Inverse Problems of Electromagnetic Geophysical Fields

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.