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Principles of electromagnetic methods in surface geophysics

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  • Title

  • Copyright

  • INTRODUCTION

  • ACKNOWLEDGMENTS

  • Chapter One. The System of Equations of the Constant Electric and Magnetic Fields

    • INTRODUCTION

    • 1.1 EQUATIONS OF THE CONSTANT ELECTRIC FIELD IN A CONDUCTING AND POLARIZABLE MEDIUM

    • 1.2 INTERACTION OF CURRENTS, BIOT–SAVART LAW AND MAGNETIC FIELD

      • 1.2.1 Ampere's Law and Interaction of Currents

      • 1.2.2 Magnetic Field and Biot–Savart Law

      • 1.2.3 Lorentz Force and Electromotive Force at the Moving Circuit

    • 1.3 THE VECTOR POTENTIAL OF THE MAGNETIC FIELD

      • 1.3.1 Relation between Magnetic Field and Vector Potential

      • 1.3.2 Divergence and Laplacian of Vector Potential A

    • 1.4 SYSTEM OF EQUATIONS OF THE CONSTANT MAGNETIC FIELD

    • 1.5 BEHAVIOR OF THE MAGNETIC FIELD

      • 1.5 Example 1: Magnetic Field of the Current Filament

      • 1.5 Example 2: The Vector Potential A and the Magnetic Field B of a Current in a Circular Loop

      • 1.5 Example 3: Magnetic Field of the Magnetic Dipole and its Moment

      • 1.5 Example 4: Magnetic Field due to a Current in a Cylindrical Conductor

      • 1.5 Example 5: Magnetic Field of Infinitely Long Solenoid

      • 1.5 Example 6: Magnetic Field of a Current Toroid

      • 1.5 Example 7: Magnetic Field of Current Electrode in a Uniform Medium

      • 1.5 Example 8: Current Electrode on the Surface of a Horizontally Layered Medium

      • 1.5 Example 9: The Current Flowing in the Wire Grounded at the Surface of a Horizontally Layered Medium

      • 1.5 Example 10: Magnetic Field of the Electric Dipole at the Earth's Surface

    • 1.6 THE SYSTEM OF EQUATIONS OF THE CONSTANT ELECTROMAGNETIC FIELD

    • REFERENCES

  • Chapter Two. Physical Laws and Maxwell's Equations

    • Introduction

    • 2.1 Faraday's Law

    • 2.2 The Principle of Charge Conservation

    • 2.3 Distribution of Electric Charges

      • 2.3.1 Equation for Volume Density of Charges

      • 2.3.2 Uniform Medium

      • 2.3.3 Nonuniform Medium

      • 2.3.4 Quasi-Stationary Field

      • 2.3.5 Behavior of Charge Density δ02

      • 2.3.6 Surface Distribution of Charges

      • 2.3.7 Case of Relatively Slow Varying Field (Quasi-Stationary Field)

    • 2.4 Displacement Currents

      • 2.4.1 The Second Generator of Magnetic Field

      • 2.4.2 The Total Current and the Principle of Charge Conservation

      • 2.4.3 Currents in the Circuit with a Capacitor

    • 2.5 Maxwell Equations of the Electromagnetic Field

      • 2.5.1 Introduction

      • 2.5.2 Maxwell's Equations

      • 2.5.3 The Second Form of Maxwell Equations

      • 2.5.4 Maxwell's Equations in a Piece-Wise Uniform Medium

    • 2.6 Equations for the Fields E and B

    • 2.7 Electromagnetic Potentials

    • 2.8 Maxwell's Equations for Sinusoidal Fields

    • 2.9 Electromagnetic Energy and Poynting Vector

      • 2.9.1 Principle of Energy Conservation

      • 2.9.2 Joule's Law

      • 2.9.3 Expressions for the Energy Density and Poynting Vector

      • 2.9.4 The Direct Current and Poynting Vector

      • 2.9.5 Example 1: Current Circuit

      • 2.9.6 Example 2: Transmission Line

    • 2.10 Theorem of Uniqueness of a Solution of the Forward Problem

      • 2.10.1 The Proof of the Theorem of Uniqueness

      • 2.10.2 Formulation of the Boundary Value Problem

    • References and Further Reading

  • Chapter Three. Propagation and Quasi-Stationary Field in a Nonconducting Medium

