Geophysical Interpretation using Integral Equations - L. Eskola

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Résumé :
This work gives the principles by which boundary value problems describing geophysical models can be converted into integral equations. It introduces Fredholm integral equations in a physical rather than mathematical approach.

Sommaire:
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.