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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