Natural Electromagnetic Fields in Pure and Applied Geophysics (Springer Geophysics)

Preface
Contents
1 General Introduction
	1.1 Introduction
	1.2 Preliminaries on€Electromagnetic Waves and€Their Application in€Geophysical Investigations
	1.3 Geomagnetic Fields
		1.3.1 Magnetic Field of€Internal Origin
		1.3.2 Magnetic Dipole
		1.3.3 Nondipole Field of€Internal Origin
		1.3.4 Inclination and€Declination of€the€Magnetic Field
		1.3.5 Nondipole Time Varying Magnetic Field of€External Origin
	1.4 Solar Radiation
	1.5 Solar Energy
	1.6 Sunspot Cycle
	1.7 Solar Quiet Day (Sq) Variations
	1.8 L Variations
	1.9 Equatorial ElectroJet (EEJ) and€Polar Electrojet (PEJ)
	1.10 D, Dst and€DS Variations
	1.11 Solar Flare Effect (SFE)
	1.12 Magnetic Storms
	1.13 Bay Type Variations
	1.14 Magnetic Substorms
	1.15 Interaction Between the€Sun and€the€Earth
	1.16 Magnetosphere
	1.17 Cosmic Rays
	1.18 Van Allen Radiation Belt
	1.19 Ionosphere
	1.20 Ring Current
	1.21 Magnetotail
	1.22 Geomagnetic Field Variations
	1.23 Classifications and€Causes of€the€Various Pulsations and€Micropulsations
		1.23.1 Classification by€Jacobs and€Sinno (1960)
		1.23.2 Classifications by€Madam Troitskaya (1960)
		1.23.3 Classification by Benioff’s (1960)
		1.23.4 Classification by€Tepley and€Wentworth (1962)
		1.23.5 Classification by€Vladimirov and€Kleimenova (1962)
	1.24 High-Frequency Natural Electromagnetic Signals, Spherics
	1.25 Dead Band
	1.26 Complex Structure of€Natural Source
	1.27 Earth’s Natural Electromagnetic Field as a Subject
		1.27.1 Electrotelluric Method (T)
		1.27.2 Magnetotelluric Method (MT)
		1.27.3 Geomagnetic Depth Sounding (GDS)
		1.27.4 Magnetometer Array Studies (MA)
		1.27.5 Magnetovariational Sounding (MVS)
		1.27.6 Audiofrequency Magnetotelluric Method (AMT)
		1.27.7 Sea-Floor Magnetotelluric Method (SFMT)
		1.27.8 Marine Magnetotellurics (MMT)
		1.27.9 Audiofrequency Magnetic Method (AFMAG)
	1.28 Controlled Sources
		1.28.1 Controlled-Source Audiofrequency Magnetotelluric Methods (CSAMT)
		1.28.2 Controlled-Source Marine Electromagnetics (CSEM)
		1.28.3 Long-Offset Electromagnetic Transients (LOTEM)
		1.28.4 Radio Magnetotellurics (RMT)
	1.29 Coverage of€This Book
	References
2 Electrical Conduction in€Rocks
	2.1 Introduction
	2.2 Electrical Conductivity
		2.2.1 Expression of€Electrical Conductivity for€an€Homogenous and€Isotropic Medium Due to€a€Point Source of€Current
		2.2.2 Specific Resistivity or€Conductivity
		2.2.3 Ohm’s Law
	2.3 Electrical Permittivity and€Displacement Current
		2.3.1 Dielectric Constant
		2.3.2 Electric Displacement ψ and the Displacement Vector D
		2.3.3 Tensor Electrical Permittivity
	2.4 Magnetic Induction and€Magnetic Permeability
		2.4.1 Magnetic Induction
		2.4.2 Magnetic Permeability
	2.5 Principal Methods of€Electrical Conduction
		2.5.1 Electronic Conduction (Conduction of€Current Through Metals)
		2.5.2 Conduction of€Current Through Semiconductors
		2.5.3 Conduction of€Current Through Solid Electrolytes
		2.5.4 Conduction of€Current Through Dielectric Displacement
