Inverse Problems of Electromagnetic Geophysical Fields

Abstract

Part 1 Two-dimensional problems of a magnetic exploration method involving artificial field magnetization and electric exploration by a direct current: problem statement direct problems of an electric exploration and MAM as problems of linear conjunction of analytical functions effective algorithm of the solution of a problem of linear conjunction the theoretical inverse MAM problem and electric exploration with a direct current effective algorithm for solving the inverse MAM problem taking account of demagnetization uniqueness of the solution of the inverse problem of magnetic exploration on the weak uniqueness of the solution of the inverse problem on the uniqueness of the solution of the inverse problem of potential theory in a field magnetization method using a rotating field (Sq-variation). Part 2 The effective algorithms of solution of direct and inverse three-dimensional problems of magnetic exploration taking account of demagnetization: reducing the direct problem to the integral equation of the second kind solution of the operator equation in a neighbourhood of the first eigenvalue parametrized algorithms of the solution of direct problems examples of mathematical modelling solution of the inverse problem in view of demagnetization by the method of the quasi-equivalent ellipsoid theoretical and practical examples of realization of the algorithm of the equivalent ellipsoid. Part 3 Mathematical theory and algorithms of the solution of three-dimensional inverse problems of electric exploration with a direct current: problem statement integral equations of the theoretical inverse problem of electric exploration and the method of artificial magnetization integral transformations of electromagnetic fields the algorithm of solution of (3.10) and (3.14) in the class of stellar bodies on the solution of the charge method inverse problem algorithm for solving equations (3.30) and (3.32) in the class of stellar bodies the magnetic fields of spread currents inverse problem equations two-stage method of the solution to the inverse problem of electric exploration. Part 4 Explicit equations for inverse problems of electromagnetic field: equations of electrodynamics formulation of the problem explicit TIP equations for monochromatic field the TIP equations for quasi-stationary field the TIP equations for the case s2=0 the TIP equations for arbitrary electromagnetic field algorithm for solving the TIP equations in the class of stellar bodies.