The impedance of eddy current probes above layered metals whose conductivity and permeability vary continuously

A numerical method for calculating the impedance of a cylindrical air-core probe over a layered metallic half-space is presented. The method permits the conductivity and permeability to vary as arbitrary functions of the depth into the material. The utility and accuracy of the method are illustrated by comparison to the available experimental data, and to the exact results for a conductivity profile that varies as a hyperbolic tangent. The shape of the conductivity profile has an effect on the impedance response; the steeper the profile, the larger the impedance. Preliminary experimental studies show some agreement with theory.>