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Appraisal Methods

Published:
January 01, 1992

In the preceding sections, we discussed many techniques which construct σ(z) profiles using a limited number of inaccurate MT data. For these practical data, the inverse problem is nonunique. Even for the wide-band test data used here, the range of models constructed is large (see Figures 17 and 18 for example). The vast space of acceptable solutions contains delta function, piecewise constant, and infinitely differentiable σ(z). The interpreter must grapple with this nonuniqueness in order not to be misled by a model with features not required by the data. As Jackson (1973) stated, it is essential not only to find a solution, but to represent in a meaningful way the degree of nonuniqueness permitted by the data.

In the preceding sections, we discussed many techniques which construct σ(z) profiles using a limited number of inaccurate MT data. For these practical data, the inverse problem is nonunique. Even for the wide-band test data used here, the range of models constructed is large (see Figures 17 and 18 for example). The vast space of acceptable solutions contains delta function, piecewise constant, and infinitely differentiable σ(z). The interpreter must grapple with this nonuniqueness in order not to be misled by a model with features not required by the data. As Jackson (1973) stated, it is essential not only to find a solution, but to represent in a meaningful way the degree of nonuniqueness permitted by the data.

For the MT problem, we cannot put bounds on the conductivity value at a particular depth within a constructed profile. At any depth it is possible to include arbitrarily thin layers of large or small conductivity without significantly affecting the misfit of the responses. Thus, for any practical data set, the lower bound on the conductivity is zero and the upper bound is unlimited. This leads naturally to the concept that only spatial averages of conductivity can be quantitatively assessed. An average of the conductivity may be written as

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Society of Exploration Geophysicists Geophysical Monograph Series

Inversion of Magnetotelluric Data for a One-Dimensional Conductivity

Kenneth P. Whittall
Kenneth P. Whittall
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Douglas W. Oldenburg
Douglas W. Oldenburg
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David V. Fitterman
David V. Fitterman
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Society of Exploration Geophysicists
Volume
5
ISBN electronic:
9780931830563
Publication date:
January 01, 1992

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