Contents 1 Introduction 2 Statistical Tools and Concepts

Transcription

1 1 Introduction Objectives and Approach Scope of Resource Modeling Critical Aspects Data Assembly and Data Quality Geologic Model and Definition of Estimation Domains Quantifying Spatial Variability Geologic and Mining Dilution Recoverable Resources: Estimation Recoverable Resources: Simulation Validation and Reconciliation Resource Classification Optimal Drill Hole Spacing Medium- and Short-term Models Grade Control Historical Perspective... 8 References Statistical Tools and Concepts Basic Concepts Probability Distributions Univariate Distributions Parametric and Non-parametric Distributions Quantiles Expected Values Extreme Values Outliers Multiple Variable Distributions Spatial Data Analysis Declustering Declustering with Multiple Variables Moving Windows and Proportional Effect Trend Modeling Gaussian Distribution and Data Transformations Data Integration and Inference Exercises Part One: Calculus and Algebra Part Two: Gaussian Distribution Part Three: Uniform Distribution vii

2 viii Part Four: Small Declustering Part Five: Large Declustering References Geological Controls and Block Modeling Geological and Mineralization Controls Geologic Interpretation and Modeling Distance Functions and Tonnage Uncertainty Geostatistical Geologic Modeling Visualization Scale Data Block Model Setup and Geometry Coordinate Systems Stratigraphic Coordinates Block Models Block Size Block Model Geometry Block Model Volume and Variables Summary of Minimum, Good and Best Practices Exercises Part One: Vein Type Modeling Part Two: Coordinate Systems References Definition of Estimation Domains Estimation Domains Defining the Estimation Domains Case Study: Estimation Domains Definition for the Escondida Mine Exploratory Data Analysis of the Initial Database Initial Definition of Estimation Domains Tcu Grade Correlogram Models by Structural Domains Final Estimation Domains Boundaries and Trends Uncertainties Related to Estimation Domain Definition Summary of Minimum, Good and Best Practices Exercises Part One: Basic Statistics Part Two: 2-D Trend Modeling Part Three: 3-D Trend Modeling References Data Collection and Handling Data Location of Drill Holes, Trenches, and Pits Sampling Methods and Drilling Equipment Used Relative Quality of Each Drill Hole or Sample Type Sampling Conditions Core and Weight Sample Recoveries Sample Collection and Preparation Procedures Geologic Mapping and Logging Procedures Sample Preparation and Assaying Procedures Sampling Database Construction... 72

3 ix 5.2 Basics of Sampling Theory Definitions and Basic Concepts Error Basics and Their Effects on Sample Results Heterogeneity and the Fundamental Error Liberation Size Method Fundamental Sample Error, FE The Nomograph Nomograph Construction Sampling Fundamental Error Segregation or Distribution Heterogeneity Delimitation and Extraction Errors Preparation Error Sampling Quality Assurance and Quality Control General Principles Elements of a QA/QC Program Insertion Procedures and Handling of Check Material Evaluation Procedures and Acceptance Criteria Statistical and Graphical Control Tools Variables and Data Types Raw and Transformed Variables Soft Data Compositional Data Service Variables Compositing and Outliers Drill Hole Composites Composite Lengths and Methods Outliers Density Determinations Geometallurgical Data Summary of Minimum, Good and Best Practices Exercises Part One: Prerequisites for the Sampling Nomograph Part Two: Nomograph Construction and Fundamental Error References Spatial Variability Concepts Experimental Variograms and Exploratory Analysis Other Continuity Estimators Inference and Interpretation of Variograms Modeling 3-D Variograms Commonly Used Variogram Models Basic Variogram Modeling Guidelines Goodness of Variogram Fit and Cross Validation Multivariate Case Summary of Minimum, Good and Best Practice Exercises Part One: Hand Calculations Part Two: Small Set of Data Part Three: Large Set of Data Part Four: Cross Variograms Part Five: Indicator Variograms for Continuous Data References

4 x 7 Mining Dilution Recoverable Versus In-Situ Resources Types of Dilution and Ore Loss Volume-Variance Correction Affine Correction Indirect Log-normal Correction Other Permanence of Distribution Models Discrete Gaussian Method Non-Traditional Volume-Variance Correction Methods Restricting the Kriging Plan Probabilistic Estimation Methods Common Applications of Volume-Variance Correction Methods Information Effect Summary of Minimum, Good and Best Practices Exercises Part One: Assemble Variograms and Review Theory Part Two: Average Variogram Calculation Part Three: Change of Shape Models References Recoverable Resources: Estimation Goals and Purpose of Estimation Conditional Bias Volume Support of Estimation Global and Local Estimation Weighted Linear Estimation Traditional Estimation Methods Classic Polygonal Method Nearest-Neighbor Method Inverse Distance Weighting Kriging Estimators Simple Kriging Ordinary Kriging Kriging with a Trend Local Varying Mean Random Trend Model Kriging the Trend and Filtering Kriging with an External Drift Cokriging Simple Cokriging Ordinary Cokriging Collocated Cokriging Collocated Cokriging Using Bayesian Updating Compositional Data Interpolation Grade-Thickness Interpolation Block Kriging Kriging Plans Summary of Minimum, Good and Best Practices Exercises Part One: Kriging Theory Part Two: Kriging by Hand Question Part Three: Conditional Bias Part Four: Kriging a Grid References

5 xi 9 Recoverable Resources: Probabilistic Estimation Conditional Distributions Gaussian-Based Kriging Methods Multi-Gaussian Kriging Uniform Conditioning Disjunctive Kriging Checking the Multivariate Gaussian Assumption Lognormal Kriging Indicator Kriging Data Integration Simple and Ordinary IK with Prior Means Median Indicator Kriging Using Inequality Data Using Soft Data Exactitude Property of IK Change of Support with IK The Practice of Indicator Kriging Indicator Cokriging Probability Kriging Summary of Minimum, Good and Best Practices Exercises Part One: Indicator Kriging Part Two: MG Kriging for Uncertainty References Recoverable Resources: Simulation Simulation versus Estimation Continuous Variables: Gaussian-Based Simulation Sequential Gaussian Simulation Turning Bands LU Decomposition Direct Sequential Simulation Direct Block Simulation Probability Field Simulation Continuous Variables: Indicator-Based Simulation Simulated Annealing Simulating Categorical Variables SIS For Discrete Variables Truncated Gaussian Truncated PluriGaussian Co-Simulation: Using Secondary Information and Joint Conditional Simulations Indicator-Based Approach Markov-Bayes Model Soft Data Calibration Gaussian Cosimulation Stepwise Conditional Transform Super-Secondary Variables Simulation Using Compositional Kriging Post Processing Simulated Realizations Summary of Minimum, Good and Best Practices Exercises Part One: Sequential Indicator Simulation Part Two: Sequential Gaussian Simulation

6 xii Part Three: Simulation with 3D Data Part Four: Special Topics in Simulation References Resource Model Validations and Reconciliations The Need for Checking and Validating the Resource Model Resource Model Integrity Field Procedures Data Handling and Processing Resampling Cross-Validation Resource Model Validation Geological Model Validation Statistical Validation Graphical Validation Comparisons with Prior and Alternate Models Reconciliations Reconciling against Past Production Suggested Reconciliation Procedures Summary of Minimum, Good and Best Practices Exercises Part One: Cross Validation Part Two: Checking Simulation References Uncertainty and Risk Models of Uncertainty Assessment of Risk Resource Classification and Reporting Standards Resource Classification based on Drill Hole Distances Resource Classification Based on Kriging Variances Resource Classification Based on Multiple-Pass Kriging Plans Resource Classification Based on Uncertainty Models Smoothing and Manual Interpretation of Resource Classes Summary of Minimum, Good and Best Practices Exercises Part One: Sampling Uncertainty Part Two: Loss Functions References Short-term Models Limitations of Long-term Models for Short-term Planning Medium- and Short-term Modeling Example: Quarterly Reserve Model, Escondida Mine Updating the Geologic Model Selection of Ore and Waste Conventional Grade Control Methods Kriging-based Methods Example Grade Control Selection of Ore and Waste: Simulation-based Methods Maximum Revenue Grade Control Method Multivariate Cases Practical and Operational Aspects of Grade Control

7 xiii 13.6 Summary of Minimum, Good and Best Practices Exercises References Case Studies The 2003 Cerro Colorado Resource Model Geologic Setting Lithology Alteration Mineralization Types Structural Geology Database Estimation Domain Definition Database Checking and Validation Comparison of Drill Hole Types Laboratory Quality Assurance Quality Control (QA-QC) Topography Density Geologic Interpretation and Modeling Volumetric and Other Checks Exploratory Data Analysis Comparison Between Composites and Blast Hole Data Contact Analysis Correlogram Models Change of Support to Estimate Internal Dilution Predicted Grade-Tonnage Curves for TCu, Cerro Colorado The Cerro Colorado 2003 Resource Block Model The Grade Model Resource Classification Estimation of Geometallurgical Units Estimation of OXSI/OXSA and of SNSI/SNSA Estimation of Point Load Resource Model Calibration Statistical Validation of the Resource Model Visual Validation of the Resource Model Multiple Indicator Kriging, São Francisco Gold Deposit Database and Geology Geologic Modeling Class Definition for Multiple Indicator Kriging Indicator Variograms Volume-Variance Correction Block Model Definition and Multiple Indicator Kriging MIK Kriging Plans and Resource Categorization MIK Resource Model: Grade-Tonnage Curves Modeling Escondida Norte s Oxide Units with Indicators Multivariate Geostatistical Simulation at Red Dog Mine Geology and Database Multivariate Simulation Approach Profit Comparison Profit Function Reference Data Model Construction Results

8 xiv 14.5 Uncertainty Models and Resource Classification: The Michilla Mine Case Study The Lince-Estefanía Mine Developing the Model of Uncertainty Indicator Variograms for TCu and by Geologic Unit Conditional Simulation Model Probability Intervals by Area Results Grade Control at the San Cristóbal Mine Geologic Setting Maximum Revenue (MR) Grade Control Method Implementation of the MR Method Results Geometallurgical Modeling at Olympic DAM, South Australia Part I: Hierarchical Multivariate Regression for Mineral Recovery and Performance Prediction Methodology Analysis Part II: Multivariate Compositional Simulation of Non-additive Geometallurgical Variables Modeling 23 Head Grade Variables Details of the Sequential Gaussian Simulation Modeling Nine Grain Size Variables Modeling 100 Association Matrix Variables Special Considerations for the Association Data Histogram/Variogram Reproduction Conclusions References Conclusions Building a Mineral Resource Model Assumptions and Limitations of the Models Used Documentation and Audit Trail Required Future Trends References Index

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