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For the one-dimensional magnetotelluric inverse problem the ties between the impedances at neighbouring frequencies, reflecting the analytical properties of the transfer function, are expressed in terms of inequalities between the data. After the derivation of some elementary necessary constraints for data sets with two or three frequencies, a set of necessary and sufficient conditions warranting the existence of a one-dimensional conductivity model in the general M-frequency case is given. This set of constraints characterizes a 1-D data set by the signs of 2M determinants derived from the data.
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