The Fréchet derivative for the one‐dimensional electromagnetic induction problem

Abstract

Summary. From consideration of the higher order terms, it is shown that the magneto‐telluric response is Fréchet differentiable with respect to conductivity; this result remains valid for discontinuous profiles, which is not so in the case of the corresponding free‐oscdlation problem for the elastic earth. The remainder term in the Fréchet formula is shown to be O|δσ|2 and a numerical estimate is made of the bounding constant for a restricted class of conductivity models. Copyright © 1977, Wiley Blackwell. All rights reserved