Basic Steps in Geostatistics: The Variogram and Kriging (eBook)

Preface 6
Acknowledgments 8
Contents 9
1 Introduction 11
Abstract 11
1.1 Background to Geostatistics 11
1.2 Applications of Geostatistics 12
1.2.1 Mining and Engineering 12
1.2.2 Environmental Pollution 13
1.2.3 Precision Agriculture (PA) 14
1.2.4 Fisheries 16
1.3 Sampling 16
1.3.1 The Domain 17
1.3.2 The Variables 18
1.3.3 Units and Support 18
1.3.4 Practical Matters 18
1.4 The Essence of Geostatistics 19
2 Regionalized Variable Theory 20
Abstract 20
2.1 Random Variables and Regionalized Variable Theory 20
2.1.1 Stationarity 21
3 The Variogram and Modelling 23
Abstract 23
3.1 The Experimental Variogram 24
3.1.1 Computing the Variogram from Regular Sampling in One Dimension 24
3.1.2 Computing the Variogram from Regular and Irregular Sampling in Two Dimensions 26
3.2 Factors Affecting the Reliability of Experimental Variograms 27
3.2.1 Sample Size 27
3.2.2 Sampling Interval and Spatial Scale 31
3.2.3 Lag Interval and Bin Width 32
3.2.4 Statistical Distribution 33
3.2.5 Anisotropy 36
3.2.6 Trend 38
3.3 Modelling the Variogram 38
3.3.1 Principal Features of the Variogram 38
3.3.2 Variogram Model Functions 40
3.4 Factors Affecting the Reliability of Variogram Models 45
3.4.1 Fitting Models 45
4 Geostatistical Prediction: Kriging 51
Abstract 51
4.1 Introduction 51
4.2 Theory 52
4.2.1 Kriging Weights 55
4.2.1.1 Effect of the Ratio of the Nugget:Sill Variances 56
4.2.1.2 Changing the Range 58
4.2.1.3 Block Kriging 60
4.2.1.4 Kriging with Irregularly Scattered Data 60
4.2.2 Kriging Neighbourhood 61
4.2.2.1 Effect of the Kriging Neighbourhood 62
4.2.3 Punctual and Block Kriging for Mapping 65
4.2.4 Anisotropy 71
4.2.5 Simple Kriging 73
4.2.6 Lognormal Kriging 74
4.3 Cross-Validation 75
4.4 Summary 77
5 Sampling 78
Abstract 78
5.1 Sampling for the Variogram 79
5.1.1 Nested Sampling 80
5.1.1.1 Illustrative Example: Nested Sampling in the Wyre Forest 82
5.2 Sampling Plans for Mapping 87
5.2.1 Illustrative Example: Sampling to Map Chromium in the Swiss Jura 89
5.3 Summary 90
6 Dealing with Trend 91
Abstract 91
6.1 Trend 91
6.1.1 Variogram and Model 94
6.2 Example 95
6.3 Illustration from a Case Study 96
6.4 Summary 100
References 101
Index 105