    • Introduction

    • 3.1 Plane Wave in a Uniform Medium

      • 3.1.1 Solution of Eq. (3.2)

      • 3.1.2 Velocity of Propagation of Plane Wave

      • 3.1.3 Magnetic Field of the Plane Wave

      • 3.1.4 Electromagnetic Plane Wave

      • 3.1.5 Primary Source of the Plane Wave

    • 3.2 Quasi-Stationary Field in a Nonconducting Medium

    • 3.3 Induction Current in a Thin Conducting Ring Placed in a Time-Varying Field

      • 3.3.1 Equation for Induced Current in the Ring

      • 3.3.2 Transient Responses of Induced Current

      • 3.3.3 Primary Magnetic Field is the Step-Function

      • 3.3.4 Primary Magnetic Field is a Sinusoidal Function of Time

      • 3.3.5 The Range of Small Parameter ωτ0 or the Low-Frequency Spectrum of the Induced Current and Its Magnetic Field

      • 3.3.6 The Range of Large Parameter ωτ0 or the High-Frequency Part of the Spectrum

      • 3.3.7 Electromagnetic Induction and Measurements of the Electric and Magnetic Fields

    • References and Further Reading

  • Chapter Four. Propagation and Diffusion in a Uniform Medium

    • 4.1 Sinusoidal Plane Wave in a Uniform Medium

      • 4.1.1 Expressions for the Field

      • 4.1.2 Behavior of the Plane Wave as a Function of Time and Distance

      • 4.1.3 Attenuation, Velocity of Propagation, and Wavelength

    • Case 1: The High-Frequency Spectrum or the Range of Large Parameter β, (β﹥1)

    • Case 2: The Low-Frequency Spectrum or the Range of Small Parameter β, (β<1)

    • 4.2 Field of the Magnetic Dipole in a Uniform Medium (Frequency Domain)

      • 4.2.1 Introduction

      • 4.2.2 Solution of Helmholtz Equation

      • 4.2.3 Expressions for the Complex Amplitudes of the Electric and Magnetic Fields

      • 4.2.4 The Frequency Responses of the Field

      • 4.2.5 Dependence of the Field on the Distance from the Magnetic Dipole

    • 4.3 Equations for Transient Field of the Magnetic Dipole in a Uniform Conducting and Polarizable Medium

      • 4.3.1 Expression for the Vector Potential

      • 4.3.2 Expressions for the Field Components

    • 4.4 Behavior of the Field in a Nonconducting Medium

      • 4.4.1 Expressions for the Field

      • 4.4.2 Duhamel's Integral

      • 4.4.3 Behavior of the Field of the Magnetic Dipole in a Nonconducting Medium

      • 4.4.4 The Second Form of Duhamel's Integral and Representation of the Field as a Sum of Impulses

    • 4.5 Behavior of the Transient Field in a Conducting Medium

      • 4.5.1 The Electric Field at the First Arrival in Conducting Medium

      • 4.5.2 The Dependence of the Field eϕ(2) on Time (t≥τ0)

      • 4.5.3 Dependence of the Electric Field with Distance

    • 4.6 Propagation and Diffusion

    • References and Further Reading

  • Chapter Five. The External and Internal Skin Effect, Diffusion

    • Introduction

    • 5.1 The Skin Effect

      • 5.1.1 Equations for Currents in a System of Conducting Circuits

      • 5.1.2 The Law of Inertia for the Magnetic Flux

      • 5.1.3 Behavior of the Magnetic Field at the Initial Moment t=t0

      • 5.1.4 Location of Induced Currents at the Initial Instant

      • 5.1.5 The External and Internal Skin Effect

    • 5.2 Diffusion of Induced Currents

      • 5.2.1 One-Dimensional Diffusion Equation

      • 5.2.2 Expression for the Current Density

      • 5.2.3 Determination of Constant C

      • 5.2.4 Dependence of Induced Currents on Time

      • 5.2.5 Dependence of the Current Density on the Distance z

      • 5.2.6 About Diffusion of Currents

    • 5.3 Diffusion of the Magnetic Field

      • 5.3.1 Equation for the Magnetic Field

      • 5.3.2 Magnetic Field at Infinity

      • 5.3.3 Expression for the Magnetic Field

      • 5.3.4 Behavior of the Magnetic Field

    • REFERENCE AND FURTHER READING

  • Chapter Six. Quasi-Stationary Field of the Magnetic Dipole in a Uniform Medium

    • Introduction

    • 6.1 Quasi-Stationary Field of the Magnetic Dipole (Frequency Domain)