		2.5.5 Electrolytic or€Ionic Conduction
	2.6 Factors that€Control the€Electrical Conductivity of€the€Earth
		2.6.1 Porosity of€Rocks
		2.6.2 Conductivity of€Pore Fluids
		2.6.3 Size and€Shape of€Pore Spaces
		2.6.4 Conductivity of€Mineral Inclusions
		2.6.5 Size and€Shape of€Mineral Grains
		2.6.6 Temperature
		2.6.7 Frequency of€Excitation Current
		2.6.8 Ductility and€Degree of€Partial Melt in€Rocks
		2.6.9 Electrical Conductivity of€Various Types of€Rocks
		2.6.10 Chemical Activity and€Oxygen Fugacity
		2.6.11 Dependence of€Electrical Conductivity on€Pressure
		2.6.12 Dependence of€Electrical Conductivity on€Volatiles
		2.6.13 Major Geological Zones of€Weaknesses
	2.7 Piezoelectric Effect
	2.8 Hall Effect
	2.9 Maxwell’s Geoelectrical Conductivity Models
		2.9.1 Soft Rock
		2.9.2 Hard Rock
		2.9.3 Ellipsoidal Grains
		2.9.4 Alternating-Current Conduction
	2.10 Resistivities of€Metals and€Metallic Minerals
	2.11 Semiconducting Minerals
	2.12 Electrical Conductivity of€Some Common Metallic Ores
	2.13 Some Common Geological Good and€Bad Conductors
	References
3 Signal Processing
	3.1 Introduction
	3.2 Selection of€Block Size
	3.3 Editing of€Time Series
	3.4 Moving Average Algorithm
	3.5 Trend Elimination
	3.6 Fourier Series
	3.7 Complex Fourier Series
	3.8 Fourier Series for€Discrete Time-Period Signals
	3.9 Integral Transforms
	3.10 Fourier Transform
	3.11 Sinc Function
	3.12 Two-Dimensional Fourier Transform
	3.13 Aperiodic Function and€Fourier Integral
	3.14 Discrete Fourier Transform
	3.15 Fast Fourier Transform
	3.16 Dirac Delta Function
	3.17 Shannon’s Sampling Theorem
	3.18 Linear Filter
	3.19 Convolution
	3.20 Z Transform
	3.21 Filters and€Windows
	3.22 Cross-Correlation and€Autocorrelation
		3.22.1 Cross-Correlation
		3.22.2 Autocorrelation
		3.22.3 Properties of€the€Autocorrelation and€Cross-Correlation
	3.23 Autopower and€Cross-Power Spectra
		3.23.1 Energy-Density Spectrum of€Aperiodic Signals
		3.23.2 Power-Density Spectrum of€Periodic Signals
		3.23.3 Autopower Spectra
		3.23.4 Cross-Power Spectra
	3.24 Noise
		3.24.1 General Definition
		3.24.2 Geophysical Noise
		3.24.3 Geological Noise
		3.24.4 Coherent Noise
		3.24.5 Incoherent Noise
		3.24.6 Correlated Noise and€Uncorrelated Noise
		3.24.7 White Noise
		3.24.8 Man-Made Noise
		3.24.9 Natural Noise
		3.24.10 Sensor Noise
		3.24.11 An€Example of€Noise Power
	3.25 Robust Statistics
		3.25.1 Introduction
		3.25.2 Median
		3.25.3 Norm
		3.25.4 Outliers
		3.25.5 Point Defects
		3.25.6 Nonstationarity
		3.25.7 Quantile
		3.25.8 Breakdown Point
		3.25.9 Non-Gaussian Distribution
	3.26 Robust Processing
		3.26.1 Downweighting of€Outliers
		3.26.2 M-Estimator
		3.26.3 Variable Weight M-Estimator
		3.26.4 Siegel’s Repeated Median Estimator (Siegel 1982; Smirnov 2003)
		3.26.5 Field Example
	References
4 Electrotellurics
	4.1 Introduction
	4.2 Basics of€Electrotellurics
	4.3 Comparison of€Electrotelluric and€Magnetotelluric Frequencies
	4.4 Nature of€the€Telluric Field
	4.5 Electrotelluric Method
	4.6 Potential Measuring Probes
