About the Author	8
	Acknowledgements	10
	Contents	12
	1 Introduction	22
	References	23
	Part I Mine Design, Mine Mapping and Sampling	24
	2 Mining Methods	25
	2.1 Open Pit Mines	26
	2.2 Underground Mines	27
	2.2.1 Underground Selective Mining Methods	29
	2.2.1.1 Cut-and-Fill Method	29
	2.2.1.2 Shrinkage Stoping	30
	2.2.2 Underground Bulk Mining Methods	30
	2.2.2.1 Block Caving	30
	2.2.2.2 Sublevel Open Stoping	32
	2.2.2.3 Sublevel Caving	33
	2.2.2.4 Vertical Crater Retreat	34
	2.2.3 Mining of the Gently Dipping Ore Bodies	34
	2.2.3.1 Room-and-pillar Method	35
	2.2.3.2 Longwall Mining	35
	2.3 Unconventional Mining	35
	2.3.1 In situ Leach (ISL) Technique	36
	2.3.2 Dredging of the Mineral Sands	36
	References	38
	3 Mine Mapping	39
	3.1 Mine Mapping Principles	39
	3.2 Mapping Open Pit Mines	40
	3.3 Mapping of Underground Mines	43
	3.4 Mapping Using Digital Photogrammetry and Laser Technologies	50
	3.4.1 Mapping Mining Faces Using Photogrammetry	50
	3.4.2 Remote Mapping of the Mines Using Laser	53
	3.5 Optimisation of the Mine Mapping Procedures	54
	References	57
	4 Drilling Techniques and Drill Holes Logging	58
	4.1 Drilling Methods	58
	4.2 Diamond Core Drilling	60
	4.2.1 Core Quality and Representativeness	64
	4.2.2 Orientated Core	68
	4.2.3 Logging Diamond Core Holes	73
	4.2.4 Sampling Diamond Core	77
	4.3 Open Hole Percussion Drilling	78
	4.3.1 Sampling Blastholes for Grade Control Purpose in the Open Pits	79
	4.3.2 Use of `Jumbo' Drilling for Delineation of Underground Stopes	83
	4.4 Reverse Circulation (RC) Percussion Drilling	84
	4.4.1 Logging RC Holes	86
	4.4.2 Sampling RC Holes	88
	4.5 Sonic Drilling Technologies	88
	4.5.1 Strength and Weakness of the Sonic Drilling	90
	4.5.2 Logging and Sampling Sonic Drill Holes	92
	4.6 Auger Drilling	93
	4.7 Rotary Drilling Using Tricone Bit	95
	References	95
	5 Sampling of the Mine Workings	97
	5.1 Sampling Rock Faces in the Underground Mines	97
	5.1.1 Channel Sampling	98
	5.1.2 Rock Chip Sampling	98
	5.2 Sampling of the Broken Ore	100
	5.3 Trenching and Winzing	102
	References	103
	6 Geotechnical Logging and Mapping	104
	6.1 Geotechnical Logging of the Drill Core	104
	6.1.1 Drilling Parameters and Core Recovery	105
	6.1.2 Rock Weathering	105
	6.1.3 Rock Strength	106
	6.1.4 Rock Quality Designation Index (RQD)	106
	6.1.5 Natural Breaks	107
	6.2 Geotechnical Mapping	108
	6.3 Geotechnical Applications of Rock Mass Classification Schemes	109
	References	112
	7 Dry Bulk Density (DBD) of Rocks	113
	7.1 Types of the Rock Densities Used in the Mining Industry	114
	7.2 Dry Bulk Density Measurement Techniques	114
	7.2.1 Competent Non-porous Rocks	114
	7.2.2 Porous and Weathered Rocks	116
	7.2.3 Non-consolidated Sediments	120
	7.3 Spatial Distribution of the Rock Density Measurements	120
	References	126
	8 Data Points Location (Surveying)	127
	8.1 Surface Points Location	128
	8.2 Down-Hole Survey	128
	Reference	131
	Part II Sampling Errors	132
	9 Introduction to the Theory of Sampling	133
	9.1 Types of Sampling Errors	133
	9.2 Fundamental Sampling Error	135
	9.2.1 Theoretical Background	135
	9.2.2 Experimental Calibration of the Sampling Constants	137
	9.2.2.1 Modified Sampling Tree Experiment (MSTE)	137
	9.2.2.2 30-pieces Experiment	140
