IRON ORE 2015, July 2015, Perth Australia. Danny Kentwell

Transcription

1 IRON ORE 2015, July 2015, Perth Australia Danny Kentwell

2 Overview The problem Block estimation totals with a full suite of elements/oxides do they sum to 100%? Case study 2 examples dense data and sparse wide spaced data Do the assays total 100%? How do we attempt to ensure block estimates total 100%? Why would they not? Standard approach Ordinary Kriging (OK) Rigorous approach Co Kriging Slack approach ID2 Alternative approach Min/Max Autocorrelation factors (MAF) Results Conclusions 2 of 31

3 The Problem The deposit, comprising 85 domains, was estimated using ordinary kriging. Individual variables validated well against samples at zero cut off. Block total averages were all within 0.5% of 100% Howver several domains showed significant numbers of blocks exceeding +/ 3% deviation from 100%. 1. Are the block total discrepancies a material problem for JORC reporting? 2. How can we estimate so that individual block totals are closer to 100%? 3 of 31

4 The Case Study Real deposit 85 magnetite and hematite domains 8elements / oxides + LOI (and DTR) Examples from two of the domains that had the worst block total deviations from 100% Magnetite (BIF) domain samples 216 Fe Classified as majority Measured (1 km grid) Hematite (MIM) domain samples 2 Fe classified as majority Indicated (100m grid) 4 of 31

5 Scenarios Test alternative estimation methods Co kriging ID2 unrestricted ID2 restricted high grade neighborhoods Min/Max Autocorrelation factors 5 of 31

6 Assay Suite Total Examples Element / Oxide % in Hematite % in Magnetite Fe 2 O 3 or Fe 3 O SiO Al2O MgO LOI S P2O MnO K2O Total don t forget the oxide conversions if your assays are supplied as elements rather than oxides don t forget loss on ignition (LOI) LOI can be negative! 6 of 31

7 Correlations Magnetite (domain 22401) VARIABLE FE SIO2 AL2O3 MGO LOI FE SIO AL2O MGO LOI Hematite (domain 31521) VARIABLE FE SIO2 AL2O3 MGO LOI FE SIO AL2O MGO LOI Examples from case study samples 7 of 31

8 Standard Approach - Ordinary Kriging Industry default method Accounts for different spatial variability of each variable by using independent variogram models Available in many different software packages 8 of 31

9 Problems with OK Estimates one variable at a time Independent variogram models Takes no account of any correlation Takes no account of 100% total Can have different search neighborhoods for each variable Individual block totals can be much further away from 100% than the assays used to estimate! Variogram : FE Distance (m) Variogram : SIO Distance (m) Variogram : AL2O Distance (m) Variogram : MGO Distance (m) Variogram : LOI Distance (m) 9 of 31

10 Rigorous Approach Co-Kriging Estimates several variables at once Accounts for different spatial variability of each variable by using variogram models and cross variograms for all variables at once Accounts for correlations Used a single search neighborhood Improves block totals Co Kriging of 5 elements requires 15 variograms to be modelled simultaneously in three directions (5 primary variograms and 10 cross variograms) 10 of 31

11 Problems with Co-Kriging Difficult and time consuming to model variograms and cross variograms n variables require simultaneous fitting of n(n+1)/2 variogram models This problem is exacerbated if there are many domains The case study deposit had 85 domains and 9 assay suite variables to estimate in each. 765 variograms to model for ordinary kriging 3825 variograms for full co kriging! Can produce negative estimates 11 of 31

12 Slack Approach - Inverse Distance Squared - ID2 Simple to implement Zero time to model spatial variability! Exactly the same spatial variability assumption for all variables Improves block totals if used with a single search neighborhood 12 of 31

13 Problems with ID2 Poor local and global estimator No account for different spatial variability of different variables Only limited control over orientation of trends via changes in search neighborhood 13 of 31

