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Optimisation of ISL Resource Models by Incorporating Algorithms For Quantification Risks: geostatistical approach Dr. M.Abzalov

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Page 1: Optimisation of ISL Resource Models by Incorporating ... · by Incorporating Algorithms For Quantification Risks: geostatistical approach ... What is geostatistics? 6 ... 1997:Geostatistics

Optimisation of ISL Resource Models by Incorporating Algorithms For

Quantification Risks:geostatistical approach

Dr. M.Abzalov

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This presentation has been prepared by Rio Tinto plc and Rio Tinto Limited (“Rio Tinto”) and consisting of the slides for a presentation concerning Rio Tinto. By reviewing/attending this presentation you agree to be bound by the following conditions.

Forward-Looking StatementsThis presentation includes forward-looking statements. All statements other than statements of historical facts included in this presentation, including, without limitation, those regarding Rio Tinto’s financial position, business strategy, plans and objectives of management for future operations (including development plans and objectives relating to Rio Tinto’s products, production forecasts and reserve and resource positions), are forward-looking statements. Such forward-looking statements involve known and unknown risks, uncertainties and other factors which may cause the actual results, performance or achievements of Rio Tinto, or industry results, to be materially different from any future results, performance or achievements expressed or implied by such forward-looking statements.

Such forward-looking statements are based on numerous assumptions regarding Rio Tinto’s present and future business strategies and the environment in which Rio Tinto will operate in the future. Among the important factors that could cause Rio Tinto’s actual results, performance or achievements to differ materially from those in the forward-looking statements include, among others, levels of actual production during any period, levels of demand and market prices, the ability to produce and transport products profitably, the impact of foreign currency exchange rates on market prices and operating costs, operational problems, political uncertainty and economic conditions in relevant areas of the world, the actions of competitors, activities by governmental authorities such as changes in taxation or regulation and such other risk factors identified in Rio Tinto's most recent Annual Report on Form 20-F filed with the United States Securities and Exchange Commission (the "SEC") or Form 6-Ks furnished to the SEC. Forward-looking statements should, therefore, be construed in light of such risk factors and undue reliance should not be placed on forward-looking statements. These forward-looking statements speak only as of the date of this presentation.

Nothing in this presentation should be interpreted to mean that future earnings per share of Rio Tinto plc or Rio Tinto Limited will necessarily match or exceed its historical published earnings per share.

Cautionary Statement

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It is based on detailed and reliable It is based on detailed and reliable exploration, sampling and testing exploration, sampling and testing ……. The locations are spaced . The locations are spaced closely enough to confirm closely enough to confirm geological and grade continuity geological and grade continuity

Tonnage,Tonnage, densities, shape, physical densities, shape, physical characteristics,characteristics, grade and mineral content grade and mineral content can be estimated with a can be estimated with a high level high level of of confidenceconfidence

Measured

The locations are too widely or The locations are too widely or inappropriately spaced to confirm inappropriately spaced to confirm geological and /or grade geological and /or grade continuity but are spaced closely continuity but are spaced closely enough for continuity to be enough for continuity to be assumed assumed

TonnageTonnage, , densities, shape, physical densities, shape, physical characteristics,characteristics, grade and mineral content grade and mineral content can be estimated with a can be estimated with a reasonable levelreasonable level of of confidenceconfidence

Indicated

May be limited or of uncertain quality May be limited or of uncertain quality and reliability and reliability Tonnage, grade and mineral content can be Tonnage, grade and mineral content can be

estimated withestimated with low levellow level of confidenceof confidenceInferred

LowHigh

Confidence levelDataDefinitionCategory

It is based on detailed and reliable It is based on detailed and reliable exploration, sampling and testing exploration, sampling and testing ……. The locations are spaced . The locations are spaced closely enough to confirm closely enough to confirm geological and grade continuity geological and grade continuity

Tonnage,Tonnage, densities, shape, physical densities, shape, physical characteristics,characteristics, grade and mineral content grade and mineral content can be estimated with a can be estimated with a high level high level of of confidenceconfidence

Measured

The locations are too widely or The locations are too widely or inappropriately spaced to confirm inappropriately spaced to confirm geological and /or grade geological and /or grade continuity but are spaced closely continuity but are spaced closely enough for continuity to be enough for continuity to be assumed assumed

TonnageTonnage, , densities, shape, physical densities, shape, physical characteristics,characteristics, grade and mineral content grade and mineral content can be estimated with a can be estimated with a reasonable levelreasonable level of of confidenceconfidence