      • 6.1.1 Expressions for the Field

      • 6.1.2 Two Forms of Field Presentation

      • 6.1.3 An Asymptotic Behavior of the Field

      • 6.1.4 Behavior of the Field as a Function of Parameter p

      • 6.1.5 Expression for Induced Currents

      • 6.1.6 The Induced Current jϕ(0)

      • 6.1.7 Behavior of the Quadrature and In-Phase Components of the Current Density

    • 6.2 Transient Field of the Magnetic Dipole in Uniform Medium

      • 6.2.1 Expressions of the Field

      • 6.2.2 Transient Responses of the Field

    • References and Further Reading

  • Chapter Seven. The Hilbert and Fourier Transforms

    • Introduction

    • 7.1 Hilbert Transform

      • 7.1.1 Cauchy Formula

      • 7.1.2 Hilbert Transform

      • 7.1.3 Relationships between the Amplitude and Phase of the Spectrum

      • 7.1.4 Zeroes of the Spectrum on the Upper Part of the ω−Plane

    • 7.2 Fourier Integrals

      • 7.2.1 Different Forms of Fourier Transform

      • 7.2.2 The Step Function of Excitation

    • References and Further Reading

  • Chapter Eight. Vertical Magnetic Dipole in the Presence of Uniform Half Space

    • 8.1 Formulation of Boundary Value Problem

    • 8.2 Solution of Helmholtz Equations

    • 8.3 Expressions for the Vector Potential

    • 8.4 The Field of the Magnetic Dipole in a Conducting Medium Provided that h=0, k0=0

    • 8.5 The Field Expressions at the Earth's Surface

    • 8.6 The Range of Small Parameter p or Near Zone

    • 8.7 The Range of Large Parameters p or Wave Zone

      • 8.7.1 The Dipole and Observation Point are at the Earth's Surface

      • 8.7.2 The Field Beneath the Earth's Surface (h=0)

    • 8.8 Frequency Responses of the Field

    • 8.9 The Vertical Magnetic Dipole on the Surface of a Uniform Half Space (Time Domain)

      • 8.9.1 Expressions for the Field

      • 8.9.2 Early Stage of the Transient Response of the Electric and Magnetic Fields

      • 8.9.3 Transient Field at the Late Stage

      • 8.9.4 Transient Responses of the Field

    • References and Further Reading

  • Chapter Nine. Quasi-Stationary Field of Vertical Magnetic Dipole on the Surface of a Horizontally Layered Medium

    • Introduction

    • 9.1 The Field Expressions on the Surface of N-Layered Medium

      • 9.1.1 Formulation of Boundary Value Problem

      • 9.1.2 Three-Layered Medium

    • 9.2 Expressions for the Field in N-Layered Medium

    • 9.3 Behavior of the Field when Interaction between Induced Currents is Negligible

      • 9.3.1 The Quadrature Component of Magnetic Field and In-Phase Component of Electric Field

      • 9.3.2 The Role of Initial Part of Integration

      • 9.3.3 Assumption about Interaction of Induced Currents

      • 9.3.4 Concept of Geometric Factor

      • 9.3.5 Behavior of Geometric Factors

      • 9.3.6 Generalization for N-Layered Medium

      • 9.3.7 About the Depth of Investigation

    • 9.4 The Field of a Vertical Magnetic Dipole in the Range of Small Parameters r/δi

      • 9.4.1 Expansion of the Internal Integral, 0≤m≤|α2|

      • 9.4.2 Expansion of the External Integral

      • 9.4.3 Expression for the Vector Potential at the Range of Small Parameters

      • 9.4.4 The Expression for the Field at the Range of Small Parameters r/δi

      • 9.4.5 Behavior of the Field at the Range of Small Parameters r/δi

      • 9.4.6 Comparison of Both Components of the Field at the Range of Small Parameters

      • 9.4.7 The Range of Small Parameters on the Surface of N-Layered Medium

    • 9.5 Approximate Method of Field Calculation

    • 9.6 The Field within the Range of Small Parameters when Basement is an Insulator

