Potential Theory in Applied Geophysics

This book 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. Discussion includes behaviours of the scalar and vector potential and the nature of the solutions of these boundary value problems, along with the use of complex variables and conformal transformation, Green's theorem, Green's formula and Green's functions.

Résumé

"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.

Contenu
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.