Reconstruction of a Media Boundary Based on the Spatial Distribution of Stray Magnetic Fields. II. Definition and Method of Solving the Inverse Geometric Problem of Magnetostatics

The formulation of the inverse geometric problem of magnetostatics in application to the problem of determining the shapes and dimensions of surface flaws by magnetic inspection methods is considered. The fundamental difficulties in solving inverse problems, which are related to possible solution nonuniqueness and instability, are discussed. It is shown that Tikhonov's conditional correctness requirements are met for a function of boundary shape represented by a segment of a Fourier series with finite coefficients. A method for solving the inverse magnetostatics problem is suggested. A computational experiment demonstrates the potential of the solution method.