    • 9.7 The Field on the Surface of a Layered Medium at the Wave Zone

      • 9.7.1 Derivation of Asymptotic Formulas (the First Approach)

      • 9.7.2 Behavior of the Field when r/λ ﹥1 (Wave Zone)

      • 9.7.3 The Field in the Wave Zone when the Basement is an Insulator ρN→∞

    • 9.8 The Second Approach of Deriving the Asymptotic Formulas for Wave Zone

      • 9.8.1 Deformation of the Contour Integration

      • 9.8.2 Evaluation of Integrals along Branch Cuts and Poles

    • 9.9 Transient Field at the Range of Large Parameter r/τ at the Surface of a Layered Medium (Wave Zone)

      • 9.9.1 Comparison of Fields in the Ranges of Large Parameters r/δ and r/τ for Uniform Half Space

      • 9.9.2 Derivation of Formulas for the Range of Large Parameters r/τ

      • 9.9.3 Behavior of the Field at the Surface of Two-Layered Medium (Early Stage)

    • 9.10 The Late Stage of the Transient Field on the Surface of a Layered Medium

      • 9.10.1 Expansion of the Field in Series by Powers t−n

      • 9.10.2 Contribution of the First Sum of Eq. (9.132) into the Late Stage

      • 9.10.3 Derivation of the Asymptotic Formulas

      • 9.10.4 Formulas for the Late Stage when Basement is Not an Insulator

      • 9.10.5 Formulas for the Late Stage when Basement is an Insulator

    • 9.11 Field of a Vertical Magnetic Dipole in the Presence of a Horizontal Conducting Plane

      • 9.11.1 Formulation of the Boundary Value Problem in the Frequency Domain

      • 9.11.2 Boundary Conditions at the Plane S

      • 9.11.3 Expressions for the Field Components

      • 9.11.4 The Range of Small Parameters ps

      • 9.11.5 The Range of Large Parameters ps

    • 9.12 Transient Responses of Currents in a Conducting Plane

      • 9.12.1 Derivation of Formulas

      • 9.12.2 The Dipole and Observation Point are Located at the Same Axis

      • 9.12.3 The Dipole and Observation Point are Situated on the Plane S

      • 9.12.4 The Dipole and Observation Point are at the Height h above the Plane S

    • References and Further Reading

  • Chapter Ten. Horizontal Magnetic Dipole above the Surface of a Layered Medium

    • 10.1 Formulation of Boundary Value Problem for Vector Potential

      • 10.1.1 Relation between the Vector Potential and Electromagnetic Field

      • 10.1.2 Boundary Value Problem for the Component Ax

      • 10.1.3 Expressions for the Horizontal Component Ax

      • 10.1.4 The System of Equations for Ax∗ and Its Solution

      • 10.1.5 Remarkable Behavior of the Vertical Component of Electric Field Ez

      • 10.1.6 The Vertical Component of the Electric Field above the Earth's Surface

    • 10.2 The Vertical Component of the Vector Potential Az∗

      • 10.2.1 Integral Representation of Az∗

      • 10.2.2 The First Form of Coefficient F0∗ for Three-Layered Medium

      • 10.2.3 The Second Form for the Coefficient F0∗

    • 10.3 The Component of the Magnetic Field Bx

      • 10.3.1 Derivation of Expression for Bx

      • 10.3.2 Quadrature Component of the Field at the Range of Small Parameters r/δ

      • 10.3.3 Geometric Factors of Layers

    • Reference and Further Reading

  • Chapter Eleven. Principles of Magnetotellurics

    • Introduction

    • 11.1 Invention of the Method

    • 11.2 Wave Zone, Quasi-Plane Wave and the Impedance of Plane Wave

      • 11.2.1 Wave Zone and Quasi-Plane Wave

    • 11.3 The Impedance of the Plane Wave

    • 11.4 The Apparent Resistivity and Its Behavior in a Horizontally Layered Medium

      • 11.4.1 Impedance of a Uniform Half Space

      • 11.4.2 Apparent Resistivity for a Two-Layered Medium

    • 11.5 Development of magnetotelluric Inverse Problem Solution

      • 11.5.1 Determination of Two–Layer Resistivity Model Parameters by Matching

      • 11.5.2 The Use of Asymptotic Behavior and Special Points of the Curves

      • 11.5.3 Apparent Resistivity Curves for Three-Layered Medium

    • 11.6 Solution of Inverse Problem of the Electromagnetic Soundings for the Horizontally Layered Medium

