Introduction to Mining Geostatistics : Intuitive Applications with Excel and R.

Introduction to Mining Geostatistics: Intuitive Applications with Excel and R is a practical and accessible guide to geostatistical techniques in mineral exploration, with a strong focus on reserves estimation.

Bibliographic Details
Main Author:	Modis, Konstantinos
Corporate Author:	Knovel (Firm)
Format:	eBook
Language:	English
Published:	Chantilly : Elsevier, 2025.
Edition:	1st ed.
Subjects:	Mining engineering. Statistics. Electronic books.
Online Access:	Connect to the full text of this electronic book

Table of Contents:

Front Cover
Introduction to Mining Geostatistics: Intuitive Applications With Excel and R
Copyright Page
Dedication
Contents
About the authors
Prolegomena
Acknowledgments
1 Introduction to ore reserves estimation
Synopsis
Prerequisites
Learning objectives
Terminology
1.1 A day in a classroom
1.2 The problem of estimation
1.2.1 Description
1.2.2 Deterministic interpolation methods
1.3 The big picture, or where we stand in the production chain
1.4 Basic concepts
1.5 Steps involved in developing the block model
1.6 Joint distribution of actual and estimated values
1.7 Challenges encountered in developing a numerical model
1.8 The evolution of geostatistics
1.9 Introduction to the statistical programming language R
Exercises
Exercise 1.1
Answer
Exercise 1.2
Answer
Exercise 1.3
Answer
References
2 Essential statistics and exploratory data analysis
Synopsis
Prerequisites
Learning objectives
Terminology
2.1 Nonparametric statistics of one variable
2.2 Joint distribution of two random variables
2.3 Vector representation of random variables
2.4 Joint distribution of multiple random variables
2.5 Linear dependency in the space of random variables
2.6 Exploratory data analysis
2.6.1 Assimilation of geological knowledge
2.6.2 Spatial distribution of geological information
2.6.3 Sample distribution and correlation analysis of a random variable
2.7 Data transformations
2.7.1 Detrending
2.7.2 Normalization
2.7.3 Formulation of indicators
Exercises
Exercise 2.1
Answer
Exercise 2.2
Answer
Exercise 2.3
Answer
Exercise 2.4
Answer
Exercise 2.5
Answer
Exercise 2.6
Answer
Exercise 2.7
Answer
References
3 Introduction to sampling and relevant errors
Synopsis.
Prerequisites
Learning objectives
Terminology
3.1 Introduction to ore and mineral sampling
3.2 Sampling during exploration
3.2.1 Sampling directed to outcrops
3.2.2 Sampling in slopes
3.2.3 Sampling with diamond drillings
3.2.4 Sampling with reverse circulation drilling
3.3 Sampling during the production phase
3.3.1 Blasthole sampling
3.3.2 Stope and bench sampling
3.3.3 Heap sampling from truckloads and conveyor belts
3.3.4 Sampling in ore processing plants
3.4 Sampling bias
3.5 Compositing
3.6 Sampling protocols
3.7 Sampling theory for particulate materials
3.8 Graphical solution of the sample reduction problem
Exercises
Exercise 3.1
Answer
References
4 The stochastic model of estimation
Synopsis
Prerequisites
Learning objectives
Terminology
4.1 Amid the aroma of coffee and steam, echoes of alternate realities gleam
4.2 The concept of a Random Function
4.3 Distributions and parameters associated with a Random Function
4.4 An important property of the covariance function
4.5 Simplified Random Function models
4.6 The function of increments of a Random Function
4.7 Continuing with the example of random walk
4.8 Case study
Answer
Exercises
Exercise 4.1
Answer
References
5 Variograms and the structural analysis of a random function
Synopsis
Prerequisites
Learning objectives
Terminology
5.1 Spatial continuity and its quantification
5.2 Practical approaches for computing the experimental variogram
5.3 Important aspects of the variogram
5.4 Indicator variogram
5.5 Case study: structural analysis of a lignite orebody
Exercises
Exercise 5.1
Answer
Exercise 5.2
Answer
References
6 Fitting theoretical models of variograms
Synopsis
Prerequisites
Learning objectives
Terminology.
6.1 Current variogram models
6.1.1 Nugget effect model
6.1.2 Spherical model
6.1.3 Exponential model
6.1.4 Gaussian model
6.2 Nested structures
6.3 Anisotropic structures
