Reciprocity Formulas For Electromagnetic Induction Systems

A general formula is developed from reciprocity principles relating electromagnetic<br>induction measurements to an arbitrary distribution of subsurface conductivity<br>and permeability. This relation expresses the measurement (the induced emf in the<br>receiving coil) explicitly in terms of the subsurface parameters while bypassing the<br>intermediate step of integrating the magnetic flux through the coil or the electric field<br>around the coil. The reciprocity formula can also be used to compute analytic derivatives<br>of the measurements with respect to the subsurface model parameters. Such<br>derivatives are needed in performing sensitivity analyses and in iterative inversion<br>algorithms.