Applied Mineral Inventory Estimation,9780521791038

Applied Mineral Inventory Estimation

by
ISBN13: 9780521791038
ISBN10: 0521791030
Format: Hardcover
Pub. Date: 2002-05-20
Publisher(s): Cambridge University Press
List Price: $200.00

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Summary

Applied Mineral Inventory Estimation presents a comprehensive applied approach to the estimation of mineral resources/reserves with particular emphasis on the geological basis of such estimations, the need for and maintenance of a high quality assay data base, the practical use of comprehensive exploratory data evaluation, and the importance of a comprehensive geostatistical approach to the estimation methodology. Practical problems and real data are used throughout as illustrations. Each chapter ends with a summary of practical concerns, a number of exercises and a short list of references for supplementary study. This textbook is suitable for any university or mining school that offers senior undergraduate and graduate student courses on mineral resource/reserve estimation.

Author Biography

Alistair J. Sinclair is an Emeritus Professor of Geological Engineering and former Head of the Department of Earth and Ocean Sciences at The University of British Columbia. Garston H. Blackwell is an Associate Professor and former Associate Head of the Department of Mining Engineering at Queen's University, Canada, and former Chief Mine Engineer at the Brenda Mine (Noranda Group) near Peachland, B.C. Canada.

Table of Contents

Preface xiii
Acknowledgments xvii
Mineral Inventory: An Overview
1(30)
Introduction
1(1)
Mineral Inventory Estimates
2(2)
Some Essential Concepts in Mineral Inventory
4(11)
Ore
4(1)
Cutoff Grade
5(2)
Continuity
7(1)
Reserves and Resources
8(1)
Dilution
9(1)
Regionalized Variable
10(1)
Point and Block Estimates
11(2)
Selective Mining Unit
13(1)
Accuracy and Precision
14(1)
A Systematic Approach to Mineral Inventory Estimation
15(1)
Traditional Methods of Mineral Inventory Estimation
16(7)
Method of Sections
17(1)
Polygonal Methods
17(2)
Method of Triangles
19(1)
Inverse Distance Weighting Methods
19(1)
Contouring Methods
20(2)
Commentary
22(1)
Mine Revenues
23(3)
Mining Software - Applications
26(1)
Practical Considerations
27(1)
Selected Reading
28(1)
Exercises
28(3)
Geologic Control of Mineral Inventory Estimation
31(28)
Introduction
31(1)
Geologic Mapping
32(4)
General Geology
36(1)
General Geometry of a Mineralized/Ore Zone
37(2)
Geometric Errors in Geologic Modeling
39(6)
Ore Deposit Models
45(6)
General Concepts
45(1)
Volcanogenic Massive Sulphide Deposits
46(1)
Besshi-Type Cu-Zn Deposits
47(2)
Porphyry-Type Deposits (see Also Sinclair and Postolski, 1999)
49(1)
General Summary
50(1)
Mineralogy
51(4)
Geologic Domains
55(1)
Practical Considerations
56(2)
Selected Reading
58(1)
Exercises
58(1)
Continuity
59(17)
Introduction
59(1)
Geologic Continuity
59(4)
Value Continuity
63(2)
Continuity Domains
65(1)
Continuity in Mineral Inventory Case Histories
66(6)
Silver Queen Deposit
66(2)
JM Zone, Shasta Deposit
68(1)
South Pit, Nickel Plate Mine
69(2)
Discussion
71(1)
Practical Considerations
72(1)
Selected Reading
73(1)
Exercises
73(3)
Statistical Concepts in Mineral Inventory Estimation: An Overview
76(28)
Introduction
76(1)
Classic Statistical Parameters
77(3)
Central Tendency
77(1)
Dispersion
78(2)
Covariance
80(1)
Skewness and Kurtosis
80(1)
Histograms
80(3)
Continuous Distributions
83(7)
Normal Distribution
83(1)
Standard Normal Distribution
84(1)
Approximation Formula for the Normal Distribution
85(1)
Lognormal Distribution
86(2)
Binomial Distribution
88(1)
Poisson Distribution
