Abstract
This article deals with the one-dimensional electromagnetic inverse problem of geophysics. The problem is shown to have the structure of a Riemann–Hilbert problem, analogously to the quantum mechanical inverse scattering problem. A trace-type formula for the electric conductivity is derived. Further it is shown that the Born approximation of this formula contains all the information of the possible discontinuities of the conductivity profile. The proof is based on the idea of singularity expansions of pseudodifierential operators.
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