Geophysical Electromagnetic Theory and Methods (eBook)

Front Cover 1
Geophysical Electromagnetic Theory and Methods 4
Copyright Page 5
Contents 6
Preface 18
Part I: Introduction to Field Theory 22
Chapter 1. Differential Calculus of Vector Fields and Differential Forms 24
1.1 The Basic Differential Relationships of Field Theory 24
1.2 The Basic Integral Relationships of Field Theory 33
1.3 Differential Forms in Field Theory 40
References and Recommended Reading 49
Chapter 2. Foundations of Field Theory 50
2.1 Field Generation 51
2.2 Stationary Field Equations and Methods of Their Solutions 63
2.3 Scalar and Vector Potentials of the Stationary Field 70
2.4 Nonstationary Fields and Differential Forms 75
References and Recommended Reading 82
Part II: Foundations of Electromagnetic Theory 84
Chapter 3. Electromagnetic Field Equations 86
3.1 Maxwell's Equations and Boundary Conditions 88
3.2 Time-Harmonic Electromagnetic Field 104
3.3 Electromagnetic Energy and Poynting's Theorem 107
3.4 Electromagnetic Green's Tensors 114
3.5 Reciprocity Relations 117
References and Recommended Reading 124
Chapter 4. Models of Electromagnetic Induction in the Earth 126
4.1 Models of Electromagnetic Fields 127
4.2 Static Electromagnetic Fields 128
4.3 Electromagnetic Field Diffusion in Conductive Media 151
4.4 Electromagnetic Waves 171
References and Recommended Reading 172
Chapter 5. Electromagnetic Fields in Horizontally Stratified Media 174
5.1 Plane Wave Propagation in a Layered Earth 175
5.2 Spectral Method of Computing EM Fields in Horizontally Stratified Media 189
5.3 Electromagnetic Field of an Arbitrary System of Magnetospheric Currents in a Horizontally Homogeneous Medium 212
5.4 Eectromagnetic Fields Generated in Layered Earth by Electric and Magnetic Dipole Transmitters 221
References and Recommended Reading 251
Chapter 6. Electromagnetic Fields in Inhomogeneous Media 254
6.1 Integral Equation Method 256
6.2 Integral Equation Method in Models with Inhomogeneous Background Conductivity 268
6.3 Family of Linear and Nonlinear Integral Approximations of the Electromagnetic Field 275
6.4 Differential Equation Methods 291
References and Recommended Reading 313
Part III: Inversion and Imaging of Electromagnetic Field Data 318
Chapter 7. Principles of Ill-Posed Inverse Problem Solution 320
7.1 Ill-Posed Inverse Problems 321
7.2 Foundations of Regularization Theory 324
7.3 Regularization Parameter 334
References and Recommended Reading 340
Chapter 8. Electromagnetic Inversion 342
8.1 Linear Inversions 343
8.2 Nonlinear Inversion 358
8.3 Quasi-Linear Inversion 368
8.4 Quasi-Analytical Inversion 369
References and Recommended Reading 372
Chapter 9. Electromagnetic Migration 374
9.1 Electromagnetic Migration in the Time Domain 375
9.2 Analytic Continuation and Migration in the (k,.) Domain 380
9.3 Finite Difference Migration 391
9.4 Visualization of Geoelectric Structures by Use of Migration in the Frequency and Time Domains 398
9.5 Migration Versus Inversion 402
References and Recommended Reading 411
Part IV: Geophysical Electromagnetic Methods 414
Chapter 10. Electromagnetic Properties of Rocks and Minerals 416
10.1 Properties and Units 417
10.2 Properties in a Parametric Sense 423
10.3 Effective Conductivity of Heterogeneous Multiphase Rocks 448
10.4 Properties in an Existential Sense 456
10.5 Properties of Large-Scale Geoelectric Structures 461
References and Recommended Reading 467
Chapter 11. Generation and Measurement of Electromagnetic Fields in Geophysical Applications 470
11.1 Field Generation 471
11.2 Measurement of Electric and Magnetic Fields 480
11.3 Preprocessing of the Data 499
References and Recommended Reading 510
Chapter 12. Direct Current and Induced Polarization Methods 512
12.1 Vertical Electric Sounding and Apparent Resistivity 514
12.2 Induced Polarization (IP) Methods 529
12.3 Physical and Mathematical Models of the IP Phenomenon 536
12.4 Nonlinear Regularized Inversion of IP Data Based on the Cole-Cole Model 551
References and Recommended Reading 559
Chapter 13. Magnetotelluric and Magnetovariational Methods 564
13.1 Earth EM Field of External Origin 566
13.2 The Tikhonov-Cagniard Model of the MT Field 575
13.3 Theory of the MT and MV Transfer Functions 585
13.4 Magnetotelluric Fields in Horizontally Inhomogeneous Media 595
13.5 Magnetotelluric and Magnetovariational Surveys 600
13.6 Processing and Analysis of MT and MV Data 604
13.7 One-Dimensional Interpretation of MT Data 620
13.8 Interpretation of MVP and GDS Data 633
13.9 Rapid Three-Dimensional Magnetotelluric Inversion Based on Linear and Quasi-Linear Approximations 640
13.10 Rigorous 3-D Magnetotelluric Inversion 658
References and Recommended Reading 666
Chapter 14. Electromagnetic Methods in the Frequency and Time Domains 670
14.1 Electromagnetic Sounding in the Frequency and Time Domains 671
14.2 Interpretation of Controlled-Source Time Domain EM Data Using the thin-sheet Approach 698
14.3 Electromagnetic Profile and Array Surveys 710
References and Recommended Reading 712
Chapter 15. Marine Electromagnetic Methods 716
15.1 Marine Magnetotelluric Method 717
15.2 Marine Controlled-Source Electromagnetic Methods 725
References and Recommended Reading 752
Chapter 16. Other Platforms, Other Methodologies 756
16.1 Airborne Electromagnetic Methods 757
16.2 Ground Penetrating Radar (GPR) 777
16.3 Borehole Assisted Methods 785
16.4 Other Electromagnetic Methods 795
References and Recommended Reading 801
A. Algebra of Differential Forms 804
A.1 Differential Forms in Three-Dimensional Space 805
A.2 Differential Forms in Multidimensional Spaces 811
B. Calculus of Differential Forms 820
B.1 Exterior Differentiation of the Forms 820
B.2 Integration of the Forms 827
C. Mathematical Notations 832
D. Definition of Fields and Units 836
E. Linear Operators and Their Matrices 840
Bibliography 844
Index 866