| Preface to the Second Edition |
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xvii | |
| Preface |
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xix | |
| Introduction |
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xxiii | |
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PART 1 INTRODUCTION TO FIELD THEORY |
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Chapter 1 Differential Calculus of Vector Fields and Differential Forms |
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3 | (24) |
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1.1 The Basic Differential Relationships of Field Theory |
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4 | (8) |
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1.1.1 Concept of the Physical Field |
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4 | (2) |
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1.1.2 Dot (Scalar) and Cross (Vector) Products of Vectors |
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6 | (1) |
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1.1.3 Vector Differential Operators |
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7 | (4) |
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1.1.4 Differentiation of the Products of Scalar and Vector Fields |
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11 | (1) |
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1.2 The Basic Integral Relationships of Field Theory |
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12 | (6) |
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1.2.1 Concept of Work and Flux of a Field |
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12 | (2) |
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1.2.2 Gauss's Theorem and Its Vector Formulations |
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14 | (2) |
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1.2.3 Stokes's Theorem and Its Vector Formulations |
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16 | (1) |
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17 | (1) |
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1.3 Differential Forms in Field Theory |
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18 | (9) |
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1.3.1 Concept of the Differential Form |
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18 | (3) |
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1.3.2 Exterior (Wedge) Product of the Linear Forms |
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21 | (1) |
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1.3.3 Canonical Representations of the Differential Forms in Three-Dimensional Euclidean Space |
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22 | (1) |
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1.3.4 The Exterior Derivative |
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23 | (3) |
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References and Recommended Reading to
Chapter 1 |
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26 | (1) |
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Chapter 2 Foundations of Field Theory |
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27 | (30) |
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28 | (10) |
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2.1.1 Harmonic Functions; Liouville's Theorem |
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28 | (1) |
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2.1.2 Uniqueness of Determination of the Scalar Field by Its Gradient and the Vector Field by Its Divergence and Curl |
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29 | (2) |
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2.1.3 Field Generation Conditions |
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31 | (1) |
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2.1.4 Sources of the Field and Their Physical Meaning |
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32 | (3) |
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2.1.5 Vortices of the Field and Their Physical Meaning |
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35 | (2) |
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2.1.6 Source Field and Vortex Field |
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37 | (1) |
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2.2 Stationary Field Equations and Methods of Their Solutions |
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38 | (6) |
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2.2.1 Poisson's Equations for Scalar and Vector Fields |
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38 | (2) |
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2.2.2 Point Source; Dirac Singular Function |
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40 | (1) |
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2.2.3 Fundamental Green's Function for the Laplace Equation |
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41 | (3) |
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2.3 Scalar and Vector Potentials of the Stationary Field |
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44 | (4) |
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2.3.1 Scalar Potential of the Source Field |
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44 | (1) |
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2.3.2 Vector Potential of the Vortex Field |
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45 | (1) |
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2.3.3 Helmholtz Theorem and Classification of the Vector Fields |
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46 | (2) |
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2.4 Nonstationary Fields and Differential Forms |
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48 | (9) |
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2.4.1 Nonstationary Vector Fields and Differential Forms in Four-Dimensional Space E4 |
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48 | (1) |
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2.4.2 Differential Form Equations |
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49 | (2) |