      • 11.6.1 The Useful Signal and Noise

      • 11.6.2 Stable and Unstable Parameters

      • 11.6.3 The Main Steps of Interpretation

    • References and Further Reading

  • Chapter Twelve. Electromagnetic Soundings

    • 12.1 Development of the Frequency and Transient Soundings

    • 12.2 Frequency Soundings in the Far Zone

    • 12.3 Transient Sounding in the Far Zone

    • 12.4 Transient Sounding

    • 12.5 Apparent Resistivity Curves

      • 12.5.1 Apparent Resistivity Curves for Two-Layer Model

      • 12.5.2 Apparent Resistivity Curves for Three-Layer Model

    • 12.6 Frequency Sounding

    • References and Further Reading

  • Chapter Thirteen. Quasi-Stationary Field of Electric Dipole in a Horizontally Layered Medium

    • Introduction

    • 13.1 The Constant Electric and Magnetic Fields (ω=0) in a Uniform Medium

    • 13.2 Quasi-Stationary Field of the Electric Dipole in a Uniform Medium

      • 13.2.1 Derivation of Equations for the Field

      • 13.2.2 The Near Zone p<1

    • 13.3 The Harmonic Field of the Horizontal Electric Dipole on the Surface of a Uniform Half Space

      • 13.3.1 Formulation of Boundary Value Problem

      • 13.3.2 Integral Representation for Ax∗

      • 13.3.3 Integral Representation for Az

      • 13.3.4 Expression for divA∗

      • 13.3.5 Equations for the Electric Field on the Earth's Surface

      • 13.3.6 Equations for the Magnetic Field on the Earth's Surface

      • 13.3.7 The Range of Small Parameter p=r/δ, (the Low-Frequency Spectrum)

      • 13.3.8 The Range of Large Parameters (Wave Zone)

      • 13.3.9 Behavior of the Field on the Earth's Surface

    • 13.4 The Horizontal Electric Dipole on the Surface of a Horizontally Layered Medium

      • 13.4.1 Integral Representation for Components of the Vector Potential

      • 13.4.2 Boundary Conditions for the Functions X and Z

      • 13.4.3 Derivation of Recursive Relations for Functions X and V

      • 13.4.4 Expression for the Component Ax

      • 13.4.5 Expressions for Functions V1 and V1′

      • 13.4.6 Expressions for Az∗ and U∗

      • 13.4.7 Potentials on the Earth's Surface when k0=0

      • 13.4.8 Expressions for the Electric and Magnetic Fields

    • 13.5 Transition to the Stationary Field

    • 13.6 The Range of Large Induction Number (Wave Zone)

    • 13.7 The Transient Field from the Electric Dipole Source on the Surface of a Uniform Half Space

      • 13.7.1 Equations of the Field

      • 13.7.2 The Early Stage

      • 13.7.3 The Late Stage

    • 13.8 Transient Field on the Surface of Two-Layer Medium

      • 13.8.1 Relationship between Fields Caused by Current when it is Turned off and Turned on

      • 13.8.2 The Early Stage of the Transient Field

      • 13.8.3 The Late Stage of the Field on the Surface of Two-Layer Medium (Horizontal Components)

      • 13.8.4 Apparent Resistivity Curves

      • 13.8.5 Screening Effect

    • References and Further Reading

  • Chapter Fourteen. Behavior of the Fields Caused by Currents in Confined Conductors

    • Introduction

    • 14.1 Conductive Sphere in a Uniform Magnetic Field (Frequency Domain)

      • 14.1.1 Formulation of Boundary-Value Problem

      • 14.1.2 Solution of Helmholtz Equation

      • 14.1.3 Expressions for the Field

    • 14.2 Behavior of the Field Caused by Currents in a Nonmagnetic Sphere (The Frequency Domain)

      • 14.2.1 Equivalence to the Magnetic Dipole

      • 14.2.2 Presentation of the Function D as a Series

      • 14.2.3 The Low-Frequency Part of the Spectrum

      • 14.2.4 The High-Frequency Part of the Spectrum (p≫1)

