Spatial Modeling Principles in Earth Sciences (eBook)

Prof. Dr. Zekai Sen is a researcher at the Istanbul Technical University, Turkey. His main interests are renewable energy (especially solar energy), hydrology, water resources, hydrogeology, hydrometeorology, hydraulics, philosophy of science, and science history. He has been appointed by the United Nations as a member of the Intergovernmental Panel on Climate Change (IPCC) for research on the effects of climate change. He published more than 200 papers in about 50 scientific journals, and 3 books: Applied Hydrogeology for Scientists and Engineers (1995, CRC Lewis Publishers), Wadi Hydrology (2008, CRC Lewis Publishers), and Solar Energy Fundamentals and Modeling Techniques: Atmosphere, Environment, Climate Change and Renewable Energy (2008, Springer).

Preface 6
Contents 8
1 Introduction 11
1.1 General 11
1.2 Earth Sciences Phenomena 12
1.3 Variability 17
1.4 Determinism Versus Uncertainty 22
1.5 Earth, Environment, and Atmospheric Researches 26
1.6 Random Field (RF) 27
1.7 Regionalized Variable (ReV) 28
References 29
2 Data Types and Logical Processing Methods 30
2.1 General 30
2.2 Observations 31
2.3 Numerical Data Types 34
2.4 Sampling 36
2.5 Number of Data 40
2.5.1 Small Sample Length of Independent Models 42
2.5.2 Small Sample Length of Dependent Models 44
2.6 Regional Representation 50
2.6.1 Variability Range 51
2.6.2 Inverse Distance Models 54
2.7 Sub-areal Partition 55
2.7.1 Triangularization 56
2.8 Polygonizations 60
2.8.1 Delaney, Varoni, and Thiessen Polygons 61
2.8.2 Percentage-Weighted Polygon (PWP) Method 64
2.9 Areal Coverage Probability 76
2.9.1 Theoretical Treatment 78
2.9.2 Extreme Value Probabilities 81
2.10 Spatio-Temporal Drought Theory and Analysis 82
2.10.1 Drought Parameters 85
References 90
3 Classical Spatial Variation Models 92
3.1 General 92
3.2 Spatio-Temporal Characteristics 92
3.3 Spatial Pattern Search 93
3.4 Spatial Data Analysis Needs 95
3.5 Simple Uniformity Test 102
3.6 Random Field 104
3.7 Cluster Sampling 107
3.8 Nearest Neighbor Analysis 108
3.9 Search Algorithms 111
3.9.1 Geometric Weighting Functions 112
3.10 Trend Surface Analysis 115
3.10.1 Trend Model Parameter Estimations 117
3.11 Multisite Kalman Filter Methodology 118
3.11.1 One-Dimensional Kalman Filter 121
3.11.2 Kalman Filter Application 124
References 135
4 Spatial Dependence Measures 136
4.1 General 136
4.2 Isotropy, Anisotropy, and Homogeneity 138
4.3 Spatial Dependence Function 141
4.4 Spatial Correlation Function 144
4.4.1 Correlation Coefficient Drawback 145
4.5 Semivariogram Regional Dependence Measure 149
4.5.1 SV Philosophy 149
4.5.2 SV Definition 153
4.5.3 SV Limitations 158
4.6 Sample SV 159
4.7 Theoretical SV 162
4.7.1 Simple Nugget SV 165
4.7.2 Linear SV 166
4.7.3 Exponential SV 168
4.7.4 Gaussian SV 168
4.7.5 Quadratic SV 169
4.7.6 Rational Quadratic SV 169
4.7.7 Power SV 170
4.7.8 Wave (Hole Effect) SV 171
4.7.9 Spherical SV 171
4.7.10 Logarithmic SV 172
4.8 Cumulative Semivariogram 173
4.8.1 Sample CSV 176
4.8.2 Theoretical CSV Models 178
4.8.2.1 Linear Model 178
4.8.2.2 Power Model 180
4.8.2.3 Exponential CSV 181
4.8.2.4 Logarithmic CSV 182
4.8.2.5 Gaussian CSV 183
4.9 Point Cumulative Semivariogram 184
4.10 Spatial Dependence Function 190
References 208
5 Spatial Modeling 211
5.1 General 212
5.2 Spatial Estimation of ReV 213
5.3 Optimum Interpolation Model 215
5.3.1 Data and Application 219
5.3.1.1 Spatial Correlation Function 223
5.3.1.2 Expected Error 226
5.3.1.3 Data Search and Selection Procedure 227
5.3.1.4 Cross-Validation of the Model 230
5.4 Geostatistical Analysis 231
5.4.1 Kriging Technique 233
5.4.1.1 Intrinsic Property 234
5.5 Geostatistical Estimator (Kriging) 236
5.5.1 Kriging Methodologies and Advantages 238
5.6 Simple Kriging 240
5.7 Ordinary Kriging 247
5.8 Universal Kriging 253
5.9 Block Kriging 256
5.10 Triple Diagram Model 257
5.11 Regional Rainfall Pattern Description 264
References 274
6 Spatial Simulation 278
6.1 General 278
6.2 3D Autoregressive Model 280
6.2.1 Parameters Estimation 281
6.2.2 2D Uniform Model Parameters 283
6.2.3 Extension to 3D 286
6.3 Rock Quality Designation Simulation 288
6.3.1 Independent Intact Lengths 288
6.3.2 Dependent Intact Lengths 297
6.3.2.1 Correlation Measurement 299
6.3.2.2 RQD Formulation and Discussion 300
6.3.2.3 Applications 306
6.4 RQD and Correlated Intact Length Simulation 307
6.4.1 Proposed Models of Persistance 310
6.4.1.1 The Independent Process 310
6.4.1.2 First-Order Markov Process 311
6.4.1.3 ARIMA (1, 1) Process 312
6.4.2 Simulation of Intact Lengths 312
6.5 Autorun Simulation of Porous Material 317
6.5.1 Line Characteristic Function of Porous Medium 319
6.5.2 Autorun Analysis of Sandstone 319
6.5.3 Autorun Modeling of Porous Media 323
6.6 CSV Technique for Identification of Intact Length Correlation Structure 328
6.6.1 Intact Length CSV 330
6.6.2 Theoretical CSV Model 331
6.7 Multidirectional RQD Simulation 340
6.7.1 Fracture Network Model 341
6.7.2 RQD Analysis 342
6.7.3 RQD Simulation Results 345
References 347