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Operating in the magnetoquasistatic regime (a few hertz to perhaps a few 100 kHz), electromagnetic induction (EMI) sensing has recently emerged as one of the most promising avenues for discrimination of subsurface metallic objects, e.g., unexploded ordnance. The technique of thin-skin approximation (TSA) was devised to deal with numerical problems caused by the rapid decay of fields beneath the scatterer's surface. The rather nonintuitively broad applicability and specific error patterns of the TSA formulation are explained here by theoretical analysis based on analytical solutions and approximate Monte Carlo simulation. In the limiting case of infinitesimal skin depth (EMI perfect reflection), the scatterer aspect ratio (AR) is inferred without regard to metal type. Alternatively, the AR of some homogeneous magnetic objects is inferred from the pattern of transverse to axial response ratio over the entire EMI ultrawideband. Use of the method in inversions for electromagnetic parameters reveals fundamental nonuniqueness problems and shows their basis, which is not dependent on the method of forward solution.