      • 14.2.5 The Second Form of Function D and Time Constant

      • 14.2.6 Frequency Responses of the Secondary Magnetic Field

      • 14.2.7 Sensitivity of the Field to the Parameter τ

      • 14.2.8 The Role of This Example for Development of Inductive Methods

    • 14.3 The Conducting Sphere in a Uniform Magnetic Field (Time Domain)

      • 14.3.1 Expressions for the Field Outside the Sphere

      • 14.3.2 The Early and Late Stage

      • 14.3.3 About Sensitivity of the Field at the Late Stage

      • 14.3.4 Induced Currents in the Sphere

    • 14.4 Influence of Magnetization on the Field Behavior

      • 14.4.1 Frequency Domain

      • 14.4.2 Transient Responses of the Field

    • 14.5 Conductive Sphere in the Field Caused by a Current Loop with Axial Symmetry

      • 14.5 Introduction

      • 14.5.1 Expressions for the Field

      • 14.5.2 Formulas for Coefficients and Their Asymptotic Behavior

      • 14.5.3 Transition to a Uniform Field

    • 14.6 The Circular Cylinder in a Uniform Magnetic Field (Frequency Domain)

      • 14.6 Introduction

      • 14.6.1 Solution of the Boundary-Value Problem

    • 14.7 Transient Responses of the Field Caused Currents in a Circular Cylinder

    • 14.8 Equations for the Field Caused by Currents in a Confined Conductor

      • 14.8 Introduction

      • 14.8.1 The Integral Equation for the Current Density

      • 14.8.2 Transition to the System of Linear Equations

      • 14.8.3 Representation of the Currents and the Field as a Sum of Simple Fractions

    • 14.9 Behavior of the Field due to Currents in a Confined Conductor

      • 14.9.1 The Low-Frequency Part of the Spectrum

      • 14.9.2 Approximate Representation of the Spectrum

      • 14.9.3 The High-Frequency Part of the Spectrum

      • 14.9.4 Early Stage of the Transient Field

      • 14.9.5 The Late Stage of the Transient Field

    • 14.10 Influence of Geological Noise Represented by Confined Conductors

      • 14.10 Introduction

      • 14.10.1 Direct Current Method and Geological Noise

      • 14.10.2 Frequency-Domain Methods and Geological Noise (Confined Inhomogeneity)

      • 14.10.3 Time-Domain Method and Geological Noise

    • 14.11 Influence of a Surrounding Medium on the Field due to a Confined Conductor (Charges are Absent)

      • 14.11.1 Approximate Method of Field Calculation

      • 14.11.2 Influence of Surrounding Medium on the Depth of Investigation

        • 14.11.2 Introduction

      • 14.11.3 Equivalence and Difference between the Frequency and Transient Methods

    • 14.12 Elliptical Polarization of the Electric and Magnetic Field

      • 14.12.1 The Elliptical Polarization of the Electric Field

      • 14.12.2 Method of Charged Body with Alternating Current

      • 14.12.3 Elliptical Polarization of the Magnetic Field

    • 14.13 Development of the Inductive Methods of Mining Prospecting

      • 14.13.1 Equipotential Lines Method

      • 14.13.2 “Infinitely” Long Cable Method (CSMT)

        • 14.13.2.1 Sunberg Method of Measurement

        • 14.13.2.2 Turam Modification

    • 14.14 Dipole Electromagnetic Profiling

      • 14.14 Introduction

      • 14.14 Example One

      • 14.14 Example Two (Shoot-Back Technique)

    • 14.15 Modern Systems of Electromagnetic Profiling

      • 14.15 Example One: MaxMin System

      • 14.15 Example Two: EM-31

      • 14.15 Example Three: EM-34

      • 14.15 Example Four: EM-38

    • 14.16 The Transient Method of the Mining Prospecting

      • 14.16.1 The Beginning

      • 14.16.2 The Principle of Measurement of Time Domain

      • 14.16.3 General Features of the Transient Systems

        • 14.16.3 Example One: TEM-47

        • 14.16.3 Example Two: TEM57-MK2

        • 14.16.3 Example Three: TEM-67

    • 14.17 Influence of Charges on Resolution of Electromagnetic Methods of Mining Prospecting