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2.4.3 Ampere-Type Differential Forms and a Continuity Equation |
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51 | (1) |
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2.4.4 Faraday-Type Differential Forms and the Four-Potential |
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52 | (1) |
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2.4.5 Nonstationary Vector Field Equations |
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53 | (1) |
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References and Recommended Reading to
Chapter 2 |
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54 | (3) |
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PART 2 FOUNDATIONS OF ELECTROMAGNETIC THEORY |
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Chapter 3 Electromagnetic Field Equations |
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57 | (34) |
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3.1 Maxwell's Equations and Boundary Conditions |
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59 | (14) |
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3.1.1 Basic Equations in the Theory of Electromagnetic Fields |
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59 | (3) |
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3.1.2 Physical Interpretation of Maxwell's Equations |
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62 | (6) |
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3.1.3 Boundary Conditions for the Vector Field |
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68 | (4) |
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3.1.4 The Field in a Homogeneous Medium |
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72 | (1) |
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3.2 Time-Harmonic Electromagnetic Field |
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73 | (2) |
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3.3 Electromagnetic Energy and Poynting's Theorem |
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75 | (7) |
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3.3.1 Radiation Conditions |
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76 | (1) |
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3.3.2 Poynting's Theorem in the Time Domain |
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77 | (1) |
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3.3.3 Energy Inequality in the Time Domain |
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78 | (2) |
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3.3.4 Poynting's Theorem in the Frequency Domain |
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80 | (2) |
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3.4 Electromagnetic Green's Tensors |
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82 | (2) |
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3.4.1 Green's Tensors in the Frequency Domain |
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82 | (1) |
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3.4.2 Green's Tensors in the Time Domain |
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83 | (1) |
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3.5 Reciprocity Relations |
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84 | (7) |
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84 | (2) |
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3.5.2 Reciprocity Relations for the Green's Tensors and Electromagnetic Fields |
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86 | (1) |
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3.5.3 Electromagnetic Green's Tensor Representation Theorems |
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87 | (2) |
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References and Recommended Reading to
Chapter 3 |
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89 | (2) |
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Chapter 4 Models of Electromagnetic Induction in the Earth |
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91 | (42) |
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4.1 Models of Electromagnetic Fields |
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91 | (2) |
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4.2 Static Electromagnetic Fields |
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93 | (19) |
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4.2.1 Electrostatic Fields and Electrostatic Potentials |
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93 | (2) |
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4.2.2 Boundary Conditions for Electrostatic Potential |
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95 | (2) |
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4.2.3 Calculation of the Electrostatic Field of a Specified Charge Distribution |
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97 | (1) |
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4.2.4 Analogy Between Constant Current Fields and Electrostatic Fields |
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98 | (3) |
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4.2.5 Direct Current Flow, Associated Magnetic Field, and the Biot-Savart Law |
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101 | (2) |
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4.2.6 Point and Dipole Sources on a Uniform Earth |
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103 | (6) |
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4.2.7 DC Potential in an Anisotropic Earth |
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109 | (3) |
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4.3 Electromagnetic Field Diffusion in Conductive Media |
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112 | (17) |
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4.3.1 Monochromatic Quasi-Static EM Fields |
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113 | (2) |
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4.3.2 Plane Electromagnetic Waves in a Homogeneous Medium |
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115 | (6) |
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4.3.3 Electromagnetic Potentials |
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121 | (1) |
