Principles of Electric Methods in Surface and Borehole Geophysics (eBook)

Front cover 1
Methods in Geochemistry and Geophysics: Principles of Electric Methods in Surface and Borehole Geophysics 4
Copyright page 5
Dedication page 6
Contents 8
Introduction 12
Acknowledgments 14
List of Symbols 16
Part One: Electric Field in a Conducting Medium 18
Chapter One: Coulomb's Law and Stationary Electric Field 20
1.1. Interaction of electric charges and Coulomb's law 20
1.2. Surface, linear, and point charges 24
1.3. The electric field 28
1.4. The electric field caused by surface charge 31
1.5. Electrostatic induction 35
1.6. Voltage of the electric field 40
1.7. The first equation of the electric field 46
1.8. Flux of the electric field 48
1.9. The second equation of the electric field 50
1.10. System of equations of the electric field 52
1.11. Potential of the electric field 54
1.12. The electric dipole and double layer 61
1.13. Solutions of Poisson's equation and uniqueness 75
1.14. Polarization of a medium 84
1.15. The potential and electric field caused by polarization 86
1.16. Vector of electric induction and system of equations of electric field 89
1.17. Distribution of bound charges 93
Chapter Two: Electric Field and Steady Current Flow in Conducting Media 96
2.1. Electric current 96
2.2. Ohm's law in differential form 101
2.3. Principle of charge conservation 105
2.4. System of equations of the field j 110
2.5. Non-Coulomb force, Ohm's law, and electromotive force 111
2.6. Distribution of electric charges in a conducting and polarizable medium 118
2.7. System of equations of the electric field and potential 131
2.8. Uniqueness theorem 137
2.9. Resistance 147
2.10. Grounding resistance 158
2.11. Work done by Coulomb and extraneous forces, Joule's law 164
Chapter Three: The Electric Field, Current Density, and Potential in a Conducting Medium 170
3.1. Influence of inhomogeneity on the electric field and current density 170
3.2. A conducting sphere in a uniform electric field 178
3.3. Elliptical cylinder in a uniform electric field 184
3.4. The spheroid in a uniform electric field 194
3.5. Grounding resistance of a strongly elongated spheroid 199
3.6. Plane interface 201
3.7. Vertical contact beneath the earth's surface 207
3.8. Method of mirror reflection 214
3.9. Distribution of charges in a layered medium and asymptotic field behavior 218
3.10. Boundary conditions for electric field in the vicinity of thin layers 223
3.11. Theorem of reciprocity 229
3.12. Relationship between potential and boundary conditions 233
Part Two: Electric Methods of Surface Geophysics 238
Chapter Four: Electric Soundings 240
4.1. Arrays of the electric methods 240
4.2. Apparent resistivity and array coefficient 242
4.3. The electric field on the surface of a two-layered medium 248
4.4. Asymptotic behavior of the field when a base is an insulator 262
4.5. Asymptotic behavior of the field when the base is an ideal conductor 267
4.6. Apparent resistivity curves for a two-layered medium 274
4.7. Electric field in the presence of a thin horizontal layer 277
4.8. The electric field on the surface of a three-layered medium 281
4.9. Electric field on the earth's surface of an n-layered medium 289
4.10. Electric field when the current electrode is at the bottom of the upper layer 293
4.11. Electric field at the bottom of the upper layer in the presence of the plane T 298
4.12. Potential and electric field in an anisotropic medium 301
Chapter Five: Interpretation of Electric Soundings 312
5.1. Symmetric and dipole arrays of electric soundings 312
5.2. Solution of forward and inverse problems in electrical methods 315
5.3. Functions with finite spectrum and integration of Eq.[5.31] 332
5.4. Concept of uniqueness and the solution of the inverse problem 337
Chapter Six: Methods of Electrical Profiling and Mapping 348
6.1. Electric profiling 348
6.2. The charged-body or mise-à la-masse method 362
6.3. Self-potential method 368
Part Three: Electric Methods of Borehole Geophysics 376
Chapter Seven: Electrical Methods of Borehole Geophysics 378
7.1. Current electrode at the borehole axis 379
7.2. A medium with two cylindrical boundaries 392
7.3. The method of lateral soundings 396
7.4. Normal and lateral probes in a medium with two horizontal interfaces 402
7.5. Field in a borehole surrounded by anisotropic medium 412
7.6. Resistance RMN and its meaning 415
7.7. Measurements of grounding resistance 419
7.8. The Laterolog 1 421
7.9. Laterolog 3 426
7.10. Laterolog 7 429
7.11. Electric logging through casing 431
7.12. Self-potential method 443
Bibliography 450
Index 452