		4.6.1 Electrode Potential
		4.6.2 Non-polarisable Electrodes
	4.7 Field Recording
	4.8 Electrotelluric Data Analysis
		4.8.1 Interconnections Between Base and€Mobile Station Telluric Field Vectors
		4.8.2 Relative Ellipse Method
		4.8.3 Triangle Method
		4.8.4 Polygon Method
		4.8.5 Amplitude Ratio Method (Linear Polarisation)
		4.8.6 Absolute Ellipse Method
	4.9 Electrotelluric Boundary Value Problem
		4.9.1 Electrotelluric Field over€an€Asymmetric Anticline
		4.9.2 Electrotelluric Profile Across a€Step Fault
	4.10 Downward Continuation of€Telluric Field Data
	4.11 Field Examples
	4.12 Summary
	References
5 Magnetotellurics
	5.1 General Introduction
	5.2 Plane-Wave Propagation
		5.2.1 Advancing Electromagnetic Wave
		5.2.2 Plane-Wave Incidence on€the€Surface of€the€Earth
	5.3 Skin Depth
	5.4 Magnetotellurics for€1D Layered Earth: A€Few Aspects of€the€Principles
		5.4.1 Magnetotelluric Four-Layered Apparent Resistivity and€Phase Curves
		5.4.2 Magnetotellurics Is a€Low-Resolution Tool
		5.4.3 For€a€Certain Class of€1D Models, MT Fails to€Resolve the€Significant Subsurface Resistivity Contrasts Even Approximately When the€Resistivity Contrast Is More Than Ten
		5.4.4 Magnetotelluric Signals Can See a€Target that€Is at€a€Depth Beyond Its Skin Depth
		5.4.5 Granite Window Is a€Must for€Deep Magnetotelluric Surveys Because Two-km Thick Conducting Sediments on€Top Can Reduce the€Sensitivity of€the€Magnetotelluric Signals up€to€300€km from€the€Surface and€Deep Inside the€Upper Mantle
		5.4.6 Magnetotellurics Is a€Suitable Geophysical Tool for€Detecting Sediments Sandwiched Between Flood Basalt and€Crystalline Basement
	5.5 Magnetotelluric Field Work and€Field Data
		5.5.1 Field Data Acquisition
		5.5.2 Signal Strength Versus Frequency or€Period
		5.5.3 Number of€Degrees of€Freedom Versus Frequency or€Period
		5.5.4 Coherencies
		5.5.5 Different Components of€the€Impedance Tensors Versus Period
		5.5.6 Processed Fourier Spectra
		5.5.7 Processed Field Data
	5.6 Concept of€Optimum Mathematical Rotation in€Magnetotellurics
	5.7 Concept of€E and€H Polarisation (TE and€TM Mode)
	5.8 Estimation of€MT Tensor Components
		5.8.1 Estimation of€MT Tensors Using Coherencies
		5.8.2 Estimation of€MT Impedance Tensors Using Single-Station MT Data
		5.8.3 Remote Reference Magnetotellurics
		5.8.4 Robust Estimator
	5.9 TE and€TM Mode MT
	5.10 MT Tensor Decomposition
		5.10.1 Eggar’s Eigenstate Decomposition
		5.10.2 Bahr’s Tensor Decomposition
		5.10.3 Groom Bailey Decomposition
		5.10.4 Groom and Bailey’s Twist and Shear
		5.10.5 Jone’s Decomposition
	5.11 Tipper Parameters
	5.12 Rotation Invariant Parameters in€Magnetotellurics
		5.12.1 Field Apparent Resistivity Phase Curves Using Rotation Invariant Parameters
	5.13 Magnetotelluric Phases
		5.13.1 Magnetotelluric Phase Tensor
	5.14 Anisotropy
		5.14.1 Anisotropy in€Magnetotelluric Domain
		5.14.2 Phase Splitting in€Magnetotellurics
		5.14.3 Magnetotelluric Phase Above 90°
	5.15 Galvanic and€Inductive Distortion
	5.16 Magnetotelluric Current Channelling
