The Fréchet derivative for the one-dimensional electromagnetic induction problem

Summary. From consideration of the higher order terms, it is shown that the magneto-telluric response is Frechet 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 Frechet 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.