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4.3.4 Quasi-Stationary Field of a Dipole Source in a Homogeneous Medium |
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122 | (4) |
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4.3.5 Spherical Electromagnetic Waves |
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126 | (3) |
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4.4 Electromagnetic Waves |
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129 | (4) |
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References and Recommended Reading to
Chapter 4 |
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131 | (2) |
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Chapter 5 Electromagnetic Fields in Horizontally Stratified Media |
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133 | (68) |
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5.1 Plane Wave Propagation in a Layered Earth |
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134 | (11) |
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5.1.1 Plane Electromagnetic Wave in a Horizontally Stratified Medium |
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134 | (6) |
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5.1.2 Low-Frequency Behavior of Wave Impedance |
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140 | (3) |
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5.1.3 Definition of Frequency Windows |
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143 | (2) |
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5.2 Spectral Method of Computing EM Fields in Horizontally Stratified Media |
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145 | (20) |
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5.2.1 Fourier Transform in the Spatial Domain |
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145 | (3) |
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5.2.2 Point Source of the DC Field in Horizontally Stratified Medium |
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148 | (10) |
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5.2.3 Electric Field of the Point Source in a Layered Earth |
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158 | (3) |
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5.2.4 Electrical Dipole Source of the DC Field in a Horizontally Layered Medium |
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161 | (2) |
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5.2.5 Expressions for Electric Fields in a Horizontally Layered Medium Using the Hankel Transform |
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163 | (2) |
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5.3 Electromagnetic Field of an Arbitrary System of Magnetospheric Currents in a Horizontally Homogeneous Medium |
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165 | (8) |
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5.3.1 Spatial Frequency-Domain (SFD) Representation of the Electromagnetic Field in a Horizontally Layered Medium |
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166 | (2) |
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5.3.2 Lipskaya-Vanyan Formulas Concerning Impedance Ratios |
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168 | (2) |
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5.3.3 Horizontal Polarization of the Electric Field in a Horizontally Homogeneous Earth, and the Reduced Spatial Wave Number Spectrum |
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170 | (3) |
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5.4 Electromagnetic Fields Generated in Layered Earth by Electric and Magnetic Dipole Transmitters |
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173 | (28) |
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5.4.1 Spectral Representation of the Field of a Horizontal Current Dipole on the Surface of a Horizontally Layered Medium |
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173 | (5) |
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5.4.2 Electromagnetic Field of a Horizontal Current Dipole at the Surface of a Homogeneous Half-Space |
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178 | (3) |
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5.4.3 Frequency Domain Representation of the Field of a Vertical Magnetic Dipole Above a Horizontally Stratified Medium |
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181 | (2) |
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5.4.4 The Magnetic Field of a Vertical Magnetic Dipole on the Surface of a Uniform Half-Space |
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183 | (1) |
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5.4.5 Near and Far Fields |
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184 | (3) |
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5.4.6 Frequency Domain Method for Computing Transient Fields |
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187 | (3) |
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5.4.7 Transient Fields of a Dipole Source Observed in a Homogeneous Medium and on the Surface of a Homogeneous Conducting Half-Space; Fields in the Near and Far Zones |
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190 | (9) |
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References and Recommended Reading to
Chapter 5 |
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199 | (2) |
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Chapter 6 Electromagnetic Fields in Inhomogeneous Media |
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201 | (68) |
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6.1 Integral Equation Method |
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203 | (18) |
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6.1.1 Background (Normal) and Anomalous Parts of the Electromagnetic Field |
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203 | (1) |
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6.1.2 Poynting's Theorem and Energy Inequality for an Anomalous Field |
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204 | (1) |
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6.1.3 Integral Equation Method in Two Dimensions |
