Open AccessThe one‐dimensional electromagnetic induction problem: model refinement
Author(s) -
Anderssen R. S.
Publication year - 1979
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.1979.tb03772.x
Subject(s) - electromagnetic induction , inversion (geology) , mathematical analysis , inverse theory , function (biology) , physics , geophysics , mