This monograph presents a review of various approaches which invert MT data under the assumptions that the conductivity is 1-D and isotropic. Obviously, the Earth conductivity is always in disagreement with these assumptions, but this should not prevent a thorough examination of 1-D techniques. There are geologic environments (for example, under the ocean floors and in sedimentary basins) where the 1-D assumption is sometimes an adequate representation. If the conductivity is 2-D, then a 1-D inversion of a particular polarization mode gives useful information in itself. In more complicated environments, 1-D inversions of impedance tensor averages such as the square root of the determinant, or the average of its off-diagonal elements (Berdichevsky and Dmitriev, 1976) may provide a reasonable conductivity estimate to initiate more realistic 2-D or 3-D inversions. Therefore, irrespective of geology, 1-D inversions provide useful information about the conductivity.
There is another, and perhaps equally important reason for thoroughly investigating 1-D MT inversion techniques. MT represents one extreme of electromagnetic sounding methods; the other extreme is dc resistivity. An MT experiment has induction effects but no source geometry. The inducing field is assumed to be a vertically incident harmonic wave, and the field data are processed to be compatible with this assumption. On the other hand, dc resistivity experiments involve source geometry, but no induction. All other active sounding experiments have both source geometry and electromagnetic induction. Therefore, it follows that techniques developed for inverting MT data, and insight acquired regarding what information about the conductivity can and cannot be obtained, are of value when developing inversion algorithms for other types of sounding experiments.
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In this short monograph, 1D inversion methods are examined collectively using a uniform notation. One-dimensional inversion methods are still important because there are geologic regions where lateral variation is small and 1D interpretation is directly applicable; 1D inverse solutions provide good starting models for 2D inversion; and understanding the 1D inverse problem provides a foundation for solving inverse problems in higher dimensions. The 10 chapters are “Introduction”, “Existence”, “Uniqueness,” “Asymptotic Methods,” “Linearized/Iterated Methods,” “Global Penalty Functional Methods,” “Monte Carlo Methods,” “Exact Methods,” “Appraisal Methods,” and “Conclusion.”