14 Alternative Approach Min/Max Autocorrelation Factors - MAF Mathematical manipulation of a set of variables Produces a set of de correlated factors that can be estimated independently and then be back transformed to original variable distributions Removes the requirement to model cross variograms Accounts for different spatial variability of each variable As implemented in the Geovariances Isatis software package Variogram : MAF Distance (m) Variogram : MAF Distance (m) Variogram : MAF Distance (m) Variogram : MAF Distance (m) Variogram : MAF Distance (m) 14 of 31

15 Problems with MAF Designed for use with simulation, not estimation * Can produce negative estimates Only implemented in specialised software packages * The Isatis implementation of MAF is designed for use with Gaussian transformed variables for simulation. Gaussian MAF factors cannot be used for block estimation as no suitable block back transform is available. For this study raw variables were used directly for factorisation and block estimation. SRK and Geovariances are not aware of anyone else ever using MAF for direct block estimation (please let me know if you have!). 15 of 31

16 Results Block total statistics Mag Totals Count Min Max Mean Sd n < 97 n > 103 % < 97 % > 103 Composites % 0% OK % 4% ID2 (unrestricted) % 0% ID2 (restricted) % 0% 5 El MAF % 0% Co Kriged (restricted) % 0% Hem Totals Count Min Max Mean Sd n < 97 n > 103 % < 97 % > 103 Composites OK % 10% ID2 (unrestricted) % 0% ID2 (restricted) % 0% 5 El MAF % 0% Co Kriged (restricted) % 0% MAF produces the lowest Block Total standard deviation. I.E. the tightest range of total values. 16 of 31

17 Block Total distributions Standard deviation of block total distributions Magnetite OK (restricted) ID2 (unrestricted) ID2 (restricted) 5 El MAF Co Kriged (restricted) Standard deviation of block total distributions Hematite OK (restricted) ID2 (unrestricted) ID2 (restricted) 5 El MAF Co Kriged (restricted) 17 of 31

18 Deviation from 100% Number of blocks exceening +/ 3% from 100% Magnetite OK (restricted) ID2 (unrestricted) ID2 (restricted) 5 El MAF Co Kriged (restricted) Number of blocks exceeding +/ 3% from 100% Hematite OK (restricted) ID2 (unrestricted) ID2 (restricted) 5 El MAF Co Kriged (restricted) 18 of 31

19 Magnetite Totals OK ID2 ID2 Restricted Co Kriging MAF 19 of 31

20 22401 Fe OK ID2 ID2 Restricted Co Kriging MAF 20 of 31

21 22401 Al2O3 OK ID2 ID2 Restricted Co Kriging MAF 21 of 31

22 22401 Curves blocks weighted by proportion of block in domain wireframe 22 of 31

23 Hematite Totals OK ID2 ID2 Restricted Co Kriging MAF 23 of 31

24 31521 Fe OK ID2 Co Kriging MAF 24 of 31

25 31521 Al2O3 OK ID2 ID2 Restricted Co Kriging MAF 25 of 31

26 31251 Curves 513 blocks weighted by proportion of block in domain wireframe 26 of 31

27 Variogram Modelling OBSERVATION: Variogram modelling had more effect on the sensitivity of the block totals that any of the estimation methods, particularly in domains with sparse data. 27 of 31

28 Implications for public reporting and JORC code classification None There are no significant change in tonnages and grades at reporting cut off for either domain between OK and Co Kriging and MAF. The results of the different estimation methods do not change the potential economic viability of the Resource. I.E. Globally there is no significant difference between the estimation methods (excluding ID2). 28 of 31

29 Implications for detailed mine planning and grade control Where close spaced sampling is available MAF and Co Kriging produce more robust estimates than OK. I.E. Locally MAF and Co Kriging are likely to be superior to OK in terms of final selectivity. 29 of 31

30 Conclusions Co Kriging, MAF and ID2 all produce better block totals than OK MAF can successfully be used for estimation as well as simulation. Fitting of variograms with MAF is less time consuming than with Co Kriging. MAF and Co Kriging appear to produce similar results however both have their own anomalies at local scale that, in SRK s opinion, are most likley due to differences in variogram modelling rather than estimation method. 30 of 31

31 31 of 31 Thank you