Indicated

May be limited or of uncertain quality May be limited or of uncertain quality and reliability and reliability Tonnage, grade and mineral content can be Tonnage, grade and mineral content can be

estimated withestimated with low levellow level of confidenceof confidenceInferred

LowHigh

Confidence levelDataDefinitionCategory

Modern reporting codes (for example JORC, NI43-101) enable Mineral Resources to be classified as Measured, Indicated or Inferred depending on the confidence of their estimation

Preamble

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Probabilistic, based on GEOSTATISTICAL (i.e. mathematically sophisticated) estimation of uncertainty (i.e. error quantified)less subjective

Intuitive and highly subjective

Approaches to Define Resource Categories Vary from:Preamble

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Spherical:

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There is a better way to explain it which you will see in my next slides

What is geostatistics?

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6

GeoSTATISTICS studies this

STATISTICS studies this

What is geostatistics?

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Conditional Simulation (COSIM) is an algorithm which applies theMonte-Carlo simulation to spatially distributed variables (i.e. regionalised variables). In other words this is nothing but spatiallyconsistent Monte-Carlo simulation.The methodology allows to generate the images mimicking spatial distribution of the studied variable and honouring the actual data. Each generated image, that mimics spatial distribution of the studied variable, represents equiprobable realisation of the COSIM model. Differences between equiprobable realisations depend on spatial distribution pattern of the studied variable and data points (e.g. drilling grid).Creating statistically meaningful number of realisations (e.g. 25), uncertainty of the studied variable can be quantified by grouping COSIM realisations and statistically analysing them.Chilès and Delfiner, 1999: Geostatistics: modelling spatial uncertainty: John Wiley and Sons, New York, 695p.Goovaerts, 1997: Geostatistics for natural resources evaluation: Oxford University Press, New York, Oxford, 483p.

Principals of methodology:Estimation of Mineral resource Uncertainty

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# 1 # 25

Thickness (m)

# 1 # 25100 x 100 (m)

500 x 500 (m)

Equiprobable realisations of the SGS model showing the thickness of ore body (Abzalov and Bower, 2009)

SD0.3

SD 0.6

Principals of methodology:Estimation of Mineral resource Uncertainty

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Personal experience of using Conditional Simulation methodology at the different deposit types shows that modelling algorithms and

procedures can significantly differ depending on commodity, mineralisation styles and mining technologies.

Case studies of the methodology:Abzalov, M.Z. and Bower, J. 2009: Optimisation of the drill grid at the Weipa bauxite deposit using conditional simulation. in (eds.AusIMM) 7th International Mining Geology Conference, p.247 - 251.Abzalov, M.Z., Menzel, B., Wlasenko, M. and Phillips, J. 2007: Grade control at the Yandi iron ore mine, Pilbara region, Western Australia: comparative study of the blastholes and RC holes sampling. in (eds. AusIMM) Proceedings of the iron ore conference, 20-22 August, 2007, Perth, Western Australia, p. 37 - 43.Abzalov, M.Z. and Mazzoni, P. 2004: The use of conditional simulation to assess process risk associated with grade variability at the Corridor Sands detrital ilmenite deposit. in (eds. R.Dimitrakopoulus and S.Ramazan) Ore body modelling and strategic mine planning: uncertainty and risk management, p.93-101.Abzalov, M.Z. and Humphreys, M. 2002: Resource estimation of structurally complex and discontinuous mineralisation using non-linear geostatistics: case study of a mesothermal gold deposit in northern Canada. Exploration and Mining Geology, v.11, No1-4, p.19-29.

The current paper discusses specific features of application COSIM methodology to ISL-projects

Principals of methodology:Estimation of Mineral resource Uncertainty

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Geological and resource models of ISL projects are mainly inferred from geophysical data with a very limited amount of directly observed geological information.Uranium grades are almost entirely estimated from downhole gammalogs which are calibrated by a small number of diamond core assays. This approach contains a significant risk of precision errors and possibly biased grade estimates.Thickness of ore grade zones and their geometry are extremely variable and these are the key parameters for accurate estimation of reserves.The resource models include different chemical and physical characteristics of mineralisation and the host rocks (e.g. U grade, carbonate content, permeability of sediments).

Specific features of ISL uranium projects which need to be addressed by COSIM methodology

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DISCLAIMERThis case study is based on data from the different ISL deposits which were combined to create a representative image of a sandstone-hosted deposit resembling several known ISL amenable deposits but not exactly matching any of them.For confidentiality reason the grade and thickness values have been changed by multiplying on a constant.

