Spatial Modeling Principles in Earth Sciences / Edition 1

by Zekai Sen

Overview

Data collection in the earth, sciences is often difficult and expensive. It requires special care to gather accurate information. Spatial simulation methodologies in the earth sciences are essential in order to understand the variability in features for example fracture frequencies, rock quality, and grain size distribution in rock and porous media. This book is a comprehensive presentation of spatial modeling techniques used in the earth sciences. It also presents original techniques developed by the author.

This book outlines in a detailed yet accessible way the main spatial modeling techniques, in particular the Kriging methodology. It presents many unique physical approaches, field cases, and sample interpretations. Since Kriging's origin in the 1960s it has been developed into a number of new methods such as cumulative (CSV), point CSV (PCSV), and spatial dependence function, which have been applied in different aspects of the earth sciences. Each one of these techniques is explained in this hook, as well as how they are used to model earth science phenomena such as earthquakes, meteorology, and hydrology. In addition to Kriging methodology and its variants, several alternatives are presented and the necessary steps in their application are clearly explained. Simple spatial variation prediction methodologies are also revised with up-to-date literature, and the way in which they relate to more advanced spatial modeling methodologies are explained.

The book is a valuable resources for students, researchers and professionals within a broad range of discipline including geology, geography, hydrology, meteorology, environment, image processing, spatial modeling and relatedtopics.

Product Details

ISBN-13:	9781402096716
Publisher:	Springer Netherlands
Publication date:	07/16/2009
Edition description:	2009
Pages:	351
Product dimensions:	6.20(w) x 9.20(h) x 1.00(d)

About the Author

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).

Table of Contents

1 Introduction 1

1.1 General 1

1.2 Earth Sciences Phenomena 2

1.3 Variability 8

1.4 Determinism Versus Uncertainty 12

1.5 Earth, Environment, and Atmospheric Researches 16

1.6 Random Field (RF) 17

1.7 Regionalized Variable (ReV) 18

References 19

2 Data Types and Logical Processing Methods 21

2.1 General 21

2.2 Observations 22

2.3 Numerical Data Types 25

2.4 Sampling 27

2.5 Number of Data 33

2.5.1 Small Sample Length of Independent Models 33

2.5.2 Small Sample Length of Dependent Models 35

2.6 Regional Representation 41

2.6.1 Variability Range 42

2.6.2 Inverse Distance Models 45

2.7 Sub-areal Partition 46

2.7.1 Triangularization 47

2.8 Polygonizations 52

2.8.1 Delaney, Varoni, and Thiessen Polygons 52

2.8.2 Percentage-Weighted Polygon (PWP) Method 55

2.9 Areal Coverage Probability 67

2.9.3 Theoretical Treatment 69

2.9.2 Extreme Value Probabilities 72

2.10 Spatio-Temporal Drought Theory and Analysis 73

2.10.1 Drought Parameters 76

References 81

3 Classical Spatial Variation Models 83

3.1 General 83

3.2 Spatio-Temporal Characteristics 84

3.3 Spatial Pattern Search 85

3.4 Spatial Data Analysis Needs 87

3.5 Simple Uniformity Test 93

3.6 Random Field 95

3.7 Cluster Sampling 98

3.8 Nearest Neighbor Analysis 100

3.9 Search Algorithms 102

3.9.1 Geometric Weighting Functions 103

3.10 Trend Surface Analysis 106

3.10.1 Trend Model Parameter Estimations 108

3.11 Multisite Kalman Filter Methodology 110

3.11.1 One-Dimensional Kalman Filter 112

3.11.2 Kalman Filter Application 115

References 126

4 Spatial Dependence Measures 127

4.1 General 127

4.2 Isotropy, Anisotropy, and Homogeneity 129

4.3 SpatialDependence Function 132

4.4 Spatial Correlation Function 135

4.4.1 Correlation Coefficient Drawback 136

4.5 Semivariogram Regional Dependence Measure 140

4.5.1 SV Philosophy 140

4.5.2 SV Definition 144

4.5.3 SV Limitations 149

4.6 Sample SV 151

4.7 Theoretical SV 153

4.7.1 Simple Nugget SV 156

4.7.2 Linear SV 157

4.7.3 Exponential SV 159

4.7.4 Gaussian SV 159

4.7.5 Quadratic SV 160

4.7.6 Rational Quadratic SV 160

4.7.7 Power SV 161

4.7.8 Wave (Hole Effect) SV 162

4.7.9 Spherical SV 162

4.7.10 Logarithmic SV 163

4.8 Cumulative Semivariogram 164

4.8.1 Sample CSV 167

4.8.2 Theoretical CSV Models 169

4.9 Point Cumulative Semivariogram 175

4.10 Spatial Dependence Function 183

References 199

5 Spatial Modeling 203

5.1 General 204

5.2 Spatial Estimation of ReV 205

5.3 Optimum Interpolation Model 207

5.3.1 Data and Application 211

5.4 Geostatistical Analysis 224

5.4.1 Kriging Technique 225

5.5 Geostatistical Estimator (Kriging) 228

5.5.1 Kriging Methodologies and Advantages 230

5.6 Simple Kriging 232

5.7 Ordinary Kriging 239

5.8 Universal Kriging 245

5.9 Block Kriging 249

5.10 Triple Diagram Model 250

5.11 Regional Rainfall Pattern Description 256

References 266

6 Spatial Simulation 271

6.1 General 272

6.2 3D Autoregressive Model 273

6.2.1 Parameters Estimation 274

6.2.2 2D Uniform Model Parameters 276

6.2.3 Extension to 3D 279

6.3 Rock Quality Designation Simulation 281

6.3.1 Independent Intact Lengths 281

6.3.2 Dependent Intact Lengths 290

6.4 RQD and Correlated Intact Length Simulation 300

6.4.1 Proposed Models of Persistance 303

6.4.2 Simulation of Intact Lengths 305

6.5 Autorun Simulation of Porous Material 310

6.5.1 Line Characteristic Function of Porous Medium 312

6.5.2 Autorun Analysis of Sandstone 312

6.5.3 Autorun Modeling of Porous Media 316

6.6 CSV Technique for Identification of Intact Length Correlation Structure 321

6.6.1 Intact Length CSV 323

6.6.2 Theoretical CSV Model 324

6.7 Multidirectional RQD Simulation 333

6.7.1 Fracture Network Model 334

6.7.2 RQD Analysis 335

6.7.3 RQD Simulation Results 338

References 340

Index 343