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205 | (3) |
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6.1.4 Calculation of the First Variation (Frechet Derivative) of the Electromagnetic Field for 2-D Models |
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208 | (2) |
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6.1.5 Integral Equation Method in Three Dimensions |
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210 | (1) |
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6.1.6 Contraction Integral Equation Method |
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211 | (2) |
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6.1.7 Calculation of the First Variation (Frechet Derivative) of the Electromagnetic Field for 3-D Models |
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213 | (3) |
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6.1.8 Integral Equation Method in Anisotropic Medium |
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216 | (2) |
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6.1.9 Discrete Form of the Anisotropic IE Forward Modeling Method |
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218 | (1) |
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6.1.10 Contraction Integral Equation as the Preconditioned Conventional Integral Equation |
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219 | (2) |
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6.2 Integral Equation Method in Models With Inhomogeneous Background Conductivity |
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221 | (5) |
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6.2.1 Model With Inhomogeneous Background Conductivity |
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221 | (3) |
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6.2.2 Accuracy Control of the IBC IE Method |
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224 | (2) |
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6.3 Family of Linear and Nonlinear Integral Approximations of the Electromagnetic Field |
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226 | (14) |
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6.3.1 Born and Extended Born Approximations |
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227 | (1) |
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6.3.2 Quasi-Linear Approximation and Tensor Quasi-Linear Equation |
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228 | (1) |
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6.3.3 QL Approximation Using a Multigrid Approach |
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229 | (1) |
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6.3.4 Quasi-Analytical Solutions for a 3-D Electromagnetic Field |
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230 | (3) |
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6.3.5 Quasi-Analytical and Quasi-Born Approximations for a Model With Variable Background |
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233 | (3) |
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6.3.6 Quasi-Analytical Solutions for 2-D Electromagnetic Fields |
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236 | (1) |
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6.3.7 Localized Nonlinear Approximation |
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236 | (2) |
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6.3.8 Localized Quasi-Linear Approximation |
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238 | (2) |
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6.4 Differential Equation Methods |
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240 | (29) |
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6.4.1 Field Equations and Boundary Conditions |
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240 | (3) |
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6.4.2 Electromagnetic Potential Equations and Boundary Conditions |
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243 | (2) |
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6.4.3 Finite Difference Approximation of Boundary-Value Problem |
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245 | (1) |
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6.4.4 Discretization of Maxwell's Equations Using a Staggered Grid |
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246 | (3) |
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6.4.5 Contraction Preconditioner for a System of FD Equations |
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249 | (2) |
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6.4.6 Discretization of the Electromagnetic Potential Differential Equations |
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251 | (3) |
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6.4.7 Finite Element Solution of Boundary-Value Problems |
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254 | (3) |
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6.4.8 Edge-Based Finite Element Method |
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257 | (4) |
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References and Recommended Reading to
Chapter 6 |
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261 | (8) |
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PART 3 INVERSION AND IMAGING OF ELECTROMAGNETIC FIELD DATA |
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Chapter 7 Principles of Ill-Posed Inverse Problem Solution |
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269 | (20) |
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7.1 ILL-Posed Inverse Problems |
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270 | (2) |
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7.1.1 Formulation of Well-Posed and Ill-Posed Problems |
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270 | (1) |
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271 | (1) |
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7.1.3 Quasi-Solution of the Ill-Posed Problem |
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271 | (1) |
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7.2 Foundations of Regularization Theory |
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272 | (10) |
