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"Potential Theory in Applied Geophysics" introduces the principles of gravitational, magnetic, electrostatic, direct current electrical and electromagnetic fields, with detailed solutions of Laplace and electromagnetic wave equations by the method of separation of variables. Behaviour of the scalar and vector potential and the nature of the solutions of these boundary value problems are shown along with the use of complex variables and conformal transformation, Green's theorem, Green's functions and its use in integral equation. Finite element and finite difference methods for two-dimensional potential problems are discussed in considerable detail. The analytical continuation of the potential field and inverse theory, used for the interpretation of potential field data, are also demonstrated.
List of contents
Elements of Vector Analysis.- Introductory Remarks.- Gravitational Potential and Field.- Electrostatics.- Magnetostatics.- Direct Current Flow Field.- Solution of Laplace Equation.- Direct Current Field Related Potential Problems.- Complex Variables and Conformal Transformation in Potential Theory.- Green's Theorem in Potential Theory.- Electrical Images in Potential Theory.- Electromagnetic Theory (Vector Potentials).- Electromagnetic Wave Propagation Problems Related to Geophysics.- Green's Function.- Numerical Methods in Potential Theory.- Analytical Continuation of Potential Field.- Inversion of Potential Field Data.
Summary
"Potential Theory in Applied Geophysics" introduces the principles of gravitational, magnetic, electrostatic, direct current electrical and electromagnetic fields, with detailed solutions of Laplace and electromagnetic wave equations by the method of separation of variables. Behaviour of the scalar and vector potential and the nature of the solutions of these boundary value problems are shown along with the use of complex variables and conformal transformation, Green's theorem, Green's functions and its use in integral equation. Finite element and finite difference methods for two-dimensional potential problems are discussed in considerable detail. The analytical continuation of the potential field and inverse theory, used for the interpretation of potential field data, are also demonstrated.
Additional text
From the reviews:
"With 17 chapters and more than 600 pages, this is a comprehensive M.Sc.-level textbook on potential theory and electromagnetic theory with particular emphasis on geophysical applications." (Sven Ivansson, Mathematical Reviews, Issue 2008 k)
"This book has been used as textbook teaching post-graduate students in India. The book introduces theory and computational methods applied to electrical and electromagnetic fields in geophysics. … The mathematics algorithms are discussed and they are related to boundary value problems, conformal transformation, Green’s theorem, Green’s functions, finite element and finite difference methods for two-dimensional potential problems." (Chengshu Wang, Zentralblatt MATH, Vol. 1152, 2009)
Report
From the reviews:
"With 17 chapters and more than 600 pages, this is a comprehensive M.Sc.-level textbook on potential theory and electromagnetic theory with particular emphasis on geophysical applications." (Sven Ivansson, Mathematical Reviews, Issue 2008 k)
"This book has been used as textbook teaching post-graduate students in India. The book introduces theory and computational methods applied to electrical and electromagnetic fields in geophysics. ... The mathematics algorithms are discussed and they are related to boundary value problems, conformal transformation, Green's theorem, Green's functions, finite element and finite difference methods for two-dimensional potential problems." (Chengshu Wang, Zentralblatt MATH, Vol. 1152, 2009)