SCOPE of the CURRENT STUDY: ( 1 ) Resource Classification and Optimisation Production Drilling Grids( 2 ) Downhole Geophysical Logs vs. Diamond Core Assays( 3 ) Calibration and Correction of the Geophysical (gamma) Logs

Case Study: Quantification of ISL Resource Uncertainty

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A deposit contains several generations of the tabular and roll-type mineralisation which was formed by multiple hydrothermal episodes

Thickness (m)

U (%)

Geological Background

Scatter diagram: U% vs. Thickness

300 m

N

Case Study: Quantification of ISL Resource Uncertainty

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13Representative cross section of a deposit

Geological Background

20 m

50 m

West East

Case Study: Quantification of ISL Resource Uncertainty

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Average U Grade, %

Total Thickness of the Ore Grade Intersections

Grade and Thickness of Uranium Mineralisationbased on drill holes shown as black dots on the maps

Geological Background

Case Study: Quantification of ISL Resource Uncertainty

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( 1 ) Resource Classification and Optimisation Production Drilling Grids

( 2 ) Downhole Geophysical Logs vs. Diamond Core Assays( 3 ) Calibration and Correction of the Geophysical (gamma) Logs

In this study it will be shown how Conditional Simulation methodology can be applied to quantitatively measure the Level of Confidence of the Uranium Resources

Case Study: Quantification of ISL Resource Uncertainty

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Classification and Production Grids

Example: 3 equiprobable models (realisations) of the Total Thickness of uranium mineralisation

(#00044) (#00021)

Metres

(#00002)

Uncertainty in Thickness and Grade were estimated by Conditional Simulation which was applied to existing data

Case Study: Quantification of ISL Resource Uncertainty

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Errors in Estimated Thickness of the Uranium Mineralisation (95% CL) [point model]

Absolute Error (2SD)

+/- metres

Classification and Production Grids

Case Study: Quantification of ISL Resource Uncertainty

Absolute Error (2SD)

+/- U%

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Err. %Errors in Estimated Thickness of the Uranium Mineralisation (95% CL) [production cells 50 x 50 m]

Absolute Error (2SD)

+/- metresRelative Error (2SD/Mean)

Classification and Production Grids

Case Study: Quantification of ISL Resource Uncertainty

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Errors in Estimated Uranium Grade (95% CL) [production cells 50 x 50 m]

Relative Error (2SD/Mean)

Absolute Error (2SD)

+/- U%Err. %

Classification and Production Grids

Case Study: Quantification of ISL Resource Uncertainty

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20

50

0

Err % Indicated (3)U% 0.105 +/-0.016200

100

150

0.20

0.10

0.05

0.

U%

Indicated (2)U% 0.088 +/-0.020

Indicated (1)U% 0.119 +/-0.026

MeasuredU% 0.094 +/-0.008

InferredU% 0.101 +/-0.018

Resource Categories and their Estimation Uncertainties – U gradeResults

Case Study: Quantification of ISL Resource Uncertainty

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Indicated (3)(metr.) 13.2 +/-0.97

50

0

Err %200

100

150

20

15

50

metres

Indicated (2)(metr.) 9.2+/-1.12

Indicated (1)(metr.) 15.9 +/-1.45

Measured(metr.) 16.7 +/-0.47

InferredThickness (metres) 9.2 +/-0.76

10

Case Study: Quantification of ISL Resource Uncertainty

Resource Categories and their Estimation Uncertainties – ThicknessResults

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( 1 ) Resource Classification and Optimisation Production Drilling GridsThe proposed approach allows to define resource categories non-subjectively using their estimation uncertainty as a criteria of the resource CONFIDENCE;Uncertainty of production cells (e.g. square 50 x 50 m studied in Case 1) can be quantitatively measured and this can be used as additional criteria for optimisation of production grids;The proposed approach allows us to non-subjectively correlate different reporting systems, in particular the GKZ systems, officially adopted in the FSU countries, and JORC Code resources Practice of application the above methodology to ISL projects require consideration of reliability of geophysical data which are the main data source for estimation of Uranium grades of the ISL amenable uranium mineralisation

( 2 ) Downhole Geophysical Logs vs. Diamond Core Assays( 3 ) Calibration and Correction of the Geophysical (gamma) Logs

Case Study: Quantification of ISL Resource Uncertainty

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( 1 ) Resource Classification and Optimisation Production Drilling Grids( 2 ) Downhole Geophysical Logs vs. Diamond Core Assays