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7.2.1 Definition of Misfit Functional |
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272 | (3) |
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7.2.2 Regularizing Operators |
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275 | (1) |
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7.2.3 Stabilizing Functionals |
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276 | (5) |
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7.2.4 Tikhonov Parametric Functional |
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281 | (1) |
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7.3 Regularization Parameter |
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282 | (7) |
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7.3.1 Tikhonov Method of Regularization Parameter Selection |
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282 | (3) |
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7.3.2 L-Curve Method of Regularization Parameter Selection |
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285 | (1) |
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References and Recommended Reading to
Chapter 7 |
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286 | (3) |
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Chapter 8 Electromagnetic Inversion |
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289 | (28) |
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290 | (12) |
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290 | (1) |
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8.1.2 Discrete Linear EM Inverse Problem |
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291 | (1) |
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8.1.3 The Tikhonov Regularization Method of Linear Inversion |
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292 | (1) |
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8.1.4 Definition of the Weighting Matrices for Model Parameters and Data |
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293 | (2) |
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8.1.5 Approximate Regularized Solution of Linear Inverse Problem |
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295 | (2) |
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8.1.6 The Levenberg-Marquardt Method |
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297 | (1) |
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8.1.7 Conductivity Imaging by the Born Approximation |
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297 | (4) |
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8.1.8 Iterative Born Inversions |
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301 | (1) |
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302 | (9) |
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8.2.1 Formulation of the Nonlinear EM Inverse Problem |
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302 | (1) |
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8.2.2 Regularized Solution of Nonlinear Discrete EM Inverse Problem |
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302 | (1) |
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8.2.3 The Steepest Descent Method for Nonlinear Regularized Least-Squares Inversion |
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303 | (1) |
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8.2.4 The Newton Method for Nonlinear Regularized Least-Squares Inversion |
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304 | (1) |
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8.2.5 Numerical Schemes of the Newton Method for Nonlinear Regularized Least-Squares Inversion |
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305 | (1) |
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8.2.6 Nonlinear Least-Squares Inversion by the Conjugate Gradient Method |
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306 | (1) |
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8.2.7 The Numerical Scheme of the Regularized Conjugate Gradient Method for Nonlinear Least-Squares Inversion |
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307 | (1) |
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8.2.8 Frechet Derivative Calculation |
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308 | (2) |
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8.2.9 Frechet Derivative Calculation Using Quasi-Born Approximation |
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310 | (1) |
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8.3 Quasi-Linear Inversion |
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311 | (1) |
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8.3.1 Principles of Quasi-Linear Inversion |
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311 | (1) |
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8.3.2 Localized Quasi-Linear Inversion |
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312 | (1) |
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8.4 Quasi-Analytical Inversion |
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312 | (5) |
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8.4.1 Frechet Derivative Calculation |
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312 | (2) |
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8.4.2 Inversion Based on the Quasi-Analytical Method |
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314 | (1) |
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References and Recommended Reading to
Chapter 8 |
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314 | (3) |
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Chapter 9 Electromagnetic Migration |
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317 | (36) |
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9.1 Electromagnetic Migration in the Time Domain |
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318 | (4) |
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9.1.1 Physical Principles of Electromagnetic Migration |
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318 | (1) |
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9.1.2 Migration in a Model With Homogeneous Background Conductivity |
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319 | (1) |
