. 5 DeutschC.V.JournelA.G.GSLIB: Geostatistical Software Library and User’s Guide19982New YorkOxford University Press ChilèsJ.P.DelfinerP.Geostatistics: Modeling Spatial Uncertainty1999New YorkWiley0922.62098 AlabertF.Stochastic imaging of spatial distributions using hard and soft information. Master’s thesis1987StanfordStanford University Matheron, G.: The Theory of Regionalized Variables and its Applications. Cahiers du Centre de Morphologie Mathématique de Fontainebleau, Ecole Nationale Supérieure des Mines de Paris, Paris (1971) Vargas, R., Gustafson, L.B., Vukasovic, M., Tidy, E., Skewes, M.A.: Ore breccias in the Río Blanco-Los Bronces porphyry copper deposit, Chile. In: Skinner, B.J. (ed.) Geology and Ore Deposits of the Central Andes, pp. 281–297. Society of Economic Geologists, Littleton (1999), Special Publication no. 7 OrtizJ.M.EmeryX.Geostatistical estimation of mineral resources with soft geological boundaries: a comparative studyJ. S. Afr. Inst. Min. Metall.20061068577584 EmeryX.Using the Gibbs sampler for conditional simulation of Gaussian-based random fieldsComput. Geosci.200733452253710.1016/j.cageo.2006.08.0032367793doi:10.1016/j.cageo.2006.08.003 GemanS.GemanD.Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of imagesIEEE Trans. Pattern Anal. Mach. Intell.1984667217410573.6203010.1109/TPAMI.1984.4767596 DavisM.W.Production of conditional simulations via the LU triangular decomposition of the covariance matrixMath. Geol.19871929198 RobertsG.O.SahuS.K.Updating scheme, correlation structure, blocking and parametrization for the Gibbs samplerJ. R. Stat. Soc. B.19975922913170886.6208310.1111/1467-9868.000701440584doi:10.1111/1467-9868.00070 G.O. Roberts (9106_CR23) 1997; 59 M.A. Skewes (9106_CR26) 2003; 38 A.G. Journel (9106_CR18) 1989; 21 A.G. Journel (9106_CR15) 1974; 69 X. Freulon (9106_CR11) 1993 J.M. Ortiz (9106_CR22) 2006; 106 C. Lantuéjoul (9106_CR19) 2002 S. Geman (9106_CR14) 1984; 6 X. Emery (9106_CR9) 2007; 69 F. Alabert (9106_CR1) 1987 X. Emery (9106_CR8) 2007; 33 P.H. Frikken (9106_CR12) 2005; 100 M. Armstrong (9106_CR3) 2003 J.P. Chilès (9106_CR4) 1999 A. Galli (9106_CR13) 2001; 33 H. Wackernagel (9106_CR28) 2003 M.W. Davis (9106_CR5) 1987; 19 C.V. Deutsch (9106_CR7) 1998 A.G. Journel (9106_CR17) 1978 9106_CR21 9106_CR25 X. Freulon (9106_CR10) 1994 9106_CR24 9106_CR27 F. Alabert (9106_CR2) 1987; 19 A.G. Journel (9106_CR16) 1986; 18 C.V. Deutsch (9106_CR6) 1997 P. Larrondo (9106_CR20) 2004 |
| References_xml | – reference: ChilèsJ.P.DelfinerP.Geostatistics: Modeling Spatial Uncertainty1999New YorkWiley0922.62098 – reference: LantuéjoulC.Geostatistical Simulation: Models and Algorithms2002BerlinSpringer0990.86007 – reference: GemanS.GemanD.Stochastic relaxation, Gibbs distributions, and the Bayesian restoration of imagesIEEE Trans. Pattern Anal. Mach. Intell.1984667217410573.6203010.1109/TPAMI.1984.4767596 – reference: EmeryX.Using the Gibbs sampler for conditional simulation of Gaussian-based random fieldsComput. Geosci.200733452253710.1016/j.cageo.2006.08.0032367793doi:10.1016/j.cageo.2006.08.003 – reference: JournelA.G.Constrained interpolation and qualitative information: the soft kriging approachMath. Geol.198618326928610.1007/BF00898032823434doi:10.1007/BF00898032 – reference: JournelA.G.RossiM.E.When do we need a trend model in kriging?Math. Geol.198921771573910.1007/BF00893318doi:10.1007/BF00893318 – reference: OrtizJ.M.EmeryX.Geostatistical estimation of mineral resources with soft geological boundaries: a comparative studyJ. S. Afr. Inst. Min. Metall.20061068577584 – reference: SkewesM.A.HolmgrenC.SternC.R.The Donoso copper-rich, tourmaline-bearing breccia pipe in central Chile: petrologic, fluid inclusion and stable isotope evidence for an origin from magmatic fluidsMiner. Depos.200338122110.1007/s00126-002-0264-9doi:10.1007/s00126-002-0264-9 – reference: AlabertF.The practice of fast conditional simulations through the LU decomposition of the covariance matrixMath. Geol.198719536938610.1007/BF00897191doi:10.1007/BF00897191 – reference: WackernagelH.Multivariate Geostatistics: An Introduction with Applications20033BerlinSpringer1015.62128 – reference: ArmstrongM.GalliA.Le Loc’hG.GeffroyF.EschardR.Plurigaussian Simulations in Geosciences2003BerlinSpringer – reference: GalliA.GaoH.Rate of convergence of the Gibbs sampler in the Gaussian caseMath. Geol.20013366536771011.8600810.1023/A:10110941312731956389doi:10.1023/A:1011094131273 – reference: AlabertF.Stochastic imaging of spatial distributions using hard and soft information. Master’s thesis1987StanfordStanford University – reference: JournelA.G.HuijbregtsC.J.Mining Geostatistics1978LondonAcademic Press – reference: DeutschC.V.JournelA.G.GSLIB: Geostatistical Software Library and User’s Guide19982New YorkOxford University Press – reference: DeutschC.V.BaafiE.Y.SchofieldN.A.Direct assessment of local accuracy and precisionGeostatistics Wollongong’961997DordrechtKluwer Academic115125 – reference: EmeryX.GonzálezK.E.Incorporating the uncertainty in geological boundaries into mineral resources evaluationJ. Geol. Soc. India.20076912938 – reference: RobertsG.O.SahuS.K.Updating scheme, correlation structure, blocking and parametrization for the Gibbs samplerJ. R. Stat. Soc. B.19975922913170886.6208310.1111/1467-9868.000701440584doi:10.1111/1467-9868.00070 – reference: Serrano, L., Vargas, R., Stambuk, V., Aguilar, C., Galeb, M., Holmgren, C., et al: The late Miocene to early Pliocene Río Blanco-Los Bronces copper deposit, Central Chilean Andes. In: Camus, F., Sillitoe, R.H., Petersen, R. (eds.) Andean Copper Deposits: New Discoveries, Mineralizations, Styles and Metallogeny, pp. 119–130. Society of Economic Geologists, Littleton (1996), Special Publication no. 5 – reference: LarrondoP.LeuangthongO.DeutschC.V.MagriE.OrtizJ.KnightsP.HenríquezF.VeraM.BarahonaC.Grade estimation in multiple rock types using a linear model of coregionalization for soft boundariesInternational Conference on Mining Innovation Minin 20042004SantiagoGecamin187196 – reference: FreulonX.ArmstrongM.DowdP.A.Conditional simulation of a Gaussian random vector with nonlinear and/or noisy observationsGeostatistical Simulations1994DordrechtKluwer Academic5771 – reference: Vargas, R., Gustafson, L.B., Vukasovic, M., Tidy, E., Skewes, M.A.: Ore breccias in the Río Blanco-Los Bronces porphyry copper deposit, Chile. In: Skinner, B.J. (ed.) Geology and Ore Deposits of the Central Andes, pp. 281–297. Society of Economic Geologists, Littleton (1999), Special Publication no. 7 – reference: DavisM.W.Production of conditional simulations via the LU triangular decomposition of the covariance matrixMath. Geol.19871929198 – reference: FrikkenP.H.CookeD.R.WalsheJ.L.ArchibaldD.SkarmetaJ.SerranoL.Mineralogical and isotopic zonation in the Sur-Sur tourmaline breccia, Río Blanco - Los Bronces Cu-Mo deposit, Chile: implications for ore genesisEcon. Geol.2005100593596110.2113/100.5.935doi:10.2113/100.5.935 – reference: Matheron, G.: The Theory of Regionalized Variables and its Applications. Cahiers du Centre de Morphologie Mathématique de Fontainebleau, Ecole Nationale Supérieure des Mines de Paris, Paris (1971) – reference: Robles, L., Emery, X., Ortiz, J.M.: Geostatistical simulation of mineral grades in the presence of spatial trends. In: Magri, E.J. (ed.) 33rd International Symposium on Applications of Computers and Operations Research in the Mineral Industry APCOM 2007, pp. 87–93. 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| SubjectTerms | Algorithms Copper Earth and Environmental Science Earth Sciences Geotechnical Engineering & Applied Earth Sciences Hydrogeology Mathematical Modeling and Industrial Mathematics Minerals Original Paper Rocks Simulation Soil Science & Conservation Statistics Studies |
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| Title | Simulation of mineral grades with hard and soft conditioning data: application to a porphyry copper deposit |
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