Solving the Structural Inverse Problem of Magnetic Prospecting with Respect to Demagnetization for a Two-Layer Medium Model

摘要

The integral equations of the direct problem of magnetic prospecting with respect to demagnetization are derived for a two-layer medium model; a method of determining the intensity of a secondary magnetic field for the case of magnetizing by a static field, whose potential is a harmonic function, is described. The respective integral equations are written based on the theory of a simple layer potential. An iteration algorithm for solving the three-dimensional structural inverse problem of magnetic prospecting with respect to demagnetization for the sampled medium model is proposed based on the modified method of local corrections. Its numerical implementation is less computer-intensive than, for example, the gradient methods of nonlinear minimization, the sampling accuracy being equal. Note that problems of electric and magnetic prospecting with respect to demagnetization and thermometry are mathematically equivalent for stationary fields. Therefore, the obtained results can be used in interpreting the data of these methods.