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Theoretical inverse problem is the terminology (in the Russian literature) for a geophysical inverse problem in which the field is given by an explicit expression. This can arise, for example, when data are approximated by singular sources (monopoles, dipoles, etc.) in a half-space. This chapter derives explicit integrodifferential equations of theoretical inverse problems for 3-D electromagnetic fields satisfying the Helmholtz, telegraphic, and diffusion equations. Functional equations for a perfect conductor are presented, and some numerical examples are given.

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