The theoretical modeling of eddy currents in conducting structures play an important role in many science and engineering applications. In nondestructive evaluation (NDE), where eddy currents are used to detect and characterize defects in conducting materials, these models are useful in providing quantitative estimates of the flaw characteristics. Such quantitative procedures in NDE bring about significant financial savings to industry, by establishing a sound basis for laying accept/reject criteria of in-service and manufactured material components. On the other hand, in geophysics, these models can be used to study and map the conductivity structure within the earth\u27s crust for purposes ranging from oil and mineral exploration to providing an understanding of the physical processes occurring within the interior of the earth;In this dissertation, we establish a theoretical basis for the modeling of the eddy current response of inhomogeneities in conducting structures. Further, we develop methods to characterize inhomogeneities by inverting this response. We first present a new formalism, based on which we derive the integral equations for the electromagnetic fields induced by an arbitrary-shaped, time-harmonic current source (the eddy current probe) in the presence of a conducting halfspace. Two situations are considered: a homogeneous halfspace and a halfspace containing a 3D inhomogeneity. Solutions for the fields from these equations are used to evaluate the impedance change in the eddy current probe;Next, the integral equations (derived above for all frequencies) are examined under the weak scattering (Born) and the low frequency limits. For certain geometries of the current source and inhomogeneity, the weak scattering and low frequency asymptotics are found to be equivalent. For the general case, it is found that the low frequency electromagnetic fields map to the fields existing inside an infinite conductor, containing the inhomogeneity and its image, under the influence of an even-ordered, incident electric field;Finally, for the first time, we initiate work on the characterization of flaws by directly inverting the eddy current response (here, the impedance change). The Born approximation is used to linearize the relevant integral equations. For a 3D reconstruction of the inhomogeneity from the impedance change in a spatially periodic current sheet, it is seen that a coupled Fourier-Laplace transform has to be inverted in the frequency domain. These transforms decouple in the time domain and an explicit inversion algorithm is obtained. When the inversion algorithm is specialized to one-dimension (variation of conductivity with depth), it is found that certain exact features of the conductivity profile are preserved in the Born reconstructions. These features provide a potentially exact method for estimating the conductivity and depth of surface coatings, even for large variations in conductivity of the coating from that of the underlying halfspace.
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