Basic Linear Geostatistics

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 Urheberrecht

Verweise auf dieses Buch

 Geostatistics for Environmental ScientistsEingeschränkte Leseprobe - 2007
 Applied Spatial Statistics for Public Health DataEingeschränkte Leseprobe - 2004
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