( 3 ) Calibration and Correction of the Geophysical (gamma) Logs

In the previous study (Case 1) uncertainty of the resources have been estimated assuming that downhole gamma survey accurately represents the actual U% grade and thickness of the mineralised zones. In other words, correlation between U% grades and thicknesses deduced from geophysical logs is identical (i.e. their correlation > 0.95)

In reality, correlation between geophysical data and actual grades and/or thicknesses of mineralised zones can be significantly lower then was assumed in the Case 1 study. In order to assess an impact of poor correlation between geophysical data and results deduced from diamond core assays the two other cases have been studies:

Case 2: gamma logs moderately correlate with diamond core assays (r ~ 0.8)Case 3: gamma logs poorly correlate with diamond core assays (r ~ 0.7)

Case Study: Quantification of ISL Resource Uncertainty

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Uranium Grade (U, %)Gamma Logs vs. Diamond Core Assays

‘True’ grade Case 2: model generated from gamma logs (r = 0.81)

Case 3: model generated from gamma logs (r = 0.72)

U% (Target)

U%: case 2 Gamma Log

U% (Target)

U%: case 1 Gamma Log

r = 0.72r = 0.81

0.30

0.10

0.05

0

U%

Case Study: Quantification of ISL Resource Uncertainty

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Thickness (m)Gamma Logs vs. Diamond Core Assays

True Thickness (Target)

Thickness: case 2 Gamma LogThickness: case 1 Gamma Log

r = 0.69r = 0.82True Thickness (Target)

‘True’ thickness Case 2: model generated from gamma logs

Case 3: model generated from gamma logsmetres

30

20

10

0.

Case Study: Quantification of ISL Resource Uncertainty

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Gamma Logs vs. Diamond Core AssaysError (CL95%) in the Modelled U% GradeError (CL95%) in the Modelled Thickness

Drill Grids When Estimation Error Does not Exceed +/- 10% ThresholdHigh Quality Data (Target Variable) : 125x125 100x100Suboptimal Geophysical Data (Case 2: r = 0.8): 100x100 75x75

(Case 3: r = 0.7): 75x75 50x50

0

5

10

15

20

25

0 50 100 150 200 250SQUARE GRID (m)

UNCE

RTAI

NTY (

%)0

5

10

15

0 50 100 150 200 250SQUARE GRID (m)

UNCE

RTAI

NTY (

%)

Model: based on target variableModel: based on auxiliary variable (CASE 2)Model: based on auxiliary variable (CASE 3)10% threshold

Case Study: Quantification of ISL Resource Uncertainty

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( 1 ) Resource Classification and Optimisation Production Drilling Grids

( 2 ) Downhole Geophysical Logs vs. Diamond Core AssaysThe studied cases have shown that at the same deposit drill spacing required for accurate estimation of the reserves can vary from 100 x 100 m to 50 x 50 m depending on representativeness of the geophysical data:

(i) justification of the drill spacing for definition resources categories should include comparative geostatistical analysis of the downhole gamma logs and diamond core assays;

(ii) optimal ratio of the diamond core assays vs. downhole gamma-logs should be determined for each project separately and this depends on degree of the deposit’s complexity and representativeness of the geophysical data

In the previous studies we have analysed the impact of a suboptimal precision of the geophysical data (i.e. excessive noise of the logged gamma values and their poor repeatability) Unfortunately, downhole gamma values often produce the biased results which need to be corrected. This will be reviewed in the last section of this paper.

( 3 ) Calibration and Correction of the Geophysical (gamma) Logs

Case Study: Quantification of ISL Resource Uncertainty

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( 1 ) Resource Classification and Optimisation Production Drilling Grids( 2 ) Downhole Geophysical Logs vs. Diamond Core Assays( 3 ) Calibration and Correction of the Geophysical (gamma) Logs

Challenges with calibration:

Non-linear relationships between radiometric data and actual (assayed) grades

Representativity of the assay data

What portion of the geophysically (gamma) logged holes should be confirmed by diamond core drilling

Calibration algorithm

Case Study: Quantification of ISL Resource Uncertainty

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Calibration and Correction of the Gamma Logs

The different data generations are best integrated using multivariate geostatistical techniques. In particular, the casestudy by the current author (Abzalov and Pickers, 2005) has shown that integration different data significantly improves if to use geostatistical techniques of the Co-Kriging (COK) or External Drift (KED) familiesIn the current study technique known as Conditional Simulation with External Drift was applicable to ISL-projects

Comments on the Methodology

Abzalov, M.Z. and Pickers, N. 2005: Integrating different generations of assays using multivariate geostatistics: a case study. Transactions of Institute of Mining and Metallurgy. (Section B: Applied EarthScience). v.114,p. B23-B32.