88(2)
Cumulative Distributions
90(4)
Probability Graphs
90(4)
Simple Correlation
94(2)
Autocorrelation
96(1)
Simple Linear Regression
97(1)
Reduced Major Axis Regression
98(2)
Practical Considerations
100(1)
Selected Reading
100(1)
Exercises
100(4)
Data and Data Quality
104(42)
Introduction
104(1)
Numeric Data for Mineral Inventory Estimation
105(3)
Types of Samples
105(2)
Concerns Regarding Data Quality
107(1)
Location of Samples
108(1)
Error Classification and Terminology
108(5)
Definitions
108(2)
Relation of Error to Concentration
110(2)
Bias Resulting from Truncated Distributions
112(1)
Sampling Patterns
113(3)
Terminology and Concerns
113(2)
Sample Representativity
115(1)
Sampling Experiments
116(4)
Introduction to the Concept
116(1)
Comparing Sampling Procedures at Equity Silver Mine
117(1)
Sampling Large Lots of Particulate Material
118(2)
Improving Sample Reduction Procedures
120(4)
The Mineralogic Composition Factor (m)
123(1)
The Liberation Factor
123(1)
The Particle Shape Factor
123(1)
The Size Range Factor
123(1)
Applications of Gy's Equation
124(1)
Direct Solution of Gy's Equation (Simplified Form)
124(1)
User's Safety Line
124(1)
Assay Quality Control Procedures
124(5)
Introduction
124(1)
Using the Correct Analyst and Analytical Methods
125(2)
Salting and Its Recognition
127(2)
A Procedure for Evaluating Paired Quality Control Data
129(10)
Introduction
129(1)
Estimation of Global Bias in Duplicate Data
129(1)
Practical Procedure for Evaluating Global Bias
130(1)
Examples of the Use of Histograms and Related Statistics
131(1)
A Conceptual Model for Description of Error in Paired Data
132(1)
Quantitative Modeling of Error
133(6)
Improving the Understanding of Value Continuity
139(1)
A Generalized Approach to Open-Pit-Mine Grade Control
140(3)
Initial Investigations
140(1)
Development of a Sampling Program
140(1)
Sampling Personnel and Sample Record
141(1)
Implementation of Grade Control
142(1)
Mineral Inventory: Mine-Mill Grade Comparisons
142(1)
Summary
143(1)
Practical Considerations
143(1)
Selected Reading
144(1)
Exercises
144(2)
Exploratory Data Evaluation
146(21)
Introduction
146(2)
File Design and Data Input
148(1)
Data Editing
149(2)
Composites
149(2)
Univariate Procedures for Data Evaluation
151(4)
Histograms
152(1)
Raw (Native) versus Unbiased Histograms
152(1)
Continuous Distributions
152(1)
Probability Graphs
153(1)
Form of a Distribution
154(1)
Multiple Populations
154(1)
Bivariate Procedures for Data Evaluation
155(5)
Correlation
155(3)
Graphic Display of Correlation Coefficients
158(1)
Scatter Diagrams and Regression Analysis
159(1)
Spatial Character of Data
160(2)
Introduction
160(1)
Contoured Plans and Profiles
160(2)
Multivariate Data Analysis
162(3)
Triangular Diagrams
163(1)
Multiple Regression
164(1)
Practical Considerations
165(1)
Selected Reading
165(1)
Exercises
166(1)
Outliers
167(14)
Introduction
167(1)
Cutting (Capping) Outlier Values
168(2)
The Ordinary Case
168(1)
Outliers and Negative Weights
169(1)
A Conceptual Model for Outliers
170(1)
Identification of Outliers
170(2)
Graphic Identification of Outliers
170(1)
Automated Outlier Identification
171(1)
Multiple Geologic Populations
172(1)
Probability Plots
172(4)
Partitioning Procedure
173(3)
Examples
176(1)
Structured Approach to Multiple Populations
177(1)
Incorporation of Outliers into Resource/Reserve Estimates
178(1)
Practical Considerations
178(1)
Selected Reading
179(1)
Exercises
179(2)
An Introduction to Geostatistics
181(11)
Introduction
181(2)
Some Benefits of a Geostatistical Approach to Mineral Inventory Estimation
183(1)
Random Function
183(2)
Stationarity
185(1)
Geostatistical Concepts and Terminology