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9.1.3 Migration Using Integral Transformation |
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320 | (2) |
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9.2 Analytic Continuation and Migration in the (k, co) Domain |
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322 | (8) |
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9.2.1 Analytic Continuation of the EM Field |
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322 | (1) |
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9.2.2 Migration as a Spectral Transformation |
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323 | (2) |
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9.2.3 Convolution Form of Migration Operator |
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325 | (2) |
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9.2.4 Constructing a Digital Filter for EM Migration |
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327 | (1) |
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9.2.5 Spectral Characteristic of the Digital Filter |
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328 | (2) |
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9.3 Finite Difference Migration |
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330 | (7) |
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9.3.1 2-D Finite Difference Migration |
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330 | (4) |
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9.3.2 Finite Difference Migration of a 3-D EM Field |
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334 | (3) |
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9.4 Visualization of Geoelectric Structures by Use of Migration in the Frequency and Time Domains |
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337 | (3) |
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9.4.1 Migration Imaging Condition in the Frequency Domain |
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337 | (2) |
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9.4.2 Migration Imaging Condition in the Time Domain |
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339 | (1) |
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9.5 Migration Versus Inversion |
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340 | (13) |
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9.5.1 Formulation of the Inverse Problem |
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340 | (1) |
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9.5.2 General Concept of the Migration Anomalous Field |
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341 | (2) |
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9.5.3 General Migration Imaging Conditions |
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343 | (2) |
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9.5.4 Regularized Iterative Migration |
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345 | (3) |
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References and Recommended Reading to
Chapter 9 |
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348 | (5) |
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PART 4 GEOPHYSICAL ELECTROMAGNETIC METHODS |
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Chapter 10 Electromagnetic Properties of Rocks and Minerals |
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353 | (48) |
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10.1 Properties and Units |
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354 | (5) |
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10.1.1 Electrical Conductivity and Resistivity |
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354 | (1) |
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10.1.2 Dielectric Permittivity |
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355 | (2) |
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10.1.3 Magnetic Permeability |
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357 | (1) |
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357 | (2) |
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10.2 Properties in a Parametric Sense |
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359 | (23) |
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10.2.1 Electric Properties of Rock-Forming Minerals and Rocks |
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359 | (13) |
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10.2.2 Induced Polarization |
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372 | (3) |
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10.2.3 Dielectric Properties of Rock-Forming Minerals |
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375 | (5) |
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10.2.4 Magnetic Properties of Minerals |
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380 | (2) |
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10.3 Effective Conductivity of Heterogeneous Multiphase Rocks |
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382 | (8) |
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10.3.1 Mixture of Conductive Minerals in a Host Rock |
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382 | (1) |
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10.3.2 Principles of the Effective-Medium Theory |
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382 | (6) |
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10.3.3 Effective Conductivity of Heterogeneous Medium |
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388 | (2) |
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10.4 Properties in an Existential Sense |
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390 | (4) |
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10.4.1 Concepts of a Geoelectric Structure and a Geoelectric Section |
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390 | (1) |
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10.4.2 Longitudinal Conductance and Transverse Resistance of the Horizontally Layered Geoelectric Section |
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391 | (3) |
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10.5 Properties of Large-Scale Geoelectric Structures |