	9.2.2.3 Heterogeneity Test	141
	9.2.2.4 Calibration of the Sampling Constants Using Drill Hole Data	142
	9.2.3 Sampling Nomogram	142
	9.3 Grouping – Segregation Error	143
	9.4 Errors Related to the Sampling Practices	145
	9.5 Instrumental Errors	146
	References	147
	10 Quality Control and Assurance (QAQC)	148
	10.1 Accuracy Control	148
	10.1.1 Statistical Tests for Assessing Performance of the Standard Samples	149
	10.1.1.1 Estimation Accuracy by Repeat Analyses of the Certified Standards, Single Laboratory	149
	10.1.1.2 Estimation Accuracy by Repeat Analyses of the Certified Standards, Different Laboratories	150
	10.1.1.3 Estimation Accuracy by a Single Assay of the Certified Standard	151
	10.1.1.4 Within Laboratory Analytical Precision, Single Laboratory Case	151
	10.1.1.5 Assessment of the Analytical Precision Using Round Robin Analysis of a Certified Standard Sample	152
	10.1.1.6 Between Laboratories Precision	152
	10.1.2 Statistical Tests for Assessing the Data Bias Using the Duplicate Samples	153
	10.1.3 Diagnostic Diagram: Pattern Recognition Method	153
	10.2 Precision Control	155
	10.2.1 Matching Pairs of Data	155
	10.2.2 Processing and Interpretation of Duplicate Samples	156
	10.2.2.1 Method of Thompson – Howarth	156
	10.2.2.2 Relative Precision Error	158
	10.2.2.3 Geostatistical Approach of the Duplicate Samples Analysis	159
	10.2.2.4 Partitioning of the Precision Error	160
	10.2.2.5 Reduced Major Axis	160
	10.2.2.6 Relative Difference Plot	161
	10.3 Comparative Analysis of the Statistical Estimation Methods	163
	10.4 Guidelines for Optimisation of the Sampling Programmes	167
	10.4.1 Planning and Implementation of the Sampling Programmes	167
	10.4.2 Frequency of Inserting QAQC Material to Assay Batches	168
	10.4.3 Distribution of the Reference Materials	169
	10.4.4 Distribution of the Duplicate Samples	169
	References	171
	11 Twin Holes	173
	11.1 Method Overview	174
	11.1.1 Objectives of the Twinned Holes Study	174
	11.1.2 Statistical Treatment of the Results	175
	11.1.3 Distance Between Twinned Holes	175
	11.1.4 Drilling Quality and Quantity	175
	11.1.5 Comparison of Studied Variables	177
	11.1.6 Practice of Drilling Twinned Holes for Mining Geology Applications	178
	11.2 Case Studies	179
	11.2.1 Gold Deposits: Confirmation of High-Grade Intersections	180
	11.2.2 Twin Holes Studies in Iron Ore Deposits	181
	11.2.3 Mineral Sands Deposits: Validation of Historic Drilling	183
	11.2.4 Bauxites: Use of Twin Holes as a Routine Control of Drilling Quality	183
	References	186
	12 Database	188
	12.1 Construction of the Database	189
	12.2 Data Entry	191
	12.2.1 Electronic Data Transfer	191
	12.2.2 Keyboard Data Entry	191
	12.2.3 Special Values	192
	12.3 Management of the Data Flow	193
	12.4 Database Safety and Security	194
	References	194
	Part III Mineral Resources	195
	13 Data Preparation	196
	13.1 Data Compositing	196
	13.1.1 Data Coding	196
	13.1.2 Compositing Algorithms	197
	13.1.3 Choice of the Optimal Compositing Intervals	197
	13.1.4 Validating of the Composited Assays	199
	13.2 High Grade Cut-Off	200
	References	201
	14 Geological Constraints of Mineralisation	202
	14.1 Introduction to Wireframing	202
	14.2 Characterisation of the Mineralisation Contacts	204
