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

On the inverse problem of magnetostatics

“…The inverse problem for monitoring the surface of a ferromagnetic item was formulated in [7][8][9]. To the best of our knowledge, these are the only works in which the inverse problem of MMNDT is really formulated.…”

“…As a result we obtain a nonlinear integral equation in the form (8) where u(x, y 0 ) is the x or y component of the magnetic field measured on the line y = y 0 ; u 0 (x, y 0 ) is the x or y component of the magnetic field created by the magnetizing device; and K(…) is a known function. This integral equation is more complex than those that arise in geophysics, since there is a rather com plicated function, ϕ 0 , under the integral, which equals a constant in problems of geophysics.…”

“…A large number of studies [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15] have been devoted to solving the inverse problem. Numerical analysis of the magnetic field configurations of the ferromagnetic objects of limited length, which have surface and subsurface defects, was performed in [12,13] by the method of spatial integral equations.…”