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394 | (7) |
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10.5.1 Geoelectric Mesostructures and Megastructures |
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394 | (1) |
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395 | (2) |
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397 | (2) |
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References and Recommended Reading to
Chapter 10 |
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399 | (2) |
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Chapter 11 Generation and Measurement of Electromagnetic Fields in Geophysical Applications |
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401 | (38) |
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402 | (8) |
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11.1.1 Sources of EM Fields |
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402 | (3) |
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405 | (1) |
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11.1.3 Grounding Structures |
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405 | (5) |
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11.2 Measurement of Electric and Magnetic Fields |
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410 | (17) |
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11.2.1 Voltage, Potential, and Electric Field |
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410 | (6) |
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11.2.2 Sensing the Magnetic Field |
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416 | (11) |
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11.3 Preprocessing of the Data |
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427 | (12) |
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428 | (1) |
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11.3.2 Analog-to-Digital Conversion |
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428 | (1) |
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429 | (5) |
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434 | (3) |
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437 | (1) |
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References and Recommended Reading to
Chapter 11 |
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437 | (2) |
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Chapter 12 Direct Current and Induced Polarization Methods |
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439 | (56) |
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12.1 Vertical Electric Sounding and Apparent Resistivity |
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441 | (13) |
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12.1.1 Techniques for Vertical Electric Sounding |
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441 | (7) |
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12.1.2 Three Point Electrode Array |
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448 | (2) |
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12.1.3 Dipole Electric Sounding |
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450 | (4) |
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12.2 Induced Polarization (IP) Methods |
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454 | (7) |
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12.2.1 Induced Polarization Phenomena |
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454 | (1) |
|
12.2.2 IP Method in the Frequency and Time Domains |
|
|
455 | (3) |
|
12.2.3 Resistivity/IP Model of a Typical Porphyry Copper System in the Southwestern U.S. |
|
|
458 | (3) |
|
12.3 Physical and Mathematical Models of the IP Phenomenon |
|
|
461 | (19) |
|
12.3.1 IP Phenomenon in the Context of Effective-Medium Theory |
|
|
462 | (4) |
|
12.3.2 Effective Conductivity of a Heterogeneous Polarizable Medium |
|
|
466 | (1) |
|
12.3.3 Self-Consistent Approximation for Effective Conductivity |
|
|
467 | (1) |
|
12.3.4 Anisotropy Effect in IP Data |
|
|
468 | (1) |
|
12.3.5 Fundamental IP Model I: Effective Resistivity of the Isotropic Multiphase Heterogeneous Medium Filled With Spherical Inclusions |
|
|
469 | (5) |
|
12.3.6 Fundamental IP Model II: Effective Resistivity of the Multiphase Heterogeneous Medium Filled With Elliptical Inclusions |
|
|
474 | (6) |
|
12.4 Nonlinear Regularized Inversion of IP Data Based on the GEMTIP Model |
|
|
480 | (15) |
|
12.4.1 Regularized Integral Equation (IE)-Based Inversion for Complex Resistivity |
|
|
482 | (3) |
|
12.4.2 Regularized Inversion for the GEMTIP Model Parameters |
|
|
485 | (3) |
|
12.4.3 Quantitative Interpretation of IP Data - the Road Ahead |
|
|
488 | (1) |
|
References and Recommended Reading to
Chapter 12 |
|
|
489 | (6) |
|
Chapter 13 Magnetotelluric and Magnetovariational Methods |
|
|
495 | (90) |
|
13.1 Earth EM Field of External Origin |
|
|
496 | (8) |
|
13.1.1 Quiet-Time Magnetic Field Variations |
|
|
499 | (1) |
|
|
|
500 | (3) |
|
|
|
503 | (1) |
|
|
|
503 | (1) |
|
13.2 The Tikhonov-Cagniard Model of the MT Field |
|
|
504 | (9) |
|
13.2.1 Tikhonov-Cagniard Model |
|
|
504 | (1) |
|
13.2.2 Concepts of Apparent Resistivity and Sounding |
|
|
505 | (1) |
|
13.2.3 Relationships Between the MT Sounding Curve and the Actual 1-D Resistivity Model |
|
|
506 | (7) |
|
13.3 Theory of the MT and MV Transfer Functions |
|
|
513 | (12) |
|
13.3.1 Magnetotelluric Operators: Impedance and Admittance, Telluric and Magnetic |
|
|
513 | (6) |
|
13.3.2 Induction Vectors and Magnetic and Electric Tippers |
|
|
519 | (2) |
|
13.3.3 Spectral Magnetotelluric Impedances |
|
|
521 | (4) |
|
13.4 Magnetotelluric Fields in Horizontally Inhomogeneous Media |
|
|
525 | (4) |
|
13.4.1 Concepts of External and Internal, Normal and Anomalous Parts of an Electromagnetic Field |
|
|
525 | (2) |
|
13.4.2 Anomalous Electromagnetic Fields and Their Classification |
|
|
527 | (1) |
|
13.4.3 Fields in Two-Dimensionally Inhomogeneous Media and the Concepts of E and H Polarization |
|
|
527 | (2) |
|
13.5 Magnetotelluric and Magnetovariational Surveys |
|
|
529 | (4) |
|
13.5.1 The MTS, MTP, and TCM Methods |
|
|
529 | (3) |
|
13.5.2 MVS and MVP Survey Methods |
|
|
532 | (1) |
|
13.5.3 CGDS Survey Method |
