Open AccessOn the Frechet differentiability of the one‐dimensional electromagnetic induction problem
Author(s) -
MacBain JOhn
Publication year - 1987
Publication title -
geophysical journal of the royal astronomical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0016-8009
DOI - 10.1111/j.1365-246x.1987.tb01656.x
Subject(s) - differentiable function , magnetotellurics , mathematics , fréchet derivative , mathematical analysis , function (biology) , pure mathematics , electrical resistivity and conductivity , physics , quantum mechanics , banach space , evolutionary biology , biology
Summary This paper proves that the one‐dimensional (1‐D) magnetotelluric response function is Frechet differentiable with respect to the conductivity function in the function spaces of L 1 and L 2 . Moreover, under somewhat restrictive assumptions, the electric field itself is Frechet differentiable with variations of s̀ in L 1 and L 2 permitted. The L 1 results can he extended to include the Unite delta comb generalized models.