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Tables of Contents for The Theory of Inductive Prospecting
Chapter/Section Title
Page #
Page Count
List of Symbols
xiii
Introduction
Preface to the New Edition
1
2
Introductory Remarks Adapted from the First Edition
3
7
References
10
1
Basic Electromagnetic Laws and Maxwell's Equations
Introduction
11
1
Coulomb's Law
11
32
Normal component of the electric field caused by a planar charge distribution
16
5
Effect of a conductor situated within an electric field
21
22
Biot-Savart Law
43
23
The magnetic field of a straight wire
52
3
The magnetic field of a current flowing in a rectangular loop
55
1
The vector potential and magnetic field of a current flowing in a circular loop
56
5
The magnetic field of a current flowing in a wire grounded at the surface of a horizontally layered medium
61
5
The Postulate of Conservation of Charge and the Distribution of Charges in a Conducting Medium
66
15
Exponential variation
75
1
Sinusoidal variation
76
5
Faraday's Law and the First Maxwell Equation
81
32
The vortex electric field of a solenoid
85
2
The vortex electric field of a magnetic dipole
87
3
The vortex electric field of a circular loop
90
3
The vortex electric field of an infinitely long current filament
93
2
The vortex electric field of a uniform magnetic field
95
2
Inductive currents in a thin conducting ring situated within an alternating field
97
3
Transient primary magnetic field
100
4
Harmonic primary magnetic field
104
6
Behavior of the electromagnetic field at the early stage and at high frequencies in a conductive medium
110
3
Electromagnetic Field Equations
113
13
Relationships Between Various EM Field Components
126
12
Summary
138
3
References
141
2
Frequency and Time-Domain Behavior of the Field Caused by Currents Induced in a Confined Conductor
Introduction
143
1
A Conductive Sphere in a Uniform Stationary Magnetic Field (Frequency Domain)
143
18
A Conductive Sphere in a Uniform Non-Stationary Magnetic Field (Time Domain)
161
18
A Conductive Sphere Energized by the Magnetic Field of a Circular Loop with Axial Symmetry
179
15
Equations for the Frequency and Time-Domain Fields Caused by Induced Currents in a Spherical Conductor with Axial Symmetry
194
10
The Characteristics of the Frequency and Transient Responses Caused by a Spherical Conductor with Axial Symmetry
204
31
A Right Circular Cylinder in a Uniform Magnetic Field
235
10
A Right Circular Cylinder in a Field Created by an Infinitely Long Current Filament
245
14
Equations for the Frequency and Time-Domain Fields Caused by Induced Currents in a Cylindrical Conductor with an Arbitrary Cross-Section
259
5
The Characteristics of the Frequency and Transient Responses Caused by a Cylindrical Conductor with an Arbitrary Cross-Section
264
28
A Conducting Sphere in the Field of an Arbitrarily Oriented Magnetic Dipole Source
292
4
A Circular Cylinder in the Field of an Arbitrarily Oriented Magnetic Dipole Source
296
27
Axial magnetic dipole
303
1
Radial magnetic dipole
304
1
Azimuthal magnetic dipole
304
2
Analysis of the function An
306
17
Summary
323
5
References
328
6
Resolving Capabilities and Depth of Investigation of Inductive Methods when Geologic Noise is a Confined Inhomogeneity
Introduction
329
5
Frequency-Domain Methods
334
6
Time-Domain Methods
340
2
Comparing Resolution and Depth of Investigation in the Frequency and Time Domains using Spheroid Models
342
19
Summary
361
4
The Effect of Induced Currents in the Host Medium on the Frequency and Transient Responses Caused by a Confined Conductor
The Normal Field Due to Currents in the Host Medium
365
37
Observation point at the center of the source loop
366
1
Uniform full-space
366
4
Uniform half-space
370
3
Thin conductive sheet
373
5
Two-layer medium
378
7
Electromotive force induced in combined loops
385
1
Uniform full-space
385
6
Uniform half-space
391
3
Thin conductive sheet and a two-layer medium
394
4
Concluding remarks
398
4
The Influence of Currents Induced in the Host Medium on the Secondary Electromagnetic Field of a Confined Conductor
402
39
The response of a spheroid in a uniform conductive full-space
402
3
The quadrature component for a spheroid in a full-space
405
8