	14.2.1 Contact Profile	204
	14.2.2 Determining of the Cut-Off Value for Constraining Mineralisation	207
	14.2.3 Contact Topography	208
	14.2.4 Uncertainty of the Contacts	209
	14.3 Geometry and Internal Structure of the Mineralised Domains	211
	14.3.1 Unfolding	211
	References	214
	15 Exploratory Data Analysis	215
	15.1 Objective of the EDA	215
	15.2 Overview of the EDA Techniques	216
	15.2.1 Spider Diagram	216
	15.2.2 Data Declustering	216
	15.2.3 Q-Q Plots	221
	15.2.4 Box-and-Whisker Plot (Box Plot)	221
	15.3 Grouping and Analysis of the Data	222
	15.3.1 Data Types	222
	15.3.2 Data Generations	224
	15.3.3 Grouping Samples by Geological Characteristics	224
	15.4 Statistical Analysis of the Resource Domains	225
	References	227
	16 Resource Estimation Methods	228
	16.1 Polygonal Method	229
	16.2 Estimation by Triangulation	230
	16.3 Cross-Sectional Method	231
	16.3.1 Extrapolation of the Cross-Sections	231
	16.3.2 Interpolation Between Cross-Sections	233
	16.4 Estimation by Panels	235
	16.5 Inverse Distance Weighting Method	235
	References	237
	Part IV Applied Mining Geostatistics	238
	17 Introduction to Geostatistics	239
	17.1 Regionalised Variable and Random Function	240
	17.2 Stationarity and Intrinsic Hypothesis	241
	References	242
	18 Variography	244
	18.1 Quantitative Analysis of the Spatial Continuity	244
	18.2 Intuitive Look at Variogram	245
	18.3 Geostatistical Definition of Variogram	246
	18.4 Directional, Omnidirectional and Average Variograms	247
	18.5 Properties of the Variograms	247
	18.5.1 Behaviour Near Origin	248
	18.5.2 Anisotropy	249
	18.6 Analysis of the Data Continuity Using a Variogram Map	250
	18.7 Presence of Drift	252
	18.8 Proportional Effect	252
	18.9 Variogram Sill and the Sample Variance	253
	18.10 Impact of the Different Support	254
	18.11 Variogram Models	254
	18.11.1 Common Variogram Models	254
	18.11.2 Modelling Geometric Anisotropy	256
	18.11.3 Nested Structures	257
	18.11.4 Modelling Zonal Anisotropy	257
	18.12 Troublesome Variograms	258
	18.12.1 Hole Effect	259
	18.12.2 Saw-Tooth Shaped and Erratic Variograms	259
	18.13 Alternative Measures of a Spatial Continuity	260
	18.13.1 Variograms of the Gaussian Transformed Values	261
	18.13.2 Relative (Normalised) Variograms	262
	18.13.3 Different Structural Tools	263
	18.14 Indicator Variograms	264
	18.15 Variograms in the Multivariate Environment	264
	18.15.1 Multivariate Geostatistical Functions	265
	18.15.2 Linear Model of Coregionalisation	265
	References	266
	19 Methods of the Linear Geostatistics (Kriging)	268
	19.1 Geostatistical Resource Estimation	268
	19.2 Kriging System	269
	19.2.1 Ordinary Kriging	270
	19.2.2 Simple Kriging	271
	19.2.3 Simple Versus Ordinary Kriging	272
	19.3 Properties of Kriging	272
	19.3.1 Exactitude Property of Kriging	272
	19.3.2 Negative Kriging Weights and Screening Effect	273
	19.3.3 Smoothing Effect	275
	19.3.4 Kriging Variance	278
	19.3.5 Conditional Bias	279
	19.3.5.1 Slope of the Z"026A30C Z* Regression	280
	19.3.5.2 Correlation of the Z and Z*	282
	19.3.5.3 Lagrange Multiplier	282
	19.3.5.4 Weight of the Mean Value	283
	19.4 Block Kriging	284
	19.4.1 Blocks and Point Estimates	284
	19.4.2 Kriging of the Small Blocks	285
	References	291