	5.17 Magnetotelluric Strikes
	5.18 Dimensionality Indicator
		5.18.1 One-Dimensional Structure
		5.18.2 Two-Dimensional Structure
		5.18.3 Three-Dimensional Structure
		5.18.4 Dimensionality Indicator from€Phase
		5.18.5 Dimensionality Indicator from€Eigenstate Formulation
		5.18.6 Swift Skew as€Dimensionality Indicator
		5.18.7 Complex Domain Plot of€the€Impedance Tensor as€a€Dimensionality Indicator
		5.18.8 Impedance Ellipse as€a€Dimensionality Indicator
	5.19 Complex Domain Plot of€the€Impedance Tensors and€Rotational Invariance Tensors
	5.20 Static Shift
		5.20.1 Curve Shifting
		5.20.2 Statistical Averaging
		5.20.3 EMAP
		5.20.4 Use of€Auxiliary Tools
		5.20.5 Use of€Constraining Parameters
		5.20.6 Use of€Well Log Data
		5.20.7 Higher Current Dipole Length
		5.20.8 Static Shift-Free Magnetotelluric Parameters
	5.21 Magnetotelluric Designs
	5.22 Location of€the€MT Study Area in€Eastern Part of€the€Indian Subcontinents Where a€Few Magnetotelluric Observations Were Taken for€Qualitative and€Semi-Quantitative to€Quantitative Interpretations
	5.23 Qualitative Signatures: An€Important Sector of€Magnetotelluric Data Interpretation
		5.23.1 Qualitative Signature of€a€Rift Valley or€Major Continental Fracture
		5.23.2 ΦD (Phi Determinant) Pseudosection Can Depict the Subsurface with Greater Clarity (Ranganayaki 1984)
		5.23.3 Qualitative Magnetotelluric Signatures of€Faults
		5.23.4 Qualitative Magnetotelluric Signatures of€Sukinda Thrust
		5.23.5 Pseudo 3D Pseudosections of€Rotation-Invariant Phases Across the€Sukinda Thrust
		5.23.6 Some of€the€Rotation-Invariant Parameters Are Heavy-Weight Parameters
		5.23.7 Various MT-Parameter Pseudosections from€Field Data Across the€Sukinda Thrust
		5.23.8 Qualitative Signatures in Bhar’s Telluric Vectors Across Sukinda Thrust
		5.23.9 Induction Arrows Show the Major Fractured Zones in Archean–Proterozoic Collision Zone
		5.23.10 Rotation-Invariant Parameters Less Affected by€Static Shift
		5.23.11 Profiles and€Pseudosections from€Mathematical Models
	5.24 Semi-Quantitative to€Quantitative Signatures from€MT Data
		5.24.1 One Dimensional Inversion of€Magnetotelluric Data
		5.24.2 Two-Dimensional Inversion and€2D Model
		5.24.3 2D and€Pseudo-3D Models of€the€Mahanadi Graben
	5.25 Field Example of€Processed Magnetotelluric Data
		5.25.1 Example 1
		5.25.2 Example 2
		5.25.3 Example 3
		5.25.4 Example 4
	5.26 Application of€MT in€Earth Sciences
		5.26.1 Major Breaks in€the€Crust and€Upper Mantle
		5.26.2 Detectability of€Moho
		5.26.3 MT for€Estimating Asthenosphere Temperature, as€Well as€for€Mapping High Heat Flow Areas
		5.26.4 MT for€Oil Exploration
		5.26.5 MT for€Mapping Convergent and€Divergent Plate Margins
		5.26.6 MT for€Earthquake Prediction
		5.26.7 MT Can Estimate Permafrost Thickness
		5.26.8 MT for€Groundwater Exploration
		5.26.9 Marine MT
	References
6 Auxiliary Tools for€Magnetotellurics
	6.1 Introduction
	6.2 Audiofrequency Magnetotellurics (AMT)
		6.2.1 Source Characteristics
		6.2.2 Nature of€AMT Signals
		6.2.3 Field Procedure
