Numerical methods for computing the modal decomposition of the magnetic polarizability of conducting objects
Gabbay, Jonathan Eliezer
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Numerical methods are presented for characterizing the wideband responses of conducting objects to excitation by electromagnetic induction sensors. Electromagnetic induction sensors can be used to measure the magnetic polarizability tensor of conducting targets, a tensor that encapsulates the entire scattering interaction between target and sensor. Wideband characterization of the magnetic polarizability tensor can be achieved by expanding the frequency response in pole-expansion form. The pole-expansion coefficients may then be used as a signature, which can be used for subsurface target detection. To derive the coefficients numerically, the interaction between a target of interest and the sensor is modeled as a linear system, which can then be set up as generalized eigenvalue problem. The eigenvalues of the system correspond to the pole locations of the pole expansion. The remaining coefficients can be derived from the eigenvectors of the system, which correspond to the that natural modes that are excited by the sensor. Integral methods are presented for numerically computing the pole-expansion coefficients of thin conducting sheets and shells, conducting volumes, and bodies of revolution. A differential method is also presented for conducting volumes. Computational results are compared to known analytical solutions when possible as well as to experimental measurements.