A method includes obtaining, with a plurality of receivers of a logging tool, a set of induction, multi-spacing, multi-frequency measurements of a plurality of nested casings. The method also includes inverting, with a processor, the set of measurements for magnetic permeability or electrical conductivity. The method further includes calibrating, with the processor, the set of measurements using differences between measured responses of the logging tool, and simulated responses of the logging tool resulting from inverting the set of measurements for the magnetic permeability or electrical conductivity of the plurality of nested casings, to determine a calibrated set of measurements. The method also includes inverting, with the processor, the calibrated set of measurements for thickness of individual casings of the plurality of nested casings, to determine the thickness of the individual casings.