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Identifying the magnetic permeability in multi-frequency EM data inversion. (English) Zbl 1372.65118
Summary: Electromagnetic induction surveys are among the most popular techniques for non-destructive investigation of soil properties in order to detect the presence of either ground inhomogeneities or of particular substances. In this paper we develop a regularized algorithm for the inversion of a nonlinear mathematical model well established in applied geophysics, starting from noisy electromagnetic data collected by varying both the height of the measuring device with respect to the ground level and its operating frequency. Assuming the conductivity to be known in advance, we focus on the determination of the magnetic permeability of the soil with respect to depth, and give the analytical expression of the Jacobian matrix of the forward model, which is indispensable for the application of the inversion algorithm. Finally, numerical experiments on synthetic data sets illustrate the effectiveness of the method.

MSC:
65F22 Ill-posedness and regularization problems in numerical linear algebra
65H10 Numerical computation of solutions to systems of equations
65R32 Numerical methods for inverse problems for integral equations
86A22 Inverse problems in geophysics
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