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An inverse process in remote sensing inverts the constitutive parameters of matter from measurable quantities at sensors. Analytical models relating the measurable and desired parameters are usually formulated with simplifying assumptions. However real matter and sensors often do not behave as assumed. Undue errors arising from discrepancies between assumed conditions and in situ measurements can be reduced through calibration and self-cansistency checks. Multipole expansion techniques are used here as a basis to check whether the sensors and the matter being interrogated are behaving as assumed. The self and transfer impedances of coaxial coils in an earth formation are formulated as an example to invert constitutive parameters from measurable impedances. The formulation assumes that the earth is linear, isotropic, and homogeneous and that the coils support only dipole and quadrupole interactions. For the analytical models to be self-consistent under the assumed conditions, several sets of inverted parameters from measurable impedances would have to agree to within acceptable uncertainties. Self-consistent evaluations of constitutive parameters can reduce costly undue errors that may arise, e.g., in locating gas/oil-bearing strata underground.