## Practical geostatistics: modeling and spatial analysis. ManualIn practice, application of geostatistical theory requires an integrated toolbox of statistical, geostatistical, spatial analysis and visualization techniques. This approach to the application of geostatistics for subsurface characterization is the focus of Practical Geostatistics, from a description of the data structures required, through discussion of the concepts, theory and application, to qualification of the end results. The linked, hypertext document structure facilitates the integration of theoretical discussion with detailed worked examples and numerous color images of computer visualization. It also allows multi-level progression through Practical Geostatistics at an overview, theoretical, application or interactive review level, with numerous links between. The document structure facilitates access to Practical Geostatistics through standard Internet browser technology on any computer platform. |

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### Contents

Why Geostatistics? The Requirement for Spatially Related Statistics | 1 |

Subsurface Variables | 4 |

Geological Discontinuities | 5 |

Origins in the Prediction of Gold Grades for Mining | 7 |

Applications in the Geosciences | 9 |

Integrated Computer Techniques | 10 |

Characterization Quality Concerns | 11 |

Advantages and Disadvantages of Geostatistics | 13 |

Estimation with Anisotropic Spatial Variability | 89 |

Volume Estimation of a Regionalized Variable | 91 |

The Normal Distribution Standard Error and Probability | 93 |

Spatial Variation of Uncertainty | 95 |

Standard Error as a Measure of Estimation Uncertainty | 97 |

Geological Estimation and Uncertainty | 100 |

Sampling Control Applications in Geostatistics | 102 |

Sampling Control with Estimation Uncertainty | 103 |

Disadvantages of Geostatistics | 14 |

Data Types Variables Characteristics and 3D Conventions | 16 |

Data Types | 17 |

Hole Data Structure for Borehole Samples and Observations | 21 |

Hole Data Associations | 22 |

Map Data Structure for Point Survey and Map Information | 24 |

Map Data Associations | 26 |

Volume Data Structure for Geological Structures and Stratigraphy | 27 |

Volume Geometry | 28 |

Volume Data Associations | 29 |

Grid Data Structure for a Continuous Measure of a Regionalized Variable | 31 |

3D Grid Data Associations | 32 |

Analysis of the Spatial Variability of a Regionalized Variable | 34 |

Measurement of Spatial Variability | 36 |

Derivation of a Mathematical Model of Spatial Variability | 41 |

Understanding Geostatistical SemiVariograms | 42 |

SemiVariogram Models | 43 |

Geostatistical Estimation of a Regionalized Variable | 45 |

Sample Selection Criteria for Geostatistical Estimation | 47 |

Estimating a Continuous Measure of a Regionalized Variable | 48 |

CrossValidation and Other Checks on Geostatistical Estimation | 52 |

CrossChecking of the Results of Geostatistical Estimation | 53 |

Common Problems in Geostatistical Estimation | 55 |

Analysis of Geological Influences in a Regionalized Variable | 57 |

Estimation with Geological Influences | 59 |

3D Interpretation of Geological Structures and Volumes | 60 |

3D Interpolation of Geological Volumes | 62 |

Generating Viewplane Sections Through Geological Volumes | 63 |

Considerations for 3D Interpretation | 65 |

Generation of Geological Volumes between Triangulated Surfaces | 66 |

TIN Representation of a Geological Surface | 67 |

Manipulation of TIN Surfaces | 69 |

Derivation of Volumes from TIN Surfaces | 70 |

Geostatistical Estimation with Geological Control | 72 |

Geostatistical Estimation with Geological Control | 73 |

Grid Data Structure Considerations | 75 |

Alternative Approaches to Representation of Geology | 77 |

Data Transforms for NonNormal Sample Distributions | 80 |

Log Transform | 81 |

Indicator Transform | 82 |

Rank Order Transform | 83 |

Normal Scores Transform | 84 |

Underlying Trends and Estimation of Residual Values | 86 |

Estimation with a Determinate Trend | 87 |

Anisotropy and Estimation with Directional Control | 88 |

Indicator Transforms and Probability Estimation | 106 |

Qualitative Approach | 108 |

Other Techniques for Estimation of a Regionalized Variable | 111 |

Conditional Simulation | 112 |

Direct Volume Estimation for Thin Seams | 113 |

Volumetrics Analysis of a Regionalized Variable | 115 |

Manipulation of the Results of Geostatistical Estimation | 119 |

Combining Two or More Estimated Variations | 120 |

Generation of a Net Value Variation | 122 |

Direct Volume Estimation of a Regionalized Variable | 124 |

Theoretical Basis of Direct Volume Estimation | 125 |

Practical Application of Direct Volume Estimation | 126 |

Advantages of Direct Volume Estimation | 127 |

Data Integration Issues | 128 |

Data Capture Formats | 129 |

Data Verification Techniques | 131 |

Statistical Techniques | 132 |

Geostatistical Techniques | 133 |

Visualization Techniques | 134 |

Qualification of the Results of Subsurface Characterization | 135 |

Estimation Comparisons | 136 |

Estimation Uncertainty | 137 |

Characterization Reporting | 139 |

Worked Example Grade Characterization of a Zinc Ore Deposit | 140 |

Data Review Statistics Semi Variogram Analysis of Samples | 141 |

Unconfined Geostatistical Estimation of Ore Grades | 142 |

Ore Grade Estimation with Geological Control | 143 |

Spatial Analysis of Ore Grade Variation | 144 |

Environmental Characterization and Assessment of Soil Contamination | 145 |

Data Review Statistics and Geostatistical Analysis | 146 |

Probability Estimation of Contaminant Variations | 147 |

Spatial Analysis and Volumetrics | 148 |

Sample Optimization and Quality Control | 149 |

Mineral Characterization of a Copper Ore Deposit | 150 |

Site Investigation | 151 |

Data Review Statistics SemiVariogram Analysis of Samples | 152 |

Ore Grade Estimation with Geological Control | 153 |

Spatial Analysis of Ore Grade Variation | 154 |

Geotechnical Characterization for a Tunnel Project | 155 |

Data Review Statistics SemiVariogram Analysis of Samples | 156 |

Probability Estimation of Soil Properties | 157 |

Probability Estimation of Rock Properties | 158 |

Source Data for the Worked Examples | 159 |

Credits | 160 |

### Common terms and phrases

3D grid anisotropic approach appropriate approximately associated available samples average borehole boundaries cell centroid characteristic value complex context contours conventional Cross-Validation Data Transforms defined derived Direct Volume Estimation discussed later displayed distance estimated values estimated variation estimation process Estimation Uncertainty Estimation with Geological excavation figure frequency histogram Geological Control Geological Influences geological unit Geological Volumes geometry geosciences geostatistical estimation grade variation grid data structure gridcell histogram Indicator Transforms integrated intersection interval investigation irregular volume isosurface kriging estimation manipulation map data structure mineral normal distribution obtain orientation plane Practical Geostatistics prediction Probability Estimation provides range of influence refer regionalized variable relationship relevant representation represented require sample values Sampling Control semi-variance semi-variogram analysis semi-variogram model Soil Contamination spatial analysis standard error standard error values stratigraphy subsurface characterization techniques Text documents threshold tion variogram vertical viewplane visualization volume data structure volume element volumetrics analysis XYZ coordinate zinc grades Zinc Ore Deposit