Approximate Fréchet derivatives in inductive electromagnetic soundings

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Abstract
Fréchet derivatives play dual roles in electromagnetic (EM) methods as averaging functions relating conductivity to EM fields and as sensitivity functions relating conductivity perturbations to changes in these fields. For one‐dimensional EM inductive sounding, the Fréchet derivatives are not strongly model‐dependent, even for quite diverse earth models. In fact, using a scaled version of the Fréchet derivative for a uniform half‐space to approximate the exact Jacobian in a layered earth inversion program can actually improve the convergence to an acceptable model. This lack of a strong model dependence makes it possible to consider the capabilities and limitations of EM “imaging” methods from the perspective of Fréchet derivatives. Of particular interest is that noninductive Fréchet derivatives are strongly model‐dependent and hence the EM fields generated by this mode are less amenable to imaging techniques.

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