Spatial Modeling Principles in Earth Sciences

Preface

Contents

1 Introduction

1.1 General

1.2 Earth Sciences Phenomena

1.3 Variability

1.4 Determinism Versus Uncertainty

1.5 Earth, Environment, and Atmospheric Researches

1.6 Random Field (RF)

1.7 Regionalized Variable (ReV)

References

2 Data Types and Logical Processing Methods

2.1 General

2.2 Observations

2.3 Numerical Data Types

2.4 Sampling

2.5 Number of Data

2.5.1 Small Sample Length of Independent Models

2.5.2 Small Sample Length of Dependent Models

2.6 Regional Representation

2.6.1 Variability Range

2.6.2 Inverse Distance Models

2.7 Sub-areal Partition

2.7.1 Triangularization

2.8 Polygonizations

2.8.1 Delaney, Varoni, and Thiessen Polygons

2.8.2 Percentage-Weighted Polygon (PWP) Method

2.9 Areal Coverage Probability

2.9.1 Theoretical Treatment

2.9.2 Extreme Value Probabilities

2.10 Spatio-Temporal Drought Theory and Analysis

2.10.1 Drought Parameters

References

3 Classical Spatial Variation Models

3.1 General

3.2 Spatio-Temporal Characteristics

3.3 Spatial Pattern Search

3.4 Spatial Data Analysis Needs

3.5 Simple Uniformity Test

3.6 Random Field

3.7 Cluster Sampling

3.8 Nearest Neighbor Analysis

3.9 Search Algorithms

3.9.1 Geometric Weighting Functions

3.10 Trend Surface Analysis

3.10.1 Trend Model Parameter Estimations

3.11 Multisite Kalman Filter Methodology

3.11.1 One-Dimensional Kalman Filter

3.11.2 Kalman Filter Application

References

4 Spatial Dependence Measures

4.1 General

4.2 Isotropy, Anisotropy, and Homogeneity

4.3 Spatial Dependence Function

4.4 Spatial Correlation Function

4.4.1 Correlation Coefficient Drawback

4.5 Semivariogram Regional Dependence Measure

4.5.1 SV Philosophy

4.5.2 SV Definition

4.5.3 SV Limitations

4.6 Sample SV

4.7 Theoretical SV

4.7.1 Simple Nugget SV

4.7.2 Linear SV

4.7.3 Exponential SV

4.7.4 Gaussian SV

4.7.5 Quadratic SV

4.7.6 Rational Quadratic SV

4.7.7 Power SV

4.7.8 Wave (Hole Effect) SV

4.7.9 Spherical SV

4.7.10 Logarithmic SV

4.8 Cumulative Semivariogram

4.8.1 Sample CSV

4.8.2 Theoretical CSV Models

4.8.2.1 Linear Model

4.8.2.2 Power Model

4.8.2.3 Exponential CSV

4.8.2.4 Logarithmic CSV

4.8.2.5 Gaussian CSV

4.9 Point Cumulative Semivariogram

4.10 Spatial Dependence Function

References

5 Spatial Modeling

5.1 General

5.2 Spatial Estimation of ReV

5.3 Optimum Interpolation Model

5.3.1 Data and Application

5.3.1.1 Spatial Correlation Function

5.3.1.2 Expected Error

5.3.1.3 Data Search and Selection Procedure

5.3.1.4 Cross-Validation of the Model

5.4 Geostatistical Analysis

5.4.1 Kriging Technique

5.4.1.1 Intrinsic Property

5.5 Geostatistical Estimator (Kriging)

5.5.1 Kriging Methodologies and Advantages

5.6 Simple Kriging

5.7 Ordinary Kriging

5.8 Universal Kriging

5.9 Block Kriging

5.10 Triple Diagram Model

5.11 Regional Rainfall Pattern Description

References

6 Spatial Simulation

6.1 General

6.2 3D Autoregressive Model

6.2.1 Parameters Estimation

6.2.2 2D Uniform Model Parameters

6.2.3 Extension to 3D

6.3 Rock Quality Designation Simulation

6.3.1 Independent Intact Lengths

6.3.2 Dependent Intact Lengths

6.3.2.1 Correlation Measurement

6.3.2.2 RQD Formulation and Discussion

6.3.2.3 Applications

6.4 RQD and Correlated Intact Length Simulation

6.4.1 Proposed Models of Persistance

6.4.1.1 The Independent Process

6.4.1.2 First-Order Markov Process

6.4.1.3 ARIMA (1, 1) Process

6.4.2 Simulation of Intact Lengths

6.5 Autorun Simulation of Porous Material

6.5.1 Line Characteristic Function of Porous Medium

6.5.2 Autorun Analysis of Sandstone

6.5.3 Autorun Modeling of Porous Media

6.6 CSV Technique for Identification of Intact Length Correlation Structure

6.6.1 Intact Length CSV

6.6.2 Theoretical CSV Model

6.7 Multidirectional RQD Simulation

6.7.1 Fracture Network Model

6.7.2 RQD Analysis

6.7.3 RQD Simulation Results

References