Case Study: Quantification of ISL Resource Uncertainty

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Calibration and Correction of the Gamma Logs

•The background information (case 2) is represented by numeric model of the U% grade deduced from the downhole gamma logs. •Target variable is an assayed U% grades.

DATA

TARGET grade: AVR. 0.083% U Background (Case 2): AVR 0.095% U

0.30

0.10

0.05

0.

U%

DEDUCED from GAMMA LOGS: U%

TARGET: U%

Case Study: Quantification of ISL Resource Uncertainty

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Calibration and Correction of the Gamma LogsModelled by External Drift Algorithms

150 x 150 TARGET gridBackground (Case 2)

External Drift Model: U% (generated from 100x100m)

100 x 100 TARGET grid

0.30

0.10

0.05

0.

U%

Background (case 2): U%

Target: U%

Target: U%

External Drift Model: U% (generated from 150x150m)

Target

Target: U%

Case Study: Quantification of ISL Resource Uncertainty

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Average U% grade estimated from different sets of dataCalibration and Correction of the Gamma Logs

0.075

0.080

0.085

0.090

0.095

0.100

0.105

0.110

0.115

0.120

0 50 100 150 200 250SQUARE GRID (m)

U (%

)

Model: based on target variableModel: based on auxiliary variable (CASE 2)COSIM with External DriftU% (true)

Case Study: Quantification of ISL Resource Uncertainty

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( 1 ) Resource Classification and Optimisation Production Drilling Grids

( 2 ) Downhole Geophysical Logs vs. Diamond Core Assays

( 3 ) Calibration and Correction of the Geophysical (gamma) LogsDownhole geophysical gamma logs can be calibrated using non-stationary geostatistical techniques, such as Kriging with External Drift (KED) or Conditional Simulation with external Drift (SED). In the current case study the SED approach has produced a non-biased model from a small amount of diamond core drill holes distributed as 150 x 150m grid which was integrated with geophysical data used as background information (auxiliary variable of external drift) It is noted that non-stationary geostatistical techniques honour distribution patternof the auxiliary data. Therefore, if geophysical radiometric logs poorly correlate with actual uranium grades assayed from diamond core samples this error (i.e. poor correlation) will remain in the External Drift model.

Case Study: Quantification of ISL Resource Uncertainty

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Proposed technique allows to classify ISL - project resources based on estimation errors which makes classification transparent and non-subjective;In particular, it allows non-subjectively correlate resource categories adopted by JORC and/or NI 43 -101 systems with GKZ resources used in the FSU countries; At the hands of the project managers the proposed techniques is a powerful tool for the project’s risk analysis allowing early diagnostics of the high risk areas based on the quantified uncertainty of the estimated parameters;Technique allows to find an optimal drill grid and proportions between geophysically surveyed rotary drill holes and diamond core holes for accurate definition of the resource and reserves

SUMMARY and CONCLUSIONS

Case Study: Quantification of ISL Resource Uncertainty

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THANK YOU

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Sequential Gaussian simulation (SGS) is a Gaussian-based method of conditional simulation (Chilès and Delfiner, 1999; Goovaerts, 1997). This method uses data transformed to a Gaussian distribution with a zero mean and a unit variance (ie Gaussian anamorphosis), which is then used to simulate spatial distribution of the variable of interest. Simulated realisation is achieved by defining a random path through thegrid nodes including the conditioning data, which has been migrated to the nearest grid nodes and considered as hard data. A sequential neighbourhood of the target node is established, which includes hard data (original data) and already simulated nodes used to calculate a local conditioning distribution and derive asimulated value at the target node. The simulated value is determined as:Zs = ZK + σKUwhere:Zs is SGS simulated valueZK simple kriging estimateσK standard deviation of the kriging estimateU a random normal functionAs the SGS method assumes multi-Gaussian property of the studied Random variable and its diffusive distribution model, these assumptions need to be tested prior to application of themodelling methodology. Border effect can be tested by calculating the ratios between cross-variograms of the indicators and indicator variograms (Abzalov and Humphreys, 2002, 2003).Multi-Gaussianity can be tested by calculating variograms of indicators calculated for the chosen data percentiles and comparing them with indicator variograms calculated for the same percentiles of the Gaussian transformed data (Goovaerts, 1997).

APPENDIX (1)Explanation of the Sequential Gaussian Simulation (SGS) Methodology