	20 Multivariate Geostatistics	292
	20.1 Theoretical Background of Multivariate Geostatistics	293
	20.1.1 Ordinary Co-kriging	293
	20.1.2 Collocated Co-kriging	293
	20.1.3 Properties of the Co-kriging	294
	20.2 Kriging with External Drift	294
	References	294
	21 Multiple Indicator Kriging	296
	21.1 Methodology of the Multiple Indicator Kriging	297
	21.2 Practical Notes on the Indicators Post-Processing	298
	References	299
	22 Estimation of the Recoverable Resources	300
	22.1 Change of Support Concept	301
	22.1.1 Dispersion Variance	301
	22.1.2 Volume Variance Relations	302
	22.1.3 Conditions for Change-of-Support Models	303
	22.2 Global Change of Support Methods	303
	22.2.1 Affine Correction	303
	22.2.1.1 Recovered Grade	304
	22.2.1.2 Recovered Tonnage	304
	22.2.1.3 Recovered Metal	304
	22.2.2 Discrete Gaussian Change of Support	305
	22.3 Local Change of Support Methods	306
	22.3.1 Uniform Conditioning	306
	22.3.2 Localised Uniform Conditioning	307
	22.3.3 Application of the LUC Method to the Iron Ore Deposit	311
	References	312
	23 Model Review and Validation	314
	23.1 Validating of the Global Estimates	314
	23.2 Validating of the Local Estimates	315
	23.2.1 Validating of the Local Mean	315
	23.2.2 Validating by the Drill Hole Intersections	317
	23.2.3 Cross Validation Technique	317
	23.3 Validating of the Tonnage	317
	References	318
	24 Reconciliation with New Data	319
	24.1 Validating Using the Infill Drilling Data	319
	24.2 Reconciliation with the Mine Production Data	321
	24.3 Ore Grade Control	322
	24.3.1 Grade Control at the Open Pit Mine	322
	24.3.2 Grade Control at the Underground Mines	323
	References	324
	Part V Estimating Uncertainty	325
	25 Grade Uncertainty	326
	25.1 Methods of Conditional Simulation	327
	25.1.1 Turning Bands	327
	25.1.2 Sequential Gaussian Simulation	328
	25.1.3 Sequential Indicator Simulation	328
	25.2 Application of the Conditional Simulation in the Corridor Sands Project	329
	25.2.1 Project Background	329
	25.2.2 Scope of the Conditional Simulation Study	331
	25.2.3 Implementation of the SGS Technique	331
	25.2.4 Results and Discussion	332
	25.2.4.1 Recoverable Resources	332
	25.2.4.2 Risk of Exceeding Plant Tolerance Thresholds	332
	25.2.4.3 Comparison of the SGS and OK Results	333
	References	335
	26 Quantitative Geological Models	337
	26.1 Geological Models	337
	26.2 Indicator Assisted Domaining	338
	26.2.1 Indicator Probability Model	339
	26.2.2 Structural Interpretation	341
	26.2.3 Boundary Conditions	341
	26.3 Stochastic Modelling of the Geological Structures	341
	26.3.1 Plurigaussian Conditional Simulation: Case Study	342
	26.3.1.1 Methodology of Plurigaussian Simulation	342
	26.3.1.2 Estimating of the Lithotypes Proportions	344
	26.3.1.3 Applying of the `Lithotype Rule'	344
	26.3.1.4 Plurigaussian Variograms	346
	26.3.1.5 Results and Discussion	346
	References	349
	Part VI Classification	350
	27 Principles of Classification	351
	27.1 International Reporting Systems	351
	27.2 Mineral Resources and Ore Reserves	351
	Reference	354
	28 Methodology of the Mineral Resource Classification	355
	28.1 Geostatistical Classification Methods	355
	28.2 Classification Related to the Mine Production Plans	356
	28.2.1 Classification Criteria	356