185(1)
The Variogram/Semivariogram
186(1)
Estimation Variance/Extension Variance
186(2)
Auxiliary Functions
188(1)
Dispersion Variance
189(1)
A Structured Approach to Geostatistical Mineral Inventory Estimation
189(2)
Applications of Geostatistics in Mineral Inventory Estimation
190(1)
Why Geostatistics?
191(1)
Selected Reading
191(1)
Exercises
191(1)
Spatial (Structural) Analysis: An Introduction to Semivariograms
192(23)
Introduction
192(1)
Experimental Semivariograms
193(5)
Irregular Grid in One Dimension
195(1)
Semivariogram Models
196(2)
Fitting Models to Experimental Semivariograms
198(1)
Two-Dimensional Semivariogram Models
199(5)
Anisotropy
201(3)
Proportional Effect and Relative Semivariograms
204(1)
Nested Structures
205(2)
Improving Confidence in the Model for Short Lags of a Two- or Three-Dimensional Semivariogram
207(1)
Complexities in Semivariogram Modeling
208(4)
Effect of Clustered Samples
208(1)
Treatment of Outlier Values
208(1)
Robustness of the Semivariogram
209(1)
Semivariograms in Curved Coordinate Systems
210(1)
The ``Hole Effect''
211(1)
Other Autocorrelation Functions
212(1)
Regularization
212(1)
Practical Considerations
213(1)
Selected Reading
214(1)
Exercises
214(1)
Kriging
215(27)
Introduction
215(1)
Background
216(2)
Ordinary Kriging
216(1)
Simple Kriging
217(1)
General Attributes of Kriging
218(1)
A Practical Procedure for Kriging
218(1)
An Example of Kriging
219(1)
Solving Kriging Equations
220(1)
Cross Validation
221(3)
Negative Kriging Weights
224(3)
The Problem
224(1)
The Screen Effect
225(2)
Dealing with Outliners
227(1)
Restricted Kriging
227(1)
Lognormal Kriging
228(1)
Indicator Kriging
229(4)
Kriging Indicator Values
230(1)
Multiple Indicator Kriging (MIK)
230(2)
Problems in Practical Applications of Indicator Kriging
232(1)
Conditional Bias in Kriging
233(3)
Discussion
235(1)
Kriging with Strings of Contiguous Samples
236(1)
Optimizing Locations for Additional Data
237(2)
Practical Considerations
239(1)
Selected Reading
240(1)
Exercises
241(1)
Global Resource Estimation
242(13)
Introduction
242(1)
Estimation with Simple Data Arrays
243(1)
Random and Stratified Random Data Arrays
243(1)
Regular Data Arrays
243(1)
Composition of Terms
244(1)
An Example: Eagle Vein
244(1)
Volume-Variance Relation
245(1)
Global Estimation with Irregular Data Arrays
246(2)
Estimation with Multiple Domains
247(1)
Errors in Tonnage Estimation
248(3)
Introduction
248(1)
Sources of Errors in Tonnage Estimates
248(1)
Errors in Bulk Density
248(1)
Errors in Surface (Area) Estimates
249(1)
Surface Error - A Practical Example
250(1)
Errors in Thickness
251(1)
Estimation of Co-Products and By-Products
251(2)
Linear Relations and Constant Ratios
251(1)
A General Model for Lognormally Distributed Metals
252(1)
Equivalent Grades
253(1)
Commentary
253(1)
Practical Considerations
253(1)
Selected Reading
254(1)
Exercises
254(1)
Grade-Tonnage Curves
255(13)
Introduction
255(2)
Grade-Tonnage Curves Derived from a Histogram of Sample Grades
257(1)
Grade-Tonnage Curves Derived from A Continuous Distribution Representing Sample Grades
258(1)
Grade-Tonnage Curves Based on Dispersion of Estimated Block Grades
259(3)
Introduction
259(2)
Grade-Tonnage Curves from Local Block Estimates
261(1)
Grade-Tonnage Curves by Multiple Indicator Kriging
262(1)
Example: Dago Deposit, Northern British Columbia
263(2)
Reality versus Estimates
265(1)
Practical Considerations
266(1)
Selected Reading
266(1)
Exercises
266(2)
Local Estimation of Resources/Reserves
268(16)
Introduction
268(1)
Sample Coordinates
268(1)
Block Size for Local Estimation
269(2)
Robustness of the Kriging Variance
271(1)
