Nouveaux développements en géostatistique minière. New developments in mining geostatistics

Transcription

1 Ressources Minérales : la vision du Mineur Février 2012 Nouveaux développements en géostatistique minière New developments in mining geostatistics Jacques Rivoirard Responsable de l Équipe Géostatistique Centre de Géosciences

2 2 Multi-facies block models Domaining by clustering multivariate geostatistical data Variances for mineral resources classification High grade values and topcut

3 Multi-facies block models 3

4 4 How to estimate or simulate block grades when different facies are mixed? Convenio with Codelco, application to porphyry copper deposits S. Séguret (GEOMIN 2011) H. Beucher

5 CURRENT PRACTICE (1) Drilhole 1 Drilhole 2 Data Geological interpretation Proportions by block Block grades

6 CURRENT PRACTICE (2) Each block V is divided into facies (proportions p i = v i /V) n Z(V)= p Z( ) i=1 i v i * * * i n Z (V)= p Z ( ) i=1 v i

7 7 Here facies are alteration units UNITS (1&2) Unit 303, transitional zone.

8 8 alteration units 305 CMH Chloritic marginal low grade 318 PF Background potassic 312 Qz-Mo Quartz- Molibdenite 303 ZT Transition zone 301 QSP Pervasive Quartz Sericitic 307 PI Intense potassic 3092 PIR-East Intense Relict Potasic (East part) 3091 PIR-West Intense Relict Potasic (West part)

9 Geostatistical tools to analyze transitions between facies γ p(x i, x+h i) i (h) γ ij (h) p(x i, x+h j) γ γ ij i (h) (h) p(x+h j x i, x+h i) γ iz i γ i (h) (h) E[Z(x+h) x+h i, x i]

10 10 Preferential transitions from one facies to any other (per direction) N-S E-W vertical To From

11 11 Example of interpretation: Preferential transitions along direction

12 Average Cu grade when entering within unit

13 Comparison between estimated Cu block grades: -Traditional -Cokriging facies and their partial grades 13

14 14 Conclusion: Geostatistical tools: Analysis of transitions between facies Analysis of grades at transitions Multivariate models for facies indicators and grades: allows estimation of facies proportions and grades Also possibility to simulate facies and grades Pluri-gaussian truncated model for facies (work by Hélène Beucher) Developments to be done to take into account explicitly non-stationarities

15 15 Domaining by clustering multivariate geostatistical data

16 16 Domaining = define domains that are homogeneous with respect of a number of parameters (rock type, alteration, grades ) time-consuming rapidly leads to a high combinatory Tool under development: statistical classification method in spatial context to help defining domains (i.e. clusters of data) Geological and Geostatistical Domaining Consortium (G2DC) by Géovariances with MINES-ParisTech Romary et al., 2012

17 Toy example 17 exhaustive (unknown) sample data How to classify sample data into 2 domains? (and then: delineate these domains)

18 Toy example 18 Examples of classification into 2 domains Classical k-means method based on (x,y,z) Method developed: ascending hierarchical method + spatial connections (iterative clustering of data or groups of data presenting similarities and spatially connected)

19 Uranium deposit dataset 19 Flat, elongated deposit at the contact between socle and sandstone Variables considered: Coordinates: X, Y and Z uranium grades geological factor: socle or sandstone hematization degree

20 Results of clustering data down to 6 clusters 20

21 21

22 22 The differentiation between black and red is only due to grade. Black high grades are intrincated with neighboring red lower grades We would like to mix those, but next iteration would mix black and cyan!

23 23 At present the method provides a help to domaining, but a number of developments are still to be done: Investigate different ways to connect points in 3D Identify and merge intrincated clusters Merge clusters that would give a stationary set How to treat missing values of some variables? Another point is the delineation of such clusters, when these are identified

24 24 Variances for mineral resources classification

25 25 Mineral resources classification: Largely subjective, depending on the competent person Where possible, uncertainties to be assessed by objective tools

26 26 Geostatistics to assess uncertainties coming from spatial sampling: Repeated geostatistical conditional simulations of the deposit Powerful but demanding in hypotheses See presentation by Deraisme Estimation variances for set of blocks, application to porphyry copper deposits (Codelco convenio), Rivoirard and Chilès (2011)

27 27 Example: mean grade Z(V) within a given volume V Z(V)* The estimation variance summarizes the uncertainty of Z(V) around its estimate Z(V)*

28 28 Estimation variance for a set of blocks Easy but incorrect way: combine block variances, e.g. kriging variances Block errors are correlated unless blocks are estimated by inner samples only kriging variance considers data location, but actual variances tend to be higher where grades are higher Model and apply the proportional effect between variances and means

29 Porphyry copper deposit The variability of sample grades within a block increases with their mean grade (proportional effect) samples standard deviation samples mean

30 Modeling the proportional effect : not straightforward, as the variability is also known to depend on the number and location of samples in the block > Estimation of a local variability factor, depending on variogram and local mean 30

31 kriging std Such a local variability factor can be applied to customize estimation variances 6 6 Example: 5 10 big blocks in a high grade zone 4 combining classical kriging variances: 4 3 CV = 5% estimation from inner samples + proportional effect: 1 1 CV = 12% 0 Before customization rho= customized kriging standar After customization kriging from inner data kriging from inner data 31

32 Example: 10 big blocks in a high grade zone combining classical kriging variances: CV = 5% estimation from inner samples + proportional effect: CV = 12% 32

33 33 Conclusion: Easy combination of variances for any set of informed blocks Modeling proportional effect through a local variability factor to be validated on simulations (reference known)

34 High grade values and topcut 34

35 35 Part of the general problem of handling high grade values Frequencies Collaboration with Cogéma Aréva ( ) Rivoirard, Demange, Freulon, Lécureuil, Bellot, to be published 2012

36 Topcut 36 A current practice in gold deposits (skew histogram, with few high values) One truncates the grade Z(x), and estimates the truncated grade: min(z(x), z e ), minimum between grade and topcut value z e Estimated block grades are more realistic but: Where has gone the missing metal? How to choose the topcut value z e? z e

37 Topcut model 37 Z(x) = min(z(x), z e ) + [m(z e )- z e ] 1{Z (x) > z e } + R(x) = truncated + indicator + residual variable of presence of high values Topcut value z e : chosen to put the highest amount of nugget variability in the residual Estimation: based on the truncated variable and on the indicator The model distributes the missing metal where the high grades have the higher chance to be located

38 Estimations (vertical sections) 38 Presence of values > topcut (indicator) 10m 20m Truncated grade Grade estimated using topcut model Kriged grade Fig Xavier Freulon

39 39 Conclusion Robust estimation, albeit taking high values into account Intermediary between ordinary kriging and non-linear techniques A step towards other, more general and more flexible, non-linear techniques

40 Thank you FLUMY Mines-ParisTech