Three-Dimensional Electromagnetics (eBook)

Front Cover 1
Three-Dimensional Electromagaetics 4
Copyright Page 5
CONTENTS 8
Preface 6
Part I: 3-D EM Modeling 16
CHAPTER 1. AN INTEGRAL EQUATION SOLUTION TO THE GEOPHYSICAL ELECTROMAGNETIC FORWARD-MODELLING PROBLEM 18
1. Introduction 18
2. The Integral Equation 19
3. Numerical Solution — Galerkin Approach 22
4. Edge Element Basis Vectors 23
5. The Green's Functions — Part I 25
6. Evaluation of the Integrals 25
7. The Green's Functions — Part II 26
8. Examples 28
9. Computational Efficiency 29
10. Conclusions 32
References 34
CHAPTER 2. COMPRESSION IN 3-D INTEGRAL EQUATION MODELING 36
1. Introduction 36
2. Forward Modeling with 3-D Integral Equations 37
3. Compression Matrix 40
4. Compression in Three Dimensions 41
5. Compression as Preconditioner to the Integral Equation 46
6. The ILU Preconditioned Conjugate Gradient Method 47
7. Modeling Examples 51
8. Conclusions 54
References 56
CHAPTER 3. MODELLING ELECTROMAGNETIC FIELDS IN A 3D SPHERICAL EARTH USING A FAST INTEGRAL EQUATION APPROACH 58
1. Introduction 58
2. Governing Equations 59
3. Solution Verification 62
4. Concluding Remarks 65
Appendix A. Dyadic Green's functions of radially symmetric section 65
References 68
CHAPTER 4. MODELLING INDUCTION LOG RESPONSES IN 3D GEOMETRIES USING A FAST INTEGRAL EQUATION APPROACH 70
1. Introduction 70
2. Theory 71
3. Computational Load 73
4. Numerical Examples 73
5. Concluding Remarks 77
References 77
CHAPTER 5. NONLINEAR APPROXIMATIONS FOR ELECTROMAGNETIC SCATTERING FROM ELECTRICAL AND MAGNETIC INHOMOGENEITIES 80
1. Introduction 80
2. Integral Equation Formulation 81
3. Born Approximation 83
4. Localized Approximation 83
5. Quasi-Linear Approximation 85
6. Quasi-Analytical Approximation 85
7. Numerical Results and Validation 88
8. Conclusions 91
Appendix A. Quasi-Analytical One-Dimensional Solution 95
References 98
CHAPTER 6. THREE-DIMENSIONAL MODELING CONSIDERING THE TOPOGRAPHY FOR THE CASE OF THE TIME-DOMAIN ELECTROMAGNETIC METHOD 100
1. Introduction 100
2. Theory 101
3. Numerical Checks 107
4. Numerical Examples 108
5. Conclusions 111
Appendix A. Correspondence of the Differential Coefficients between the Physical Domain and the Computational Domain 114
Appendix B. Derivation of the Finite-Difference Equations 116
References 121
CHAPTER 7. REDUCED-ORDER MODELING OF TRANSIENT DIFFUSIVE ELECTROMAGNETIC FIELDS 124
1. Introduction 124
2. Basic Equations 126
3. Reduced-Order Models for the Diffusive Electromagnetic Field 128
4. Numerical Results 130
5. Conclusions 135
Appendix A. The Lanczos Algorithm for Skew Symmetric Matrices 135
References 138
Part II: 3-D EM Inversion 140
CHAPTER 8. THREE-DIMENSIONAL MAGNETOTELLURIC MODELING AND INVERSION: APPLICATION TO SUB-SALT IMAGING 142
1. Introduction 142
2. The 3D MT Forward Problem 144
3. The 3D MT Inverse Problem 148
4. Marine MT Resolution Study 152
5. Conclusions 164
Appendix A 165
References 166
CHAPTER 9. 2-D INVERSION OF FREQUENCY-DOMAIN EM DATA CAUSED BY A 3-D SOURCE 168
1. Introduction 168
2. Inversion Theory 169
3. Synthetic Data Example 176
4. Conclusions 182
Appendix A. Expectation of Objective Function in Constrained Linearized Least- Squares Method 182
References 185
CHAPTER 10. 3-D FOCUSING INVERSION OF CSAMT DATA 188
1. Introduction 188
2. The Method of Integral Equations 189
3. The CSAMT Forward Problem 191
4. Formulation of the Inverse Problem 195
5. Bilinear Corrections with a Modified Green's Operator 200
6. Tests on Models 201
7. Inversion of Real Data 204
8. Conclusion 205
References 206
CHAPTER 11. SGILD EM MODELING AND INVERSION IN GEOPHYSICS AND NANO-PHYSICS USING MAGNETIC FIELD EQUATIONS 208
1. Introduction 208
2. Stochastic GILD EM Modeling 210
3. Stochastic GILD EM Inversion 212
4. Application 216
5. Conclusion 221
Appendix A. Integral Equations for the Magnetic Field 221
Appendix B. Theoretical Analysis 224
References 227
CHAPTER 12. APPLICATION OF A NON-ORTHOGONAL COORDINATE SYSTEM TO THE INVERSE SINGLE-WELL ELECTROMAGNETIC LOGGING PROBLEM 230
1. Introduction 230
2. Notation and Problem Statement 232
3. Oblique Coordinate System 233
4. Forward Problem 236
5. Inverse Method 238
6. Conclusions 244
References 245
Part III: 3-D EM in Practice 248
CHAPTER 13. DECOMPOSITION OF THREE-DIMENSIONAL MAGNETOTELLURIC DATA 250
1. Introduction 250
2. 3D Decomposition 252
3. Decomposition Algorithm 253
4. Synthetic Tests 255
5. Discussion 263
References 265
CHAPTER 14. ON THE DETERMINATION OF THE ELECTRICAL 3-D CONDUCTIVITY DISTRIBUTION BENEATH ICELAND WITH LONG-PERIOD MAGNETOTELLURICS 266
1. Introduction 266
2. 3-D Modelling 267
3. Results 268
4. Discussion and Conclusions 271
References 273
CHAPTER 15. THREE-DIMENSIONAL MONITORING OF VADOSE ZONE INFILTRATION USING ELECTRICAL RESISTIVITY TOMOGRAPHY AND CROSS-BOREHOLE GROUND-PENETRATING RADAR 274
1. Introduction 274
2. ERT Methodology 275
3. XBGPR Methodology 279
4. Comparison of ERT and Radar Moisture 280
5. Discussion and Conclusions 286
References 287
CHAPTER 16. POLARIMETRIC BOREHOLE RADAR APPROACH TO FRACTURE CLASSIFICATION 288
1. Introduction 288
2. Radar Polarimetry for Borehole 289
3. Numerical Simulation 291
4. Polarimetric Borehole Radar System 295
5. Field Measurement 296
6. Discussion 298
7. Conclusions 299
References 299
Author Index 302
Subject Index 304