Block Arrays and Ore/Waste Boundaries
272(2)
Estimation at the Feasibility Stage
274(2)
Recoverable ``Reserves''
274(1)
Volume-Variance Approach
275(1)
``Conditional Probability''
276(1)
Local Estimation at the Production Stage
276(4)
Effect of Incorrect Semivariogram Models
276(2)
Spatial Location of Two-Dimensional Estimates
278(1)
Planning Stopes and Pillars
279(1)
Possible Simplifications
280(1)
Block Kriging with Bench Composites
280(1)
Easy Kriging with Regular Grids
280(1)
Traditional Methods Equivalent to Kriging
280(1)
Treatment of Outliers in Resource/Reserve Estimation
281(1)
Practical Considerations
282(1)
Selected Reading
282(1)
Exercises
282(2)
An Introduction to Conditional Simulation
284(10)
Introduction
284(1)
Aims of Simulation
285(1)
Conditional Simulation as an Estimation Procedure
286(1)
A Geostatistical Perspective
286(1)
Sequential Gaussian Simulation
286(1)
Simulating Grade Continuity
287(1)
Simulation to Test Various Estimation Methods
287(5)
Introduction
287(1)
Procedure
287(1)
Verifying Results of the Simulation Process
288(1)
Application of Simulated Values
289(3)
Sequential Indicator Simulation
292(1)
Practical Considerations
292(1)
Selected Reading
292(1)
Exercises
292(2)
Bulk Density
294(7)
Introduction
294(1)
Impact of Mineralogy on Density
295(1)
Impact of Porosity on Bulk Density
296(1)
Impact of Errors in Bulk Density
296(1)
Mathematical Models of Bulk Density
297(2)
Practical Considerations
299(1)
Selected Reading
299(1)
Exercises
299(2)
Toward Quantifying Dilution
301(15)
Introduction
301(1)
External Dilution
301(5)
Vein Widths Partly Less Than Minimum Mining Width
302(1)
Silver Queen Example
303(1)
Dilution from Overbreaking
304(1)
Contact Dilution
304(2)
Internal Dilution
306(5)
A Geostatistical Perspective
306(1)
Effect of Block Estimation Error on Tonnage and Grade of Production
307(4)
Dilution from Barren Dykes
311(3)
Snip Mesothermal Deposit
311(2)
Virginia Porphyry Cu-Au Deposit
313(1)
Summary: Dilution by Barren Dykes
313(1)
Practical Considerations
314(1)
Selected Reading
314(1)
Exercises
315(1)
Estimates and Reality
316(9)
Introduction
316(1)
Recent Failures in the Mining Industry
317(1)
Resource/Reserve Estimation Procedures
318(1)
Geostatistics and Its Critics
319(3)
Why Is Metal Production Commonly Less Than the Estimate?
322(1)
Practical Considerations
323(1)
Selected Reading
323(1)
Exercise
324(1)
Resource/Reserve Classification
325(12)
Introduction
325(2)
A Geologic Basis for Classification of Mineral Inventory
327(1)
Shortcomings to Existing Classification Systems
327(1)
Factors Traditionally Considered in Classifying Resources/Reserves
328(2)
Contributions to Classification from Geostatistics
330(3)
Historical Classification Systems
333(1)
The Need for Rigor and Documentation
334(1)
Examples of Classification Procedures
335(1)
Practical Considerations
335(1)
Suggested Reading
336(1)
Exercises
336(1)
Decisions from Alternative Scenarios: Metal Accounting
337(10)
Introduction
337(1)
Definition
337(1)
Metal Accounting: Alternative Blasthole Sampling Methods
338(2)
Metal Accounting: Effect of Incorrect Semivariogram Model on Block Estimation
340(1)
Metal Accounting: Effect of Block Estimation Error on Ore Waste Classification Errors (After Postolski and Sinclair, 1998; Sinclair, 1995)
341(1)
Summary Comments
342(2)
Practical Considerations
344(1)
Selected Reading
345(1)
Exercises
346(1)
APPENDICES 347(6)
A.1 British and International Measurement Systems: Conversion Factors
349(1)
A.2 U.S. Standard Sieves
350(1)
A.3 Drill Hole and Core Diameters
351(2)
Bibliography 353(24)
Index 377

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