Basic Linear Geostatistics

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Springer Science & Business Media, 29.09.1998 - 155 Seiten
Linear Geostatistics covers basic geostatistics from the underlying statistical assumptions, the variogram calculation and modelling through to kriging. The underlying philosophy is to give the students an indepth understanding of the relevant theory and how to put it into practice. This means going into the theory in more detail than most books do, and also linking it with applications. It is assumed that readers, students and professionals alike, are familiar with basic probability and statistics, and matrix algebra needed for solving linear systems. Some reminders on these are given in an appendix at the end of the book. A set of exercises is integrated into the text.
 

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Inhalt

1 Introduction
1
13 Applications of geostatistics in mining
2
135 Gridding and contour mapping
3
15 Introductory exercise
4
151 Selective mining
5
152 Optimal recovery
6
153 Information effect
7
154 Support effect
8
63 Variance of a point within a volume
76
65 Kriges additivity relation
77
stockpiles to homogenize coal production
78
regularization
79
681 Solution
80
69 Exercises
81
7 The Theory of Kriging
83
73 Deriving the kriging equations
84

16 Does geostatistics work in the real world?
10
162 Gold case studies
11
163 More recent case studies
12
2 Regionalized Variables
15
23 Random functions
16
24 Stationary and intrinsic hypotheses
18
25 How to decide whether a variable is stationary
20
26 Spatial covariance function
21
27 Exercises
23
3 The Variogram
25
33 Range and zone of influence
26
34 Behaviour near the origin
27
35 Anisotropies
28
352 Zonal or stratified anisotropy
30
37 Nested structures
31
39 Hole effects and periodicity
32
311 Admissible models
35
312 Common variogram models
36
3122 Spherical model
37
3125 Gaussian model
38
3128 Cardinal sine model
39
314 Exercises
40
4 Experimental Variograms
47
43 In the plane
48
Calculating experimental variograms in 2D
50
47 Variogram cloud
52
48 Fitting a variogram model
53
49 Thmblesome variograms
54
492 Pseudoperiodic hiccups
55
493 Artefacts
56
410 Exercises
57
5 Structural Analysis
59
Collect and check the data
60
523 Standard statistics
62
53 Case studies
63
541 Vertical variogram
64
542 Variogram cloud
65
544 Horizontal vartograms
66
an archaean gold deposit M Hurley
68
a Witwatersrand gold deposit M Thurston
70
6 Dispersion as a Function of Block Size
73
621 Dispersion versus block size
74
74 Different kriging estimators
85
75 Ordinary kriging
86
76 The OK equations for intrinsic regionalized variables
89
Ordinary kriging of a block
90
78 Kriging the value of the mean
92
79 Simple kriging
93
710 The additivity theorem
94
711 Slope of the linear regression
96
712 Kriging is an exact interpolator
97
713 Geometric exercise showing the minimization procedure
98
7131 Quadratic form to be minimized
99
714 Exercises
101
8 Practical Aspects of Kriging
103
83 Negative weights
104
84 How the choice of the variogram model affects kriging
107
842 The effect of the choice of the nugget effect
108
85 Screen Effect
109
86 Symmetry in the equations
112
87 Testing the quality of a kriging configuration
114
Adding extra samples improves the quality of the estimate
115
9 Case Study using Kriging
117
921 Grid size for kriging
118
95 Point kriging using smaller neighbourhoods
121
952 How to eliminate these concentrations of contour lines
123
96 Kriging small blocks from a sparse grid
124
961 What size blocks can be kriged?
126
10 Estimating the Total Reserves
127
103 Extension variance
128
104 Relationship to the dispersion variance
130
1052 Composition by line and slice terms
132
106 When the limits of orebody are not known a priori
134
107 Optimal sampling grids
136
1071 For the 1km grid
137
108 Exercises
138
Review of Basic Maths Concepts
141
A12 Single and double summations
142
A13 Exercises using summations
143
Due Diligence and its Implications
145
References
147
Index
151
Author Index
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