Geophysical Interpretation using Integral Equations, Softcover reprint of the original 1st ed. 1992

Along with the general development of numerical methods in pure and applied to apply integral equations to geophysical modelling has sciences, the ability improved considerably within the last thirty years or so. This is due to the successful derivation of integral equations that are applicable to the modelling of complex structures, and efficient numerical algorithms for their solution. A significant stimulus for this development has been the advent of fast digital computers. The purpose of this book is to give an idea of the principles by which boundary-value problems describing geophysical models can be converted into integral equations. The end results are the integral formulas and integral equations that form the theoretical framework for practical applications. The details of mathematical analysis have been kept to a minimum. Numerical algorithms are discussed only in connection with some illustrative examples involving well-documented numerical modelling results. The reader is assu­ med to have a background in the fundamental field theories that form the basis for various geophysical methods, such as potential theory, electromagnetic theory, and elastic strain theory. A fairly extensive knowledge of mathematics, especially in vector and tensor calculus, is also assumed.

Introduction. General matters concerning integral equations. Demonstration of an integral equation solution. Classification of integral equations. Numerical solution. Elements of electrostatics and potential theory. Differential representation of electrical potential. Integral representation of electrical potential. Primary current electrode. Volume distribution of simple sources. Surface distribution of simple sources. Surface distribution of double sources. Electrical methods. Introduction. Resistivity of rocks. Resistivity method. Magnetometric resistivity. Mise-a-la-masse method. Surface polarization. Induced polarization. Self-potential. Electrical anisotropy. Elements of magnetostatics. Introduction. Integral representation of magnetic potential. Volume distribution of simple poles. Surface distribution of simple poles. Volume distribution of dipoles. Magnetic methods. Magnetic properties of rocks. High-susceptibility models. Demagnetization and low-susceptibility models. Numerical applications. Effect of remanence. Electromagnetic methods. Introduction. Boundary value problems for electromagnetic fields. Green's dyadics for electromagnetic boundary value problems. Volume integral equations for 3-dimensional electromagnetic fields. Volume integral equations for 2-dimensional electromagnetic fields. Surface integral equations for electromagnetic fields. Integral equation solution for electromagnetic fields in a thin conductor model. Seismic methods. Introduction. Integral formulae for elastic wave fields in an anisotropic medium. Integral formulae for elastic wave fields in an isotropic medium. Separation of elastic wave fields into a compressional and a rotational mode. Integral formulae for acoustic wave fields in the frequency domain. Integral formulae for acoustic wave fields in the time domain. Applications. Appendices. Index.