|
|
533 | (1) |
|
13.6 Processing and Analysis of MT and MV Data |
|
|
533 | (15) |
|
13.6.1 The Least-Squares Method |
|
|
534 | (6) |
|
13.6.2 Remote Reference Method |
|
|
540 | (1) |
|
13.6.3 Robust Estimation of Magnetotelluric and Induction Matrices |
|
|
541 | (4) |
|
13.6.4 Graphical Presentation of Magnetotelluric and Induction Matrices |
|
|
545 | (3) |
|
13.7 One-Dimensional Interpretation of MT Data |
|
|
548 | (11) |
|
13.7.1 Analysis of Distorted MTS Curves |
|
|
549 | (6) |
|
13.7.2 Quick and Dirty MTS Analysis |
|
|
555 | (4) |
|
13.7.3 Quantitative Interpretation of MTS Curves With One-Dimensional Models |
|
|
559 | (1) |
|
13.8 Interpretation of MVP and GDS Data |
|
|
559 | (6) |
|
13.8.1 Separation of Fields Into Internal and External Parts |
|
|
560 | (4) |
|
13.8.2 Separation of Fields Into Normal and Anomalous Parts |
|
|
564 | (1) |
|
13.9 3-D Magnetotelluric Inversion |
|
|
565 | (13) |
|
13.9.1 Tikhonov Regularization in the Full MT Impedance Tensor Inversion |
|
|
567 | (1) |
|
13.9.2 Principles of the Re-weighted Regularized Inversion |
|
|
568 | (2) |
|
13.9.3 Minimum Support Nonlinear Parameterization |
|
|
570 | (3) |
|
13.9.4 Frechet Operator and Its Adjoint for Two-Component Impedance Inversion |
|
|
573 | (1) |
|
13.9.5 Frechet Operator for the Full Magnetotelluric Impedance Tensor Inversion |
|
|
574 | (3) |
|
13.9.6 Frechet Derivative Calculation Using Quasi-Analytical Approximation for a Variable Background (QAVB) |
|
|
577 | (1) |
|
13.10 3D Inversion of Magnetotelluric Phase Tensor |
|
|
578 | (7) |
|
|
|
579 | (1) |
|
13.10.2 Frechet Derivative of the Phase Tensor |
|
|
580 | (1) |
|
References and Recommended Reading to
Chapter 13 |
|
|
581 | (4) |
|
Chapter 14 Electromagnetic Methods in the Frequency and Time Domains |
|
|
585 | (40) |
|
14.1 Electromagnetic Sounding in the Frequency and Time Domains |
|
|
586 | (24) |
|
|
|
589 | (4) |
|
14.1.2 Theoretical Curves for EM Sounding in the Frequency Domain |
|
|
593 | (4) |
|
14.1.3 Time-Domain Electromagnetic Sounding |
|
|
597 | (8) |
|
14.1.4 Properties of TDEM Sounding Curves |
|
|
605 | (5) |
|
14.2 Interpretation of Controlled-Source Time Domain EM Data Using the Thin-Sheet Approach |
|
|
610 | (9) |
|
14.2.1 The Price-Sheinman and Tikhonov-Dmitriev Thin-Film Models With Laterally Varying Conductance |
|
|
610 | (2) |
|
14.2.2 Transient Field of a Magnetic Dipole Above a Conducting Thin Sheet |
|
|
612 | (5) |
|
14.2.3 S-Inversion Method |
|
|
617 | (2) |
|
14.3 Electromagnetic Profile and Array Surveys |
|
|
619 | (6) |
|
14.3.1 Profiling With Two Loops |
|
|
620 | (1) |
|
14.3.2 Profiling With Large Fixed Sources |
|
|
620 | (1) |
|
14.3.3 Transient Electromagnetic Techniques: UTEM, LOTEM, and MTEM Methods |
|
|
620 | (1) |
|
References and Recommended Reading to
Chapter 14 |
|
|
621 | (4) |
|
Chapter 15 Marine Electromagnetic Methods |
|
|
625 | (38) |
|
15.1 Marine Magnetotelluric Method |
|
|
626 | (4) |
|
15.1.1 Main Characteristic of Seaffoor EM Equipment |
|
|
626 | (3) |
|
15.1.2 Comparison Between Land and Sea-Bottom Electromagnetic Anomalies |
|
|
629 | (1) |
|
15.2 Marine Controlled-Source Electromagnetic Methods |
|
|
630 | (8) |
|
15.2.1 Electrical Exploration in Shallow Water |
|
|
631 | (1) |
|
15.2.2 Electrical Exploration Beneath Deep Oceans |
|
|
632 | (6) |
|
15.3 MCSEM Method With Arrays of Fixed Ocean Bottom Receivers and Towed Transmitters |
|
|
638 | (13) |
|
15.3.1 General Survey Configuration of the MCSEM Method |
|
|
638 | (4) |
|
15.3.2 Interpretation of MCSEM Data |
|
|
642 | (9) |
|
15.4 Towed Streamer Electromagnetic Method |
|
|
651 | (12) |
|
15.4.1 General Principles of the Towed Streamer EM Method |
|
|
651 | (2) |
|
15.4.2 Interpretation of Towed Streamer EM Data |
|
|
653 | (2) |
|
15.4.3 Moving Sensitivity Domain Approach |
|
|
655 | (3) |
|
References and Recommended Reading to
Chapter 15 |
|
|
658 | (5) |
|
Chapter 16 Airborne Electromagnetic Methods |
|
|
663 | (20) |
|
16.1 Frequency Domain Airborne Surveys |
|
|
664 | (2) |
|
16.2 Time Domain Airborne Surveys |
|
|
666 | (3) |
|
16.3 3-D Modeling and Inversion of Airborne EM Data |
|
|
669 | (3) |
|
16.4 Ground-Based Transmitter and Natural EM Field Airborne Surveys |
|
|
672 | (11) |
|
16.4.1 Far Field AEM Methods |
|
|
672 | (3) |
|
|
|
675 | (4) |
|
References and Recommended Reading to
Chapter 16 |
|
|
679 | (4) |
|
Chapter 17 Case Histories |
|
|
683 | (30) |
|
17.1 Tectonic Studies -- EarthScope MT Survey in the Northwestern United States |
|
|
683 | (6) |
|
17.2 Crustal Studies -- the Khibini Experiment |
|
|
689 | (3) |
|
17.3 Minerals Exploration -- IP Survey in Mongolia |
|
|
692 | (5) |
|
17.4 Minerals Exploration -- Airborne Survey in Reid-Mahaffy Site, Canada |
|
|
697 | (4) |
|
17.5 Hydrocarbon Exploration -- Off-Shore EM Survey in North Sea |
|
|
701 | (4) |
|
17.5.1 The Acquisition Configuration and Survey Layout |
|
|
702 | (2) |
|
17.5.2 3D Anisotropic Inversions of the Towed Streamer EM Data |
|
|
704 | (1) |
|
17.6 Marine Magnetotellurics in the Gulf of Mexico |
|
|
705 | (8) |
|
References and Recommended Reading to
Chapter 17 |
|
|
708 | (5) |
|
Appendix A Algebra of Differential Forms |
|
|
713 | (14) |
|
A.1 Differential Forms in Three-Dimensional Space |
|
|
713 | (6) |
|
A.1.1 1-, 2-, and 3-Forms |
|
|
713 | (1) |
|
A.1.2 Exterior Product of the Differential Forms |
|
|
714 | (1) |
|
A.1.3 Basis of Differential Forms |
|
|
715 | (4) |
|
A.2 Differential Forms in Multidimensional Spaces |
|
|
719 | (8) |
|
|
|
719 | (2) |
|
A.2.2 Differential Forms in Euclidean Space En |
|
|
721 | (1) |
|
A.2.3 Differential Forms in Minkowskian Space M4 |
|
|
722 | (5) |
|
Appendix B Calculus of Differential Forms |
|
|
727 | (10) |
|
B.1 Exterior Differentiation of the Forms |
|
|
727 | (6) |
|
B.1.1 Exterior Differential Operator in Multidimensional Space En |
|
|
728 | (2) |
|
B.1.2 Exterior Differential Operator in Four-Dimensional Space M4 |
|
|
730 | (3) |
|
B.2 Integration of the Forms |
|
|
733 | (4) |
|
B.2.1 Three-Dimensional Space E3 |
|
|
733 | (2) |
|
B.2.2 Beyond Three-Dimensional Space |
|
|
735 | (2) |
|
Appendix C Linear Operators and Their Matrices |
|
|
737 | (4) |
|
Appendix D Mathematical Notations |
|
|
741 | (2) |
|
Appendix E Definition of Fields and Units |
|
|
743 | (2) |
| Bibliography |
|
745 | (18) |
| Index |
|
763 | |