6.4 Case study: structural analysis of a lignite orebody (continued from Section 5.5)
Exercises
Exercise 6.1
Answer
Exercise 6.2
Answer
Exercise 6.3
Answer
References
7 Estimation of in situ resources
Synopsis
Prerequisites
Learning objectives
Terminology
7.1 Together they stride, in unity they brew, a harmony profound, the Kriging becomes true
7.2 Random function as a model of a regionalized variable
7.3 The method of projection with known mean (simple Kriging algorithm)
7.4 The method of projection with unknown mean (ordinary Kriging algorithm)
7.5 Support effect and the block Kriging method
7.6 Indicator Kriging
7.7 Existence and uniqueness of the solution
7.8 Preparation of a Kriging plan
7.9 Synthetic case study: Kriging in one dimension using Excel and Visual Basic
Exercises
Exercise 7.1
Answer
Exercise 7.2
Answer
References
8 Verifying the accuracy of the estimation model
Synopsis
Prerequisites
Learning objectives
Terminology
8.1 Uncertainty of estimation
8.2 Cross-validation
8.3 Jackknife
8.4 Evaluation of model fit quality
8.5 Case study: validation of the variogram model at the Southern Field lignite mine using R
8.5.1 Application of cross-validation
8.5.2 Application of Jackknife validation
Exercises
Exercise 8.1
Answer
Exercise 8.2
Answer
Exercise 8.3
Answer
References
9 Multivariate geostatistics
Synopsis
Prerequisites
Learning objectives
Terminology
9.1 Professor Zeno and the lost papers
9.2 The concept of a coregionalization
9.3 Models of coregionalization.
9.3.1 The linear coregionalization model
9.4 Projecting with auxiliary variables (Cokriging)
9.4.1 Simple Cokriging
9.4.2 Ordinary Cokriging
9.5 Dimensionality reduction: the principal components analysis
9.6 Case study: modeling lignite reserves using auxiliary variables
9.7 Case study: modeling trace element patterns in soil using principal component analysis
Exercises
Exercise 9.1
Answer
Exercise 9.2
Answer
Exercise 9.3
Answer
References
10 Simulation of a random function
Synopsis
Prerequisites
Learning objectives
Terminology
10.1 A nighttime chat on the line. In some other world, lost papers might be fine
10.2 Why simulation? Uncertainty versus local estimation error
10.3 Unconditional simulation
10.3.1 The moving averages method (in one dimension)
10.3.2 LU decomposition of covariance matrix
10.4 Conditional simulation
10.4.1 LU decomposition of covariance matrix
10.4.2 The method of sequential Gaussian simulation
10.5 Sequential indicator simulation for categorical variables
10.6 Truncated Gaussian and Plurigaussian simulation
10.7 Case study: Plurigaussian simulation in the Southern Field lignite mine using R
Exercises
Exercise 10.1
Answer
Exercise 10.2
Answer
References
11 Classification schemes
Synopsis
Prerequisites
Learning objectives
Terminology
11.1 The rationale and importance of reserves classification
11.2 Definition and main features of classification schemes
11.3 The Joint Ore Reserves Committee code
11.4 The Canadian Institute of Mining, Metallurgy, and Petroleum code
11.5 The Pan-European Code
11.6 Quantification of uncertainty
Exercises
Exercise 11.1
Answer
Exercise 11.2
Answer
Exercise 11.3
Answer
References
12 Case studies
Synopsis
Prerequisites.
Learning objectives
12.1 Estimating lignite resources in Macedonia, Greece
12.1.1 Deposit and regional geology
12.1.2 Exploratory data analysis
12.1.3 Structural analysis and model development
12.2 Simulation of overburden lithofacies in a lignite deposit in Macedonia, Greece
12.2.1 Overburden geology
12.2.2 Exploratory data analysis
12.2.3 Structural analysis and model development
12.2.4 Model validation
12.3 Structural analysis of a mixed sulfide ore body in Laconia, Greece
12.3.1 Ore deposit geology
12.3.2 Experimental mining
12.3.3 Exploratory data analysis
12.3.4 Ore reserves estimation
12.4 Hydrofacies simulation in the West Thessaly basin, Greece
12.4.1 Regional geology
12.4.2 Exploratory data analysis
12.4.3 Structural analysis and model development
12.4.4 Model validation
12.5 Block modeling of a lateritic ore body in Boeotia, Greece
12.5.1 Deposit and regional geology
12.5.2 Exploratory data analysis
12.5.3 Structural analysis and model development
References
Index
Back Cover.