	28.2.2 Classification Procedures	358
	28.2.3 Classification Using Auxiliary Geostatistical Functions	360
	References	363
	29 Conversion Resources to Reserves	364
	29.1 Mining Factors	365
	29.2 Metallurgical Factors	365
	29.2.1 Metallurgical Systematics of the Ore Reserves	366
	29.2.2 Representativity of the Bulk Samples	366
	29.3 Project Economics	370
	References	371
	30 Balance Between Quantity and Quality of Samples	372
	30.1 Introduction to a Problem	372
	30.2 Geological Factor and Sampling Error	373
	References	374
	Part VII Mineral Deposit Types	376
	31 Lode Gold Deposits	377
	31.1 Geology of the Orogenic Gold Deposits	378
	31.2 Sampling and Assaying of the Gold Deposits	381
	31.2.1 Samples Preparation	381
	31.2.2 Gold Assays	383
	31.2.3 Samples Quality Control	385
	31.3 Dry Bulk Density	385
	31.4 Estimation of Resources and Reserves	386
	31.4.1 Top Cut	386
	31.4.2 Classification	387
	References	387
	32 Uranium Deposits (In-Situ Leach Projects)	389
	32.1 Sandstone Hosted Uranium Deposits	390
	32.2 Resource Definition Drilling	391
	32.3 Geophysical Logging of the Drillholes	393
	32.3.1 Gamma Logging	394
	32.3.2 Prompt Fission Neutron (PFN) Analyser	394
	32.3.3 Supplementary Geophysical Techniques	395
	32.4 Drillhole Sample Assays	395
	32.5 Data Quality and Mineral Resource Categories	395
	32.6 Geological and Geotechnical Logging of the Drillholes	396
	32.6.1 Lithology	396
	32.6.2 Hydrogeology	396
	32.6.3 Permeability	397
	32.6.4 Porosity and Rock Density	397
	32.7 Resource Estimation	397
	32.7.1 Geological Model	397
	32.7.2 Estimation of Uranium Grade	398
	32.7.3 Geostatistical Resource Estimation	398
	32.8 Viability of the Resources	399
	32.9 Reconciliation of the Resources	401
	References	401
	33 Iron-Oxide Deposits	403
	33.1 Geological Constraints of the Resource Models	403
	33.2 Resource Estimation Drilling	406
	33.3 Sampling and Assaying	407
	33.4 Dry Bulk Density of the Rocks	407
	33.5 Estimation Resources and Reserves	407
	References	408
	34 Bauxite Deposits	409
	34.1 Geological Constraints of the Resource Models	410
	34.1.1 Shape of the Bauxite Plateaus	410
	34.1.2 Contacts	410
	34.1.3 Vertical Profile of the Bauxite Seams	411
	34.1.4 Domains	413
	34.2 Drilling	415
	34.3 Sampling and Logging Holes	417
	34.4 Sample Preparation and Assaying	417
	34.4.1 Sample Preparation	417
	34.4.2 Analytical Techniques	418
	34.4.3 Sample Quality Control	419
	34.5 Dry Bulk Density of the Rocks	419
	34.6 Estimation Bauxite Grade	420
	34.7 Classification	420
	34.7.1 Mineral Resources	420
	34.7.2 Conversion to Ore Reserves	420
	34.7.2.1 Mining Parameters	420
	34.7.2.2 Metallurgical Factors	422
	References	423
	35 Mineral Sands	424
	35.1 Geology of the Selected Deposits	425
	35.1.1 Fort Dauphin	425
	35.1.2 Corridor Sands	426
	35.1.3 Richard's Bay	427
	35.2 Drilling	428
	35.3 Sample Processing and Assaying	429
	35.4 Samples Quality Control Procedures	429
	35.5 Dry Bulk Density of the Rocks	429
	35.6 Estimation and Reporting Resources	429
	References	430
	Appendices	431
	Appendix 1: List of the Exercises and Electronic Files with the Solutions	431
	Appendix 2: Mathematical Background	431
	Normal Distribution	431
	Lognormal Distribution	432
	References	433
	Index	440