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Tables of Contents for Principles of Induction Logging
Chapter/Section Title
Page #
Page Count
Acknowledgments
ix

List of Symbols
xi

Introduction
1
4
Basic electromagnetic laws and Maxwell's equations
5
114
Coulomb's law
5
29
Example I: Normal component of the electric field caused by a planar charge distribution
10
5
Example II: Effect of a conductor situated within an electric field
15
19
Biot Savart law
34
18
Example I: The magnetic field of a straight wire line
44
2
Example II: The vector potential and magnetic field of the current flowing in a circular loop
46
5
Example III: The magnetic field of a grounded electrode in a uniform conducting medium
51
1
The postulate of conservation of charge and the distribution of charges in conducting media
52
15
Example I: Exponential variation
61
1
Example II: Sinusoidal variation
62
5
Faraday's law and the first Maxwell equation
67
25
Example I: The vortex electric field of a solenoid
71
2
Example II: The vortex electric field of a magnetic dipole in a free space
73
3
Example III: The inductive electric field due to the magnetic field of a current flowing in a circular loop
76
3
Example IV: Induction of a current in a thin conducting ring situated within a primary alternating field
79
10
Example V: Behavior of the electromagnetic field at the early stage and high frequencies in a conducting medium
89
3
Electromagnetic field equations
92
15
Relationships between various responses of the electromagnetic field
107
12
Electromagnetic field of the magnetic dipole in a uniform conducting medium
119
24
Methods for the solution of direct problems of induction logging
143
44
The method of separation of variables
144
2
The method of shells
146
13
Derivation of approximate boundary conditions on a shell surface
147
2
Calculation of the electromagnetic field caused by induced currents in one shell
149
2
The field in a presence of two confocal shells
151
8
The method of integral equations
159
11
Approximate methods of field calculation in induction logging
170
17
Doll's theory of induction logging
170
6
The approximate theory of induction logging, taking into account the skin effect in the external area
176
11
Electromagnetic field of a vertical magnetic dipole on the axis of a borehole
187
124
Formulation of the boundary problem
187
2
Derivation of the formula for the vertical component of the magnetic field
189
13
The quadrature component of the magnetic field at the range of very small model parameters
202
11
Radial characteristics of a two-coil induction probe at the range of small parameters
213
9
Influence of the skin effect in the formation on the radial characteristics of a two-coil induction probe
222
7
Example I: Two-layered medium
226
2
Example II: Three-layered medium
228
1
Asymptotic behavior of the magnetic field in the borehole in the range of small parameters
229
7
Behavior of the field on the borehole axis in the near and far zones
236
9
Frequency responses of the magnetic field of the vertical magnetic dipole on the borehole axis
245
4
Influence of finite dimensions of induction probe coils
249
20
Electrical field of a current ring in a medium with cylindrical interfaces
269
21
Electrical field of a single-layer coil in a medium with cylindrical interfaces
274
3
Both transmitter and receiver of the induction probe are single-layer coils
277
13
Radial responses of two-coil induction probes displaced with respect to the borehole axis
290
9
The influence of magnetic permeability and dielectric constant in induction logging
299
12
Quasistationary magnetic field of a vertical magnetic dipole in a formation with a finite thickness
311
54
Derivation of formulae for the vertical component of the magnetic field of a vertical magnetic dipole
311
8
The field of the magnetic dipole located outside the bed
315
1
The field of the magnetic dipole located within the bed
316
2
The field of the vertical magnetic dipole in the presence of a thin conducting plane
318
1
The vertical responses of the two-coil induction probe in the range of small parameters
319
1
Geometric factor of an elementary layer
319
12
Geometric factor of a layer with a finite thickness
322
9
The theory of the two-coil induction probe in beds with a finite thickness
331
21
Curves of profiling with a two-coil induction probe in a medium with two horizontal interfaces
352
13
Thick conductive bed
363
1
Thick resistive bed
364
1
Thin conductive bed
364
1
Thin resistive bed
364
1
The two-coil induction probe on the borehole axis, when the bed has a finite thickness
365
20
Doll's theory of the two-coil induction probe located on the borehole axis when a formation has a finite thickness
366
5
The theory of a two-coil induction probe, taking into account the skin effect in an external medium
371
5
Influence of the finite thickness of the formation on the magnetic field behavior
376
9
Multi-coil differential induction probes
385
78
Methods of determination of probe parameters
386
9
Physical principles of multi-coil differential probes
395
2
Radial and vertical responses of the differential probe 1.L--1.2
397
18
Radial and vertical responses of probes 6F1M, 4F1 and 4F1.1
415
22
The influence of finite height of the invasion zone on radial responses of probes 6F1M, 4F1 and 4F1.1
437
4
Three-coil differential probe
441
12
The influence of eccentricity on focusing features of multi-coil induction probes
453
3
Choice of a frequency for differential probes
456
1
Determination of the coefficient of differential probes
457
6
Induction logging based on measuring the inphase component of the secondary field or the quadrature component difference of type QHz (ω1) - ω1/ω2 QHz (ω2)
463
14
Transient induction logging
477
56
The transient field of the magnetic dipole in a uniform medium
478
18
Transient field of the vertical magnetic dipole on the borehole axis at the late stage
496
6
Apparent resistivity curves of the transient method in a medium with cylindrical interfaces
502
6
The transient responses of a vertical magnetic dipole in a formation with a finite thickness
508
20
About a nonstationary field of the electric dipole
528
5
Principles of induction logging with transversal induction coils
533
72
Electromagnetic field of the magnetic dipole in a uniform isotropic medium
533
2
Boundary problem for the horizontal magnetic dipole on the borehole axis
535
15
Magnetic field on the borehole axis in the near zone
550
8
The magnetic field on the borehole axis in the far zone
558
8
The magnetic field in a medium with two cylindrical interfaces
566
5
Cylindrical surface with transversal resistance T
571
4
The magnetic field in a medium with one horizontal interface
575
5
The magnetic field of the horizontal dipole in the formation with finite thickness
580
18
Curves of profiling with a two-coil induction probe in a medium with horizontal interfaces
598
7
The influence of anisotropy on the field of the magnetic dipole in a conducting medium
605
22
Anisotropy of a layered medium
605
3
Electromagnetic field of the magnetic dipole in a uniform anisotropic medium
608
9
Magnetic field in an anisotropic medium with two horizontal interfaces
617
10
Mathematical modeling of the response of induction logging tools in 3D geometries
627
12
References
639
2
Subject Index
641