      • 14.17.1 Expressions for the Field in the Frequency Domain

        • 14.17.1 Case One. Wave Zone of the Normal Field

        • 14.17.1 Case Two. Near-Zone for the Normal Field

    • References and Further Reading

  • Chapter Fifteen. Magnetotelluric Soundings in a Laterally Inhomogeneous Medium

    • Introduction

    • 15.1 The Impedance Tensor

      • 15.1.1 Relation between the Normal and Total Field

      • 15.1.2 Elements of the Impedance Tensor

      • 15.1.3 Main Features of the Impedance Tensor

      • 15.1.4 Relation of the Apparent Impedance with Elements of the Impedance Tensor

      • 15.1.5 Polar Diagrams of Impedance Tensor

    • 15.2 Behavior of the Impedance Tensor

      • 15.2.1 Horizontally Layered (1D) Medium

      • 15.2.2 Two-Dimensional Model

      • 15.2.3 Polar Diagrams of Impedance for Two-Dimensional Models

      • 15.2.4 Relationship between Impedance Tensor and Apparent Impedances Zxya and Zyxa

      • 15.3 The Wiese–Parkinson Vector (Tipper)

    • 15.4 Behavior of the Plane Wave in a Nonhorizontal Layered Medium

      • 15.4.1 Introduction

      • 15.4.2 Galvanic and Vortex Parts of the Field due to an Inhomogeneity

      • 15.4.3 The Main Features of Galvanic Part of the Field

      • 15.4.4 Main Features of the Inductive Part of the Field

    • 15.5 Examples of the Field Behavior

      • 15.5.1 Vertical Contact

      • 15.5.2 The Vertical Dyke

      • 15.5.3 The Horst on the Basement Surface

      • 15.5.4 H-polarization

      • 15.5.5 E-polarization

      • 15.5.6 The Trough on the Basement Surface

      • 15.5.7 Three-Dimensional Model

    • References and Further Reading

  • Appendix One. Airborne Electromagnetic Prospecting Systems

    • A1.1 Frequency-Domain AEM Systems

      • A1.1.1 Quadrature Systems

      • A1.1.2 Rigid Frequency-Domain Systems

      • A1.1.3 Depth of Exploration of Frequency-Domain Systems

      • A1.1.4 Systems Without an Associated Transmitter

    • A1.2 Airborne Transient EM Surveys

      • A1.2.1 Fixed-Wing Transient Systems

      • A1.2.2 Helicopter Transient Systems

      • A1.2.3 Signal to Noise in Time-Domain Systems

      • A1.2.4 Comparison of Fixed-Wing and Helicopter Time-Domain Systems

      • A1.2.5 Comparative Analysis of Efficiency of Frequency and Time-Domain Systems

      • A1.2.6 Semiairborne Systems (Transmitters on the Ground and Receivers in the Air)

    • References

  • Appendix Two. Estimation of the Impedance Tensor

    • Introduction

    • Single-Input–Single-Output System

    • Estimating Impedance Tensor Elements with Least Squares

      • Robust Estimation

    • Remote-Reference Processing

    • REFERENCES AND FURTHER READING

  • Appendix Three. Relation between Amplitude and Phase for Magnetotelluric Impedance

    • REFERENCES AND FURTHER READING

  • Appendix Four. The Field of the Vertical Electric Dipole in the Layered Medium

    • Introduction

    • A4.1 Boundary Conditions at the Surface of a Plane T

    • A4.2 Mechanism of Appearance of the Secondary Field

    • A4.3 Expressions for the Normal Field at the Sea Bottom

      • A4.3.1 Boundary Conditions for the Vector Potential

      • A4.3.2 Expressions for the Vector Potential Az∗ of the Normal Field

      • A4.3.3 Expressions for the Normal Field Beneath Sea Bottom

      • A4.3.4 The Normal Field When ρ1=ρ2 (Uniform Half-Space)

      • A4.3.5 The Normal Field at the Sea Bottom When ρ1≠ρ2

    • A4.4 Influence of the Plane T

      • A4.4.1 DC Soundings

      • A4.4.2 Transient Soundings

    • REFERENCES AND FURTHER READING

  • INDEX

    • A

    • B

    • C

    • D

    • E

    • F

    • G

    • H

    • I

    • J

    • L

    • M

    • N

    • O

    • P

    • Q

    • R

    • S

    • T

    • U

    • V

    • W

    • Z

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