		6.2.4 Qualitative Interpretation
		6.2.5 Quantitative Interpretation
		6.2.6 Applications
	6.3 Controlled-Source Audiofrequency Magnetotellurics (CSAMT)
		6.3.1 Introduction
		6.3.2 Skin Depth and€Effective Penetration Depth
		6.3.3 CSAMT Pseudosections for€Theoretical Model and€Field Data
		6.3.4 CSAMT Sources
		6.3.5 Field Survey
		6.3.6 Interpretation
	6.4 Long-Offset Electromagnetic Transients (LOTEM)
		6.4.1 Introduction
		6.4.2 LOTEM Data Acquisition
		6.4.3 LOTEM Theory (Strack 1984)
		6.4.4 Data Processing
		6.4.5 Nature of€Forward and€Inverse Problem Responses of€LOTEM Data
		6.4.6 Applications
	6.5 Radiomagnetotellurics (RMT)
	References
7 Geomagnetic Depth Sounding (GDS)
	7.1 Introduction
	7.2 Separation of€External and€Internal Field
	7.3 Data Analysis
	7.4 Separation of€Normal and€Anomalous Fields
	7.5 Spherical Harmonics
		7.5.1 Solution of€Laplace Equation in€Spherical Polar Coordinates
		7.5.2 When Potential Is a Function of All Three Coordinates, i.e. Radial Distance, Polar Angle and Azimuthal Angle, i.e. ϕ = f(r, θ, ψ)
		7.5.3 Associated Legendre Polynomial
		7.5.4 Geomagnetic Potential
		7.5.5 Geomagnetic Field
	7.6 Magnetometer Array Studies
		7.6.1 Recording of€Geomagnetic Data
		7.6.2 Examples of€Magnetometer Arrays: Example from€South Africa
		7.6.3 Example from€India
		7.6.4 Magnetogram
		7.6.5 Processing Geomagnetic Data
		7.6.6 Single-Site Transfer Function
		7.6.7 Hypothetical Event Analysis
	7.7 Induction Arrows
	7.8 Parkinson’s Arrow
	7.9 Wiese Arrow
	7.10 Schmucker’s Concept of Transfer Function and Induction Arrows
	7.11 Z/H Pseudosection
	7.12 Difference Induction Arrows
	7.13 Complex Demodulation
		7.13.1 Definition and€Significance of€Complex Demodulation
		7.13.2 Relationship to€Power Spectra
		7.13.3 Computational Procedure
	7.14 Geomagnetic Depth Sounding
		7.14.1 Approach A
		7.14.2 Approach B
		7.14.3 Approach C
	7.15 Audiofrequency Magnetic Method (AFMAG)
	7.16 Concluding Remarks
	References
8 Marine Electromagnetics
	8.1 Introduction
	8.2 Marine Magnetotellurics
		8.2.1 Marine Magnetotellurics for€Solid-Earth Geophysics
		8.2.2 Marine Magnetotellurics (MMT) for€Oil Exploration
	8.3 Marine Controlled-Source Electromagnetics (CSEM)
	8.4 Field Examples of€Variation of€Electrical Conductivity with€Depth in€Marine Environments
	8.5 Magnetometric Resistivity Method (MMR)
	8.6 MOSES
	8.7 Self Potentials
	References
9 Mathematical Modelling
	9.1 Introduction
	9.2 Two- and€Three-Dimensional Problems
	9.3 Finite Element Method
		9.3.1 Concept of Virtual Work and the Energy Method in the Magnetotelluric Domain (Coggon’s Model)
		9.3.2 Formulation Steps
		9.3.3 Minimisation of€the€Integrals
		9.3.4 Galerkin’s Method in a Finite Element Magnetotelluric Domain
		9.3.5 Finite Element Formulation for€the€Helmholtz Wave Equation
		9.3.6 Element Equations
		9.3.7 TM-Mode Magnetotellurics
		9.3.8 TE-Mode Magnetotellurics
		9.3.9 Global Matrix Formulation
		9.3.10 Isoparametric Elements in€Finite Elements
	9.4 Finite Difference Method
		9.4.1 Some Mathematical Physics Preliminaries Related to€Finite Difference Modeling in€Magnetotellurics
		9.4.2 Finite Difference Modeling
		9.4.3 Fomenko and Mogi’s Finite Difference Model (2002)
		9.4.4 Calculation of€the€H Field
		9.4.5 Boundary Conditions (Mackie et al. 1993)
		9.4.6 Boundary Conditions (Fomenko and Mogi’s Model 2002)
		9.4.7 Preconditioning of€Matrix
		9.4.8 Divergence H Correction
		9.4.9 Divergence J Correction
		9.4.10 Advantages in€This Approach (Fomenko and€Mogi 2002)
	9.5 Integral Equation Method
		9.5.1 Integral Equation as€a€Mathematical Tool
		9.5.2 Formulation of€an€Electromagnetic Boundary Value Problem
		9.5.3 Green’s Function in the Vector Potential Field Solution of Helmholtz Electromagnetic Wave Equation
		9.5.4 Three-Dimensional Boundary Value Problem
	9.6 Thin-Sheet Modelling
		9.6.1 Introduction
		9.6.2 Ranganayaki and Madden’s Model (1980)
		9.6.3 Remarks
	9.7 Hybrids
		9.7.1 Introduction
		9.7.2 Different Combinations
		9.7.3 Hybrid Formulation (Lee, Pridmore and€Morrison)
	References
10 Inversion of€Geophysical Data
	10.1 Introduction
	10.2 Basic Framework of€Geophysical Data Inversion
		10.2.1 Construction of€an€Inverse Problem Algorithm and€Convergence
	10.3 Tikhnov’s Regularisation Philosophy
	10.4 Fréchet Derivative
		10.4.1 Parker’s Definition
		10.4.2 Zdhanov’s Definition
	10.5 Major Methodologies for€Inversion
	10.6 Basis Function
	10.7 Subspace
	10.8 Krylov Subspace
	10.9 Singular Value Decomposition
	10.10 Least Squares and€Weighted Least Squares Estimator
		10.10.1 Least Squares and€Ridge Regression Estimator
		10.10.2 Weighted Least Squares and€Weighted Ridge Regression
	10.11 Backus–Gilbert Inversion
		10.11.1 Introduction
		10.11.2 Backus-Gilbert Formulation
		10.11.3 Backus–Gilbert Fréchet Kernel (Oldenburg 1979)
		10.11.4 Field Example
	10.12 Multiple Source Code for€Inversion: One Field Example of€Application Multiple Source Codes for€Inversion of€Same Data Set: Application of€Marginal Probability Density Function for€Model Parameter Estimation
	10.13 Two-Dimensional Inversion
	10.14 Occam Inversion
		10.14.1 2D Occam Inversion Formulation (deGroot–Hedlin and Constable 1990)
		10.14.2 REBOCC Inversion
		10.14.3 REBOCC Formulation (Siripunvaraporn  and€Egbert 2000)
	10.15 Method of€Steepest Descent
	10.16 Conjugate Gradient Method
		10.16.1 Introduction
		10.16.2 Important Steps in€Conjugate Gradient Method
		10.16.3 Conjugate Gradient Method as€a€Direct Approach
		10.16.4 The Conjugate Gradient Method as€an€Iterative Approach
		10.16.5 Computation of€Alpha and€Beta
	10.17 Rapid Relaxation Inversion (RRI) (Smith and€Booker 1991)
	10.18 Monte Carlo Inversion
	10.19 Joint Inversion
		10.19.1 Introduction
		10.19.2 Joint Inversion of€Magnetotellurics and€DC Dipole-Dipole Resistivity Data (Sasaki 1989)
		10.19.3 Joint Inversion of€Resistivity and€Induced Polarisation Sounding Data (Roy 2014)
		10.19.4 Joint 2D Resistivity and€Seismic Inversion
		10.19.5 Joint Inversion of€Seismic Refraction and€Magnetotelluric Sounding Data (Synthetic Model)
	10.20 Appraisal
	References