Geo-Electromagnetism

Geo-Electromagnetism surveys the theoretical concepts and applications of electrical prospecting methods. This book is divided into seven chapters that specifically tackle the basic electromagnetic concepts and the special mathematical functions. This text deals first with the numerical and analytical approaches to delineate earth resistivity principles, followed by a description of the three-layer model. These topics are followed by a discussion on the theory of induced electrical polarization. The subsequent chapters are devoted to relevant electromagnetic theory of low-frequency current flow in conducting with varying fields. The discussion then shifts to the geophysical problems associated with vertical electric dipole sources, with an emphasis on the quasi-static range in which all significant distances are small compared with the free-space wavelength. The last chapters outline the relevant analytical development of the magnetotelluric theory and the theoretical principles of the transient electromagnetic methods used in geophysical exploration. Geophysicists, theoreticians, and undergraduate level students will find this book invaluable.

Table of Contents:
Preface Chapter I Earth Resistivity Principles Introduction Potentials about a Single Current Electrode for a Two-Layer Earth Model General Four-Electrode Array Three-Layer Model Formulation Discussion of Three-Layer Case Numerical and Analytical Approaches Effect of Anisotropy Current Source Excitation of Layered Anisotropic Region Current Source in Anisotropic Medium and Extensions Outcropping Vertical Dike Model Variable Resistivity with Depth—Exponential Model Variable Resistivity with Depth—General Case and the Kernel Function Resistivity for a Wedge Model Limiting Case of 180° Wedge Image Results for Acute-Angle Wedge Sphere Problems Response of a Homogeneous Conducting Sphere Current Point Source and Cylinder Problems Current Electrode on Axis of Fluid-Filled Borehole Current Electrode in Wall of Layered Tunnel Limiting Case for External Current Excitation of a Cable Cable Located in Resistive Half-Space Spheroidal Problems Resistance of Grounded Electrodes References Chapter II Theory of Induced Electrical Polarization (Quasi-Static Approach) Introduction Basic Transient Response Other Parameter Descriptions Induced Polarization Model Based on Coated Spherical Particles Response of a Layered Polarizable Earth Model General Formulation for Heterogeneous Media Resistivity and IP Analysis for a Thin Conductive Sheet Response of a Polarizable Sphere Multiregion Polarizable Models References Chapter III Electromagnetic Induction and Loop-Loop Coupling Introduction Magnetic Field of a Circular Loop of Current Circular Loop over Two-Layer Earth Extension to M-Layer Medium General Orientation of Source Dipole Explicit Field Expressions for Vertical and Horizontal Magnetic Dipole Sources Analog with dc Resistivity Low-Frequency Response Asymptotic Limiting Forms Mutual Impedance Formulation Homogeneous Half-Space Model Inclusion of Displacement Currents General Solution for a Horizontal Magnetic Dipole Electromagnetic Induction in a Conducting and Permeable Sphere Boundary Conditions at Conducting Shell and Core Boundary References Chapter IV Electromagnetic Coupling for Grounded Sources Introduction Some General Considerations Anisotropic Media Considerations Horizontal Electric Dipole Excitation Horizontal Electric Dipole over N-Layer Anisotropic Medium Mutual Impedance Formulation References Chapter V Earth Conduction Induced by Vertical Current Sources Introduction Exact Integral Solution for Raised Dipole Quasi-Static Limit and Fields within Half-Space Vertical Grounded Line Source Current Source in Borehole Transient Coupling between Grounded Finite Circuits References Chapter VI Magnetotelluric Theory Introduction Basic Plane-Wave Model Current Sheet Source Line Source Model Results Segmented Overburden Model Variable Subsurface Interface Concluding Remarks References Chapter VII Inductive Transients Introduction Pulse-Excited Loop over Layered Ground Limit of Thin Conductive Sheet Homogeneous Earth or Half-Space Guided Wave Effects Buried Source Problem Scattering from Buried Target Buried Sphere in Half-Space Final Comment on IP and EM References Appendix A Electromagnetic TM and TE Spherical Waves Introduction The Debye Potentials General Surface Impedance External Excitation of Sphere Concentrically Layered Model The Iterative Solution Dipole Excitation The Quasi-Static Limit A Further Extension References Appendix B Note on Bessel Functions Integrals Index