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Magnetotellurics is finding increasing applications for imaging electrically conductive structures below the Earth's surface - in both industrial and academic research projects. In this book the authors provide a systematic approach to understanding the modern theory of ill-posed problems which is essential to making confident meaningful interpretations of magnetotelluric and magnetovariational soundings. The interpretation is conducted in an interactive way.Magnetotellurics is finding increasing applications for imaging electrically conductive structures below the Earth's surface - in both industrial and academic research projects. In Models and Methods of Magnetotellurics the authors provide a systematic approach to understanding the modern theory of ill-posed problems which is essential to making confident meaningful interpretations of magnetotelluric and magnetovariational soundings. The interpretation is conducted in an interactive way, including the hypotheses tests and successive partial inversions with priority on the tippers, magnetic tensors and impedance-phases, which keeps out the destructive static effects of near-surface inhomogeneities. The efficiency of the interpretation is exemplified by new geoelectric models of the Baikal rift zone and the Cascadian subduction zone.