Natural Electromagnetic Fields in Pure and Applied Geophysics

ISBN-13: 9783030380991 / Angielski / Miękka / 2021 / 605 str.

Kalyan Kumar Roy

Spis treści

Chapter 1. General Introduction

1.1 Introduction

1.2 Preliminaries on Electromagnetic Waves and Their Application in Geophysical Investigation

1.3 Geomagnetic Field

1.3.1 Magnetic Field of Internal Origin

1.3.1.1 Dipole Field of Internal Origin

1.3.1.2 Nondipole Field of Internal Origin

1.3.1.3 Inclination and Declination of the Magnetic Field

1.3.2 Nondipole Time Varying Magnetic Field of External Origin

1.4 Solar Radiation

1.5 Solar Energy

1.6 Sun Spot Cycle

1.7 Solar Quiet Day (Sa) Variations

1.8 L. Variations

1.9 Equatorial Electrojet (EEJ) and Polar Electrojet (PEJ)

1.10 Solar Flare Effects (SFE)

1.11 Magnetic Storms and Substorms

1.12 D, Dst, Ds Variations

1.13 Bay Type Variations

1.14 Interaction Between the Sun and the Earth

1.15 Magnetosphere

1.16 Cosmic Rays

1.17 Van Allen Radiation Belt

1.18 Ionosphere

1.19 Ring Current

1.20 Magnetotail

1.21 Geomagnetic Field Variations

1.22 Classifications and Causes of the Different Pulsations and Micropulsations

1.22.1 Classification by Jacobs and Sinno (1960)

1.22.2 Classification by Madam Troitskaya (1962)

1.22.3 Classification by Benioff (1960)

1.22.4 Classification by Tepley and Wentworth (1962)

1.22.5 Classification by Vladimirov and Kleimenova (1962)

1.23 High Frequency Natural Electromagnetic Signals, Sferics

1.24 Earth's Natural Electromagnetic Fields as a Subject

1.24.1 Electrotelluric Method (T)

1.24.2 Magnetotelluric Methods (MT)

1.24.3 Geomagnetic Depth Sounding (GDS)

1.24.4 Magnetometer Array Studies (MA)

1.24.5 Magnetovariational Sounding (MVS)

1.24.6 Audiofrequency Magnetotelluric Method (AMT)
1.24.7 Sea Floor Magnetotelluric Method (SFMT)

1.24.8 Marine Magnetotellurics (MMT)

1.24.9 Audiofrequency Magnetic Method (AFMAG)

1.25 Controlled Sources

1.25.1 Controlled Source Audiofrequency Magnetotellurics (CSAMT)

1.25.2 Controlled Source Marine Electromagnetics (CSEM)

1.25.3 Long Offset Electromagnetic Transient (LOTEM)

1.25.4 Radio Magnetotellurics (RMT)

1.26 Coverage of This Book

1.27 References

Chapter 2. Electrical Conduction Through Rocks

2.1 Introduction

2.2 Electrical Conductivity

2.2.1 Expression of Electrical Conductivity for an Homogeneous 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 and 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 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 Electrical Displacement

2.5.5 Electrolytic or Ionic Conduction

2.6 Factors Which 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 Different 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 Piejoelectric Effect

