Magnetotelluric inversion for minimum structure

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Abstract
Structure can be measured in terms of a norm of the derivative of a model with respect to a function of depth f(z), where the model m(z) is either the conductivity σ or log σ. An iterative linearized algorithm can find models that minimize norms of this form for chosen levels of chi‐squared misfit. The models found may very well be global minima of these norms, since they are not observed to depend on the starting model. Overfitting data causes extraneous structure. Some choices of the depth function result in systematic overfitting of high frequencies, a “blue” fit, and extraneous shallow structure. Others result in systematic overfitting of low frequencies, a “red” fit, and extraneous deep structure. A robust statistic is used to test for whiteness; the fit can be made acceptably white by varying the depth function f(z) which defines the norm. An optimum norm produces an inversion which does not introduce false structure and which approaches the true structure in a reasonable way as data errors decrease. Linearization errors are often so small that models of σ (but not log σ) may be reasonably interpreted as the true conductivity averaged through known resolution functions.

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