Statistical evaluations in exploration for mineral deposits / Статистические оценки при разведке месторождений полезных ископаемых

The Most Important Notations and Abbreviations     
Introduction to Some Fundamental Statistical Concepts     
General Definitions     
Frequency Distribution     
Mineral Deposit Statistics
Treatment of the Data Set     
A Simple Case of Calculating a Frequency Distribution     
Using Class Intervals for Calculating Frequency Distributions     
Frequency Distribution of Samples with Dissimilar Specifications
Mean, Variance and Standard Deviation     
The Mean             
The Mean of Equal-Weighted Values     
The Mean of Unequally-Weighted Values     
The Mean of Data Within Class Intervals     
Variance and Standard Deviation of Sample Size and Population
Calculation for Equivalent Samples     
Determination of the Variance and Standard Deviation
for Non-Equivalent or Categorized Values     
Graphical Determination of the Variance and
Standard Deviation     
Calculation of Variance and Standard Deviation of Non-Equivalent or Categorized Values     
Coefficient of Variation     
Other Parameters (Median, Mode Value)     
The Normal Distribution     
Testing the Normal Distribution Hypothesis     
Graphical Test     
Calculation of the Cumulative Frequency     
Cumulative Frequency Function of the Normal Distribution and the Derivation of the Probability Grid     
Plotting the Cumulative Frequency Values of a Real Distribution on the Probability Grid    
Chi-Square Test     
Standard Deviation and Variance of the Mean     
Calculation of the Standard Case     
Weighting Different Variances of the Mean     
Estimation of the Error     
Confidence Intervals of a Mean Value     
The Average Error     
The Law of Perpetuation of Errors     
Skewed Distributions     
Introduction    
Measurement of Skewness     
Assessing Isolated or only a Few High Values     
Corrections Using the Graphical Cumulative Frequency     
Reducing the Highest Values to the Next-Highest     
Statistical Outlier Tests        
Test for an Extensive Data Set     
Test for a Restricted Data Set     
The FUNOP Method    
Practical Experience with the Cut Levels     
Experience from the Gold Sector     
Derivation of the Cut Level from the Lognormal Distribution     
The Use of the Lognormal Distribution     
Introduction     
The Lognormal Distribution (for Numerous High Values)    
Derivation of the Lognormal Distribution     
The Logarithmic Probability Grid     
Determination of Parameters for the Lognormal
Distribution     
Mean and Variance     
The Correction Factor 0     
Graphical Determination of the Correction Factor 0
Mathematical Determination of the Correction Factor 0
Using a-Priori Information for the Estimation of the Correction Factor 0        
Determination of the Arithmetic Mean Value for
Skewed Sample Distributions     
Introduction     
Determination of the Arithmetic Mean from the
Logarithmic Mean and Logarithmic Variance    
SichePs - Estimator     
Finney’s Diagram 
Confidence Interval of the Arithmetic Mean of
Lognormally Distributed Data    
Statistical Treatment of outlier Data Using Two Lognormally Distributed Data     
Other Distributions for the Evaluation of Mineral
Deposit Data    
Statistical Problems Encountered in Sampling and the Analytical Results    
Sample Collection    
General Remarks     
Sample Size     
Introduction     
Gy’s Sampling Formula     
Estimation of the Sample Size for a Known Standard
Deviation s     
Formula for Estimating the Sample Size     
Estimation of the Standard Deviation for Two Samples from Each Component    
Estimation of the Standard Deviation for Three or More Samples from Each Component    
The Special Case of Gold     
Check Analyses    
Discussion of the Problem     
Mathematical Comparison of Two Series of Analyses Using the Student’s t-Factors     
Comparison of Two Series of Analyses by Regression Analysis     
Graphical Comparison of Analytical Laboratories     
Comparison of Sample Series with Different Support    
Theoretical Basis for the Comparison of Sample Series with Different Support     
Derivation of an Upgrading Factor by Comparing Bulk Samples and Drilling     
