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Spatial Modeling Principles in Earth Sciences
Zekai Sen
Verlag Springer-Verlag, 2009
ISBN 9781402096723 , 351 Seiten
Format PDF, OL
Kopierschutz Wasserzeichen
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