The magnetotelluric (MT) method, pioneered by Tikhonov (1950) and Cagniard (1953), has been applied with varying degrees of success to yield information about the Earth's electrical conductivity, temperature regimes, and geologic structure. The strengths and weaknesses of the MT method are now generally appreciated and the majority of research over the past few years has concentrated on data processing, forward modeling and inversion. Historically, MT interpretation has used one-dimensional (1-D) forward modeling algorithms, 1-D inversions, and 2-D forward modeling. Algorithms for 2-D inversion and 3-D forward modeling are just now reaching maturity.
Although all researchers recognize that the Earth is geologically complicated,1-D inversion is still an important source of information. First, there are geologic regions where the lateral variation is small and therefore a 1-D interpretation is directly applicable. Second, 1-D inverse solutions provide good starting models for 2-D inversion algorithms. Third, a thorough understanding of the 1-D inverse problem, especially the nonuniqueness of the solution, provides a valuable foundation for solving inverse problems in higher dimensions.
Many years ago, some believed that the 1-D inverse problem was adequately solved and that further research would yield few additional benefits. Higher dimensional solutions were thought to be the only remaining frontier. Fortunately, the 1-D problem was further explored, and valuable insight into the nature of the electromagnetic induction problem was developed. For example, the excellent paper by Parker (1980) showed that a conductivity structure producing the least-squares fit to the observations consisted of an infinitely resistive Earth interleaved with a set of infinitely conducting sheets having finite conductance.
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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.”