Introduction     
Standard Derivation of an „Upgrading" Factor     
Derivation of an „Upgrading" Factor by Comparing Zones     
Safety Margin for an „Upgrading" Factor     
Comparison of Sample Series with Different Sample Character     
Treatment of Sample Series with Different Sample Qualities     
Assessment of Core Loss     
Introduction     
Sampling in the Event of Core Loss     
Statistical Treatment of Core Loss     
Other Problems with Different Qualities of Sample     
Channel Sampling     
Sampling for Selective Mining     
Problems Related to Cut-Off Levels     
Geostatistical Calculations     
Introduction     
TheVariogram     
Fundamental Principles for Calculating the Variogram     
Variogram Models     
Allowing for Outliers in the Calculation of Variograms     
Reserve Classification by Geostatistical Calculations     
Introduction     
Size of the Blocks     
Drill Grid     
Calculation of the Geostatistical Estimation Variance    
Reference Datum     
The Relative Estimation Variance for the Area S of the
Mineral Deposit     
The Relative Estimation Variance of the Accumulation
Value GT     
The Relative Estimation Variance for the Regular Grid     
The Relative Estimation Variance for the Random Stratified Grid     
The Relative Estimation Variance for the Irrigular Grid    
The Edge Effect    
The Relative Estimation Variance for Grades     
Example of Using Geostatistical Calculations for
Classifying Reserves     
Estimating the Grades of Individual Blocks    
Introduction    
Simple Weighting with the Corner Points of a Block     
The Inverse Squared Distance (ISD) Weighting Method    
Weighting With Factors Derived Directly from the Variogram     
Kriging     
Introduction     
Point Kriging     
Equations for the Kriging System Without and With a Known     
Example of Kriging Without a Mean     
Example of Kriging With a Known Mean     

Block Kriging     
Summary Remarks on the Calculated Weighting Factors     
Calculation of the Kriging Variance    
The Screen Effect     
Calculation of Variance by the de Wijs Variogram     
Extrapolation with Geostatistical Parameters     
Further Statistical Considerations for Evaluating
Mineral Deposits     
Bias in Reserve Calculations    
Exploration Statistics
Introduction     
Defining an Exploration Grid     
Geological Considerations     
Statistical Considerations    
Spacing Between Survey Lines     
Spacing Between Lines and Between Survey Points on the Lines    
Determining Anomalies from Geochemical Exploration Data    
Preparation of the Data Set     
Defining Anomalous Values and Populations     
Low Number of Anomalous Values     
Evaluation Using the Median and Standard Deviation     
1    Fundamentals     
2    Distribution Tests    
3    Examples of Determining the Threshold Values     
Rough Estimates Using the Median only    
Numerous Anomalous Values     
The Identification of Populations     
Simple Separation of Two Populations     
More Detailed Discrimination Between Two Populations
Determining the Threshold for Anomalous Populations
Appraising Other Distributions Obtained During Geochemical Exploration    
Determining the Relative Geochemical Contrast    
Other Methods for Defining Anomalies     
Filter Methods     
Filtering with Moving Averages     
The Fraser Filter     
Addition and Multiplication Methods     
Defining a Drill Grid    
Basic Considerations     
Probability of Intersecting a Blind Target     
The Type of Grid     
Geostatistical Methods for Determining the
Drill Spacing    
Application of the Matheron Diagram    
Consideration of Rectangular Blocks     
Defining a Random Grid Pattern     
Testing for Randomness     
Assessing the Exploration Risk    
Introductory Comments     
The Expected Monetary Value (EMV) Method     
The Expected Value of Each Discovery    
Calculating the Exploration Success by the Law of Gambler’s Ruin    
Calculation of the Minimum Exploration Budget     
Assessing Various Exploration Alternatives     
Assessment with a Decision Diagram     
Application in Mineral Exploration     
Assessment of Alternative Exploration Strategies
Using Slichter’s Method