Basic Linear GeostatisticsSpringer 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. |
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 |
147 | |
151 | |
Andere Ausgaben - Alle anzeigen
Häufige Begriffe und Wortgruppen
1m blocks 1m x 1m 2m x 2m anisotropy Archaean block grades chapter coal configuration contour lines direction distance class drillholes equations estimate the value estimated grade estimation error estimation methods estimation variance example exercise expected value experimental variogram Exponential model extension variance fitted gaussian geostatistician gives gold deposit histogram horizontal intrinsic kriged estimates kriging neighbourhood kriging standard deviation kriging system kriging variance kriging weights Lagrange multiplier linear combination linear geostatistics linear model linear regression mean obtained ordinary kriging orebody outliers parameter point kriging positive definite practical range pure nugget effect random function range of 200m regionalized variable regular reserves seam shows sill of 3.0 simple kriging Simulation slope small blocks spaced spatial covariance spherical model spherical variogram statistics structured Table thickness true grade variogram cloud variogram model variogram values vertical variogram Z(x+h zero Σα Σλ
Verweise auf dieses Buch
Geostatistics for Environmental Scientists Richard Webster,Margaret A. Oliver Eingeschränkte Leseprobe - 2007 |
Applied Spatial Statistics for Public Health Data Lance A. Waller,Carol A. Gotway Eingeschränkte Leseprobe - 2004 |