The quadrature component for a spheroid beneath a thin sheet or within a two-layer medium
413
2
The inphase component for a spheroid in a full-space
415
5
The inphase component for a spheroid beneath a thin sheet or within a two-layer medium
420
4
The difference of quadrature components for a spheroid in a full-space, beneath a thin sheet, or within a two-layer medium
424
4
The transient field for a spheroid in a full-space, beneath a thin sheet, or within a two-layer medium
428
13
An Approximate Method for Calculating the Fields Caused by Vortex Currents
441
15
Summary
456
3
References
459
3
The Effect of Surface Electrical Charge on the Behavior of Secondary Electromagnetic Fields
Introduction
461
1
General Expressions for the Electromagnetic Fields of a Conductive Sphere
462
20
Electric and magnetic field equations
462
3
The potential for oscillations of the electric type (Hr = 0)
465
2
The potential for oscillations of the magnetic type (Er = 0)
467
2
Boundary conditions for the potentials U1 and U2 at the surface of the sphere
469
1
Solutions to the Helmholtz equation for potentials in a spherical coordinate system
469
2
Potentials of the electric and magnetic types for the primary field
471
9
Potentials of the electric and magnetic types for the secondary field
480
2
A Conductive Sphere in a Plane Wave Field
482
9
A Conductive Sphere in a Magnetic Dipole Field
491
27
Radial magnetic dipole source
491
4
Transverse magnetic dipole source
495
6
The ratio of the quadrature components of the magnetic field
501
5
The ratio of the inphase components of the magnetic field
506
4
The ratio of the vortex and galvanic parts of the magnetic field in the dual-frequency method
510
3
The ratio of the vortex and galvanic parts of the transient magnetic field
513
5
A Conductive Cylinder in the Field of an Infinitely Long Current Filament Parallel to the Axis of the Cylinder
518
27
The normal field of a current filament
518
8
Frequency-domain response of the secondary field caused by the presence of a cylinder
526
11
Time-domain response of the secondary field caused by the presence of a cylinder
537
1
Considerations regarding finite length, cylindrically-shaped conductors
538
7
A Conductive Cylinder in the Field of a Magnetic Dipole
545
34
Asymptotic relationships for the galvanic contribution
562
1
Source moment is oriented along the axis of the conductor
563
3
Source moment is not oriented along the axis of the conductor
566
10
The transient response of the cylinder
576
3
Summary
579
3
References
582
2
Resolving Capabilities of Airborne Inductive Methods
Introduction
583
1
The Signal-to-Geologic-Noise Ratio
584
1
Airborne Electromagnetics
585
2
Description of the Study
587
22
Practical motivations and constraints
587
2
The systems considered in the study
589
3
The models considered in the study
592
4
Modeling software and plotting issues
596
3
An airborne impedance system
599
2
Airborne wave impedance for a vertical-axis dipole over a homogeneous earth
601
4
Airborne wave impedance for a horizontal-axis dipole over a homogeneous earth
605
4
Layered-Earth Modeling Results and Analysis
609
17
Variations in basement resistivity - nearby receiver
610
3
Variations in overburden thickness - nearby receiver
613
2
Variations in basement resistivity - offset receiver
615
5
Variations in overburden thickness - offset receiver
620
4
Some conclusions drawn from the analysis of airborne EM modeling results for layered-earth models
624
2
Three-Dimensional Modeling Results and Analysis
626
51
Model 2: A conductive ``dike''
628
1
TEM system results
628
5
HCP system results
633
6
VCP and VCA system results
639
4
Model 3: A conductive or resistive ``block''
643
1
Conductive target-variable overburden thickness models
643
7
Resistive target - variable overburden thickness models
650
5
Variable target resistivity - fixed overburden thickness models
655
6
Model 4: A buried ``anticline''
661
1
Buried conductive anticline models
661
9
Buried resistive anticline models
670
5
Some conclusions drawn from the analysis of airborne EM modeling results for three-dimensional models
675
2
Recommendations for Airborne Electromagnetic Prospecting Systems
677
3
References
680
Subject Index