2.8 Hall Effect

2.9 Maxwells Geoelectrical Conductivity Model

2.9.1 Soft Rock

2.9.2 Hard Rock

2.9.3 Ellipsoidal Grains

2.9.4 Alternating Current Conduction

2.10 Resisitivities of Metallic Rocks and Minerals

2.11 Semiconducting Minerals

2.12 Order of Electrical Conductivity of Some Common Metallic Ores

2.13 Some Common Geological Good and Bad Conductors

2.14 References

Chapter 3. Signal Processing

3.1 Introduction

3.2 Selection of Block Size

3.3 Manual 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 Signal

3.9 Integral Transforms

3.10 Fourier Transforms

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 Shanons Sampling Theorem

3.18 Linear Filter

3.19 Pulse Response of a Linear Filter

3.20 Convolution

3.21 Z. Transform

3.22 Filters and Windows

3.23 Cross Correlation and Autocorrelation

3.23.1 Cross Correlation

3.23.2 Autocorrelation

3.23.3 Properties of Auto and Cross Correlation

3.24 Autopower and Cross Power Spectrum

3.24.1 Energy Density Spectrum of a Periodic Signal

3.24.2 Power Density Spectrum of a Periodic Signal

3.24.3 Auto Power Spectra

3.24.4 Cross Power Spectra

3.25 Noise

3.26 Robust Processing

3.26.1 Introduction

3.26.2 Outliers

3.26.3 Breakdown Point

3.26.4 Median

3.26.5 Norm

3.26.6 Nongaussian Distribution

3.26.7 Seigel's Repeated Median Estimator

3.26.8 M-Estimator

3.26.9 Field Results

3.27 References

Chapter 4. Electrotellurics

4.1 Introduction

4.2 Basics of Electrotellurics

4.3 Comparison of Electrotelluric and Magnetotelluric Frequencies

4.4 Nature of 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 Relative Ellipse

4.8.1 Interconnection Between Base and Mobile Station Vectors

4.8.2 Time Domain Analysis

4.8.3 Electrotelluric Data Analysis

4.9 Triangle Method

4.10 Polygon Method

4.11 Discussion

4.12 Amplitude Ratio Method

4.13 Album of Theoretical Electrotelluric Profile Curves

4.13.1 Telluric Field over a Vertical Fault

4.13.2 Telluric Field over a Basement Asymmetric Anticlinal Structure

4.13.3 Telluric Field over Horst Type of Structure

4.13.4 Telluric Field over a Graben Type of Structure

4.13.5 Telluric Field and its Gradient over a Step Fault

4.14 Analytical Continuation of Telluric Field Data

4.15 Absolute Ellipse Method

4.15.1 Absolute Ellipses

4.15.2 Field Plotting of Absolute Ellipse

4.15.3 Model Tank Experiment for Generation of Absolute Ellipse

4.15.4 Model Tank Generated Absolute Ellipse and the Variation of the Ellipse Parameter due to Simulated Geological Inhomogeneities

4.15.5 Absolute Ellipse Generation Equations in a Model Tank

4.15.6 Absolute Ellipses over a Conducting Sphere

4.15.7 Absolute Ellipses over a Conducting Plate

4.16 Interpretation of Electrotelluric Data and Application

4.17 Concluding Remarks

4.18 References

Chapter-5. Magnetotellurics

5.1 General Introduction

5.2 Plane wave propagation

5.2.1 Advancing Electromagnetic Waves

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 points of Principle.          

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 times

5.4.4 Magnetotelluric Signal can see a target which is at depth beyond its skin depth

5.4.5 Granite Window is a must for deep magnetotelluric survey because two kilometer thick conducting sediments on top can reduce the sensitivity of the magnetotelluric signals upto three hundred kilometers from the  surface and deep inside the upper mantle

5.4.6 Magnetotellurics is a suitable geophysical tool for detecting sediments sandwiched between the flood basalt and crystalline basement

5.5 Magnetotelluric Field Work and Field Data     

5.5.1 Field Data Acquition

5.5.2 Signal Strength  Versus Frequency or Period 

5.5.3 Number of Degrees of Freedom versus period

5.5.4 Coherencies

5.5.5 Different Components of the Impedance Tensor Versus Period

5.5.6 Processed Fourier Spectra

5.5.7 Processed Apparent Resistivity and phase  Field Data with error bar

5.6 Concept of Optimum  Mathematical Rotation in Magnetotellurics

5.6.1 Optimum Rotation Angle and Related Impedance Tensor

5.7 Concept of E and H  Polarisation(TE and TM Mode)

5.8 MT Impedances

5.9 Estimation of the MT Tensor Components

5.9.1 Estimation of the MT Tensors Using Coherencies

5.9.2 Estimation of MT Impedance Using Single Station Data

5.9.3 Remote Reference Magnetotellurics       

5.10 Magnetotelluic Tensor Decomposition

5.10.1        Egger’s Eigen State Decomposition

5.10.2        Bahr’s Tensor Decomposition

5.10.3        Groom Bailey Decomposition

5.10.4        Groom Bailey’s Twist and Shear

5.10.5        Jones Decomposition

5.11           Tipper Parameters

5.12           Rotation Invariant Parameters in magnetotellurics

5.12.1        Field Apparent Resistivity Curves using Rotation Invariant Parameters

5.13           Magnetotelluric Phases

5.13.1        Magnetotelluric Phase Tensor

5.14           Anisotropy

5.14.1        Anisotropy in Direct Current Domain

5.14.2        Anisotropy in Magnetotelluric Domain

5.14.3        Phase Splitting in Magnetotellurics

5.14.4        Magnetotelluric Phase above 90⁰

5.15           Noise  

5.15.1        General Defination

5.15.2        Geophysical Noise

5.15.3        Induced Polarisation

5.15.4        Electromagnetics

5.15.5        Atmospheric/Oceanic and Meteorological Noise.

5.15.6        Seismic Noise

5.15.7        Geological Noise

5.15.8        Coherent Noise

5.15.9        Incoherent Noise

5.15.10      Correlated and Uncorrelated Noise

5.15.11      White and Nonwhite Noise

5.15.12      Man Made Noise

5.15.13      Natural Noise

5.15.14      Sensor Noise

5.16           Galvanic and Inductive Distortion

5.17           Magnetotelluric Current Channeling

5.18           Magnetotelluric Strike

 5.19          Dimensionality Indicator

5.19.1        One Dimensional Structure 

5.19.2        Two Dimensional Structure

5.19.3        Three Dimensional Structure

5.19.4        Dimensionality Indicator From Phase

5.19.5        Dimensionality Indicator From Eigen State Formulation

5.19.6        Swift Skew as a Dimensionality Indicator

5.19.7        Complex Domain Plot of the impedance Tensor as a

                  Dimensionality Indicator

5.19.8        Impedance Ellipse as a Dimensionality Indicator

5.20           Complex Domain Plot  of the Impedance Tensor

                  and Rotation Invariant Tensor

5.21           Static Shift

5.21.1        Curve Shifting

5.21.2        Statistical Averaging

5.21.4        Use of Auxilliary Tools

5.21.5        Use of Constraing Parameters

5.21.6        Use of Well Log Data

5.21.7        Higher Current Dipole Length

5.21.8        Static Shift Free Magnetotelluric Parameters

5.22           Magnetotelluric Designs

5.23           Location of the MT study area in eastern part of  Indian

                  Subcontinents  where a few magnetotelluric   observations

                   are taken for qualitative to semiquantitat Interpretation

5.24           Qualitative Signatures  a very important sector of Magnetotellurics

                  Data interpretation

5.24.1        Qualitative signature of a Rift Valley or Major Continental

                  Fracture

5.24.2        Phase determinant Pseudosection can depict the subsurface

                  with greater clarity

5.24.3        Qualitative Magnetotelluric  Signatures of faults

5.24.4        Qualitative Magnetotelluric signature of  Sukinda Thrust

5.24.5        Pseudo 3D pseudosections of rotation invariant phases across the

                  Sukinda thrust.

5.24.6        Some of the Rotation Invariant Parameters

                  are heavy weight parameters

5.24.7        Different MT parameter PseudoSections from the

                  field data across Sukinda Thrust

5.24.8        Qualitative signature in  Bahr’s Telluric Vectors across Sukinda Thrust

5.24.9        Induction Arrows show the Major Fracture zone

                  in the Archaean Proterozoic collision Zone

5.24.10      Rotation Invariant Parameters are less affected by

                      Static Shift

5.24.11      Profiles and Pseudosections from Mathematical Models

5.25           Semiquantitative to Quantitative Signatures of the MT data

5.25.1        One Dimensional Inversion of Magnetotelluric Data

5.25.2        Two Dimensional Inversion and 2D Model

5.25.3        2D and Pseudo3D model of the Mahanadi Graben            

5.26           Application of MT in Earth Sciences

5.26.1        Major breakes in Crust and Upper Mantle

5.26.2        MT for measuring Asthenosphere temperature as well as for mapping

                       High heat flow areas

5.26.3        MT for Oil Exploration

5.26.4        MT for mapping convergent and divergent plate margins

5.26.5        MT for  earthquake Prediction

5.26.6        MT can measure Permafrost Thickness

5.26.7        MT for ground water exploration

5.27           Appraisal

5.29           References

 

Chapter-6

Auxilliary Tools in Magnetotellurics

6.1             Introduction     

6.2             Audiofrequency Magnetotellurics(AMT)

6.2.1          Source Characteristics

6.2.2          Nature of the AMT signal

6.2.3          Field Procedure

6.2.4          Qualitative Interpretation

6.2.4.1       Pseudosection Plots

6.2.4.2       Pseudosections of Theoretical Models

6.2.4.3       Field examples of pseudosections

6.2.4.4       Average Resistivity Plot

6.2.4.5       Quantitative Interpretation

6.2.5          Appplication

6.3             Controlled Source Audifrequency Magnetotellurics(CSAMT)

6.3.1          Introduction

6,3,2          Skin depth and Effective Penetration Depth

6.3.3          Pseudosections of CSAMT Data

6.3.4          CSAMT sources

6.3.4.1       Electromagnetic Field Due to a Vertical Oscillating Electric Dipole

6.3,4.2       Oscillating Vertical Magnetic Dipole On the Surface of The Earth

6.3.4.3       Electromagnetic Field Due to a Long Cable On the Surface of an homogenous Earth.

6.3.4.4       Scalor CSAMTSource

6.3.4.5       CSAMT Pseudosection

6.3.4          Field Survey

6.3.5          Interpretation

6.4             Long Offset Electromagnetic Transients (LOTEM)

6.4.1          Introduction

6.4.2          LOTEM Data Acquisition

6.4.3          LOTEM Theory

6.4.4          Data Processing

6.4.4          Interpretation of LOTEM Data

6.4.5          Application

6.5             Radiomagnetotellurics(RMT)

6.6             References

 

Chapter-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 Field

7.5               Spherical Harmonics

7.5.1            Solution of Laplace Equation in Spherical Polar Coordinates

7.5.1            When Potential is a function of all the three coordinates

7.5,2            Associated Legendre’s Polynomial

7.6               Magnetometer Array Studies

7.6.1            Recording of Geomagnetic Data

7.6.2           Examples of Magnetometer Arrays

 7.6.3          Examples from India

7.6.4            Magnetogram

7.6.5            Processing of Geomagnetic data

7.6.5.1         Fourier Transform Maps

7.6.5.2         Amplitude Spectra

7.6.6            Transfer Function analysis

7.6.7            Single site Transfer Function

7.6.8            Hypothetical Event analysis

7.7.              Induction Arrows

7.8.              Parkinsons Arrors 

7.9.              Wiese Arrow

7.10             Schmukher’s Concept of Transfer Function and Induction  Arrow

7.11.            Z/A Pseudosections

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 Procedures

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)

7.10.            Concluding Remarks

7.11             References

 

Chapter-8

Marine Electromagnetics

8.1              Introduction

8.2              Marine Magnetotellurics

8.2.1           Sea Floor Magnetotellurics (SFMT) for Solid Earth

8.2,2           Marine Magnetotellurics(MMT) for Oil Exploration

8.3              Marine Controlled source Electromagnetics(CSEM) for Oil Exploration

8.4              Magneometric Resistivity Method(MMR)

8.4.1           MMR Theory for Layered Earth

8.5              Moses

8.5              Self Potentisls

8.6              References 

Chapter-9

Mathematical modeling

9.1               Introduction

9.2               Two and Three Dimensional Problems

9.2.1            Introduction

9.3               Finite Element Method

9.3.1            Concept of Virtual Work and Energy Minimisation Method

                    In Magnetotelluric Domain(Coggon’s Model)

9.3.2            Formulation Steps

9.3.3            Minimisation of the Integral

9.4               Energy Minimisation Method in Direct Current Domain

9.4.1            Derivation of Functional from Power Consideration

9.4.2            Equivalence beteween Poisson’s equation and  minimisation of Power

9.4.3            Finite  Element Formulation

9.4.4            Minimisation of power

9.5               Galerkin.s Method in  Finite Element

                     Magnetotelluric Domain

9.5.1            Introduction

9.5.2            Finite Element Formulation for Helmholtz Wave Equations

9.5.3.           Element Equation

9.5.4            TM Mode Magnetotellurics

9.5.5            TE Mode Magnetotellurics

9.5.6.           Global Matrix Formulation

9.6              Isoparametric Elements in Finite Elements

9.6.1           Introduction

9.6.2           Triangular Elements(Three Noded)

9.6.3            Quadrilateral Elements(Four Noded)

9.6.4            Eight Noded Elements

9.6.5            Shape Function using Natural Coordinate

9.7               Finite Difference Method Three Dimensional Problem Magnetotellurics Mackie,Madden and Wannamaker’s Model

9.7.1            Introduction

9.7.2              Finite Difference Formulation

9.7.3             Boundary Conditions

9.7.4             Two  Dimensional Case

9.7.5             Transverse Magnetic (TM) Mode

9.7.6            Transverse Electric (TE) Mode

9.7.7            The Equations in Matrix Form

9.7.8            Preconditioning of matrix

9.7.9            Solution of the matrix

9.8               Integral Equation Method

9.8.1            Introduction

9.8.2            Formulation of an electromagnetic boundary value problem

9.8.3            Three Dimensional Electromagnetic Boundary Value Problem (Ting and Hohmann’s Model)

9.9               Thin sheet Modelling

9.9.1            Introduction

9.9.2            Ranganayaki and Madden’s Model(1980)

9.9.3            Remarks

9.10             Hybrids

9.10.1          Introduction

9;10.2          Different Combinations

9.10.3          Hybrid Formulation   (Lee,Pridmore and Morrisons Model)

9.11              References

Chapter 10. Inversion of  Geophysical  Data 

10.1             Introduction

10.2             Convergence of an Inverse Problem

10.3             Nonuniqueness and Compact Zone 

10.4             Well Posed and Ill posed problems

10.5             Overdetertermined and Underdetermined Problems

10.6             Linear Dependence and Independence of vectors

10.7             Inner Product space

10.8             Hilnert Space

10.9             Tikhnov’s Regularisation Philosophy

10.9.1          Theoretical  Concept in Abstract Spaces                

10.9.2          Definition of the regularizing operator

10.10           Basis Function

10.11           Subspace

10.12           Krylov Subspace      

10. 13          Method of Steepest Decent         

10. 14          Conjugate Gradient Method         

10.14.1        Introduction

10.14.2        Important Steps in Conjugate Gradient Method

10.14.3        Conjugate Gradient Method as a direct approach

10.14.4        Conjugate Gradient Method  as an iterative approach

10.14.5        Computation of alpha and beta.

10.15           Lagrange Multiplier

10.16           Stochastic Inversion

10.16.1        Introduction

10.16.2        Conjunction of the state of information

10.16.3        Maximum Likelyhood  Point

10.16.4        Field Example of one Stochastic Inversion Approach

10.17           Frechet Derivative

10.17.1        Parker’s Definition

10.17.2        Zhdanov’s Definition

10.18           Bachus Gilbert Inversion

10.18.1        Introduction

10.18.2        Bachus- Gilbrert Formulation

10.18.3        Bachus Gilbert Frechet Kernel.          

10.18.4        Field Example

10.19           Occam Inversion

10.19.1        Occam Inversion Formulation

10.20           Two Dimensional Occam Inversion

10.20.1        Introduction

10.20.2        2D Occam Inversion Formulation      

10. 21          Joint Inversion

10.21.1        Introduction

10.21.2        Joint Inversion of Seismic Refraction and Magnetotelluric data

10.21.3        Joint Inversion of Resistivity and Induced Polarisation Sounding Data

10.26           References

Subject  Index

O autorze

Kalyan Kumar Roy helds  M.Sc and Ph.D from the Department of Geology and Geophysics , Indian Institute of Technology, Kharagpur, West Bengal, India. In 1966,he joined as a faculty member in the same department. In 1975 Dr. Roy was offered post doctorate fellowship  of the National Research Council of Canada,  by the Department of Environment , Ottawa, Canada for a period of one year. He returned from Canada  and joined the same department as a faculty member. He retired as a Professor of Geophysics in the year 2002 after 36 years of service. He then served as an Emeritus Scientist in the Department of Geological Sciences, Jadavpur University, Kolkata from 2003 to 2009 and as an Adjunct Professor at IIT,Kharagpur from 2010 to 2011. He was a Guest Professor of the Department of Applied Geology, Dibrugarh University , Assam from 2013 to 2015. He joined as a Visiting Professor in the Department of Earth Sciences, Indian Institute of Engineering Science and Technology, Shibpur, Howrah, West Bengal, India  in 2011 and continued upto 2019. He has published 77 papers, one single authorship book, one edited volume of multi authorship book  and contributed in several multi aurhored books.

Dr.Roy was selected as a fellow of the National Academy of Science and fellows and life members of all the important Earth Science Societies of India. He is a life member of the Society of Petroleum Geophysicists based in Houston Texas, USA and Dehradun, Uttarakhand,I ndia. He attended many international conferences organized by I.U.G.G. (International Union of Geodesy and Geophysics),I.G.C.(International Geological Congress) and Electromagnetic workshops.

Blurb

This research monograph discusses all the branches of geophysics based on natural electromagnetic fields and their associated subjects. Meant for postgraduate and research level courses, it includes research guidance and collection of magnetotelluric data in some parts of Eastern India and their qualitative and quantitative interpretation. Specific topics highlighted include (i) Electrotellurics, (ii) Magnetotellurics, (iii) Geomagnetic Depth Sounding and Magnetometer Array Studies, (iv) Audio Frequency Magnetotellurics and Magnetic Methods, (v) Marine Magnetotelluric and Marine Controlled Source Electromagnetic Methods, (vi) Electrical Conductivity of Rocks and Minerals and (vii) Mathematical Modelling and Some Topics on Inversion needed for Interpretation of Geoelectrical Data.