Geostatistical Ore Reserve Estimation

PrefaceIntroductionList of NotationsList of AbbreviationsChapter 1 Elementary Statistical Theory and Applications 1.1 The Vocabulary of Statistics in Mineral Resources Estimation 1.1.1 Universe 1.1.2 Sampling Unit and Population 1.1.3 Characterization of a Population 1.2 a Few Lines of Theory 1.2.1 A Random Variable 1.2.2 Probability Distribution 1.2.3 Characterization of a Distribution 1.3 Theoretical Models of Distributions 1.3.1 The Normal Distribution 1.3.2 The Lognormal Distribution 1.3.3 The Binomial Distribution 1.3.4 The Poisson Distribution 1.3.5 The Negative Binomial Distribution 1.4 Independent Random Variables and Dependent Random Variables 1.4.1 Definition of Independence 1.4.2 Examples 1.4.3 The Covariance of Two Random Variables 1.4.4 Covariance and Correlation Coefficient 1.5 Correlation and Regression 1.5.1 Regression Lines 1.5.2 Normal Regression 1.6 Computational Remarks on Variances and Covariances 1.6.1 Multiplying a Variable by a Constant 1.6.2 Adding Two Random Variables 1.6.3 Taking a Linear Combination of Random VariablesChapter 2 Contribution of Distributions to Mineral Reserve Problems 2.1 The Precision of a Sampling Campaign and Prediction of the Effect of Further Sampling 2.1.1 The Standard Error of the Mean 2.1.2 Conditions of Use 2.1.3 Example of Use in the Normal Case; Confidence Interval and Risk 2.1.4 Example of Use of Sichel's Tables in the Lognormal Case 2.2 The Recovery of Ore and Metal for a Given Cut-Off 2.2.1 The General Case 2.2.2 Formulae for a Few Simple Cases 2.2.3 Condition of Use 2.2.4 A Remark on Lasky Law, Cut-Off Grade and Mined Grade 2.3 Exercises on Grade-Tonnage Curves 2.3.1 The Effect of Changes in Variance on Ore Recovery 2.3.2 A Case Where the Variations May be Bigger 2.4 ConclusionChapter 3 What is an Ore Reserve Calculation? 3.1 Estimation Problems During a Mine Life 3.1.1 Grade-Tonnage Curve Problems 3.1.2 Assessment of the Quality of a Sampling Pattern 3.1.3 Definition of Minable Reserves 3.1.4 Long-Range Planning for an Open Pit 3.1.5 Short-Term Planning 3.1.6 The Need for Accurate Ore Inventory Files and Correct Concepts 3.2 What is an Ore Reserve Estimation? 3.2.1 The Concept of Extension 3.2.2 The Concept of Error of Estimation 3.2.3 The Correct Assignment of Blocks to Ore and Waste 3.2.4 The Concept of Block Variance 3.2.5 Exercise, Block and Estimation Variance 3.3 Geological Features and Magnitude of the Error 3.3.1 The Continuity of the Ore 68 3.3.2 The Zone of Influence of a Sample 3.3.3 Low-Scale Variations 3.3.4 Homogeneity of the Mineralization 3.3.5 Hints Toward the Selection of an Estimation Procedure 3.4 The Origin and Credentials of Geostatistics 3.4.1 People 3.4.2 CompaniesChapter 4 What is a Variogram? 4.1 Spatial Correlation 4.2 Definition of the Variogram 4.3 The Variogram as a Geological Features Descriptor 4.3.1 The Continuity 4.3.2 The Zone of Influence 4.3.3 The Anisotropics 4.3.4 Conclusion 4.4 The Variogram as the Fundamental Function in Error Computations 4.4.1 The Variance of the Error of Estimation 4.4.2 The Variance of the Grade of Blocks 4.4.3 The Covariance of the Grade of a Block and the Grade of a Sample 4.4.4 The Covariance of the Grades of Two Samples 4.5 Conclusion 4.6 Exercises 4.6.1 Variances and the Variogram 4.6.2 Back-of-Cigarette-Pack Geostatistics 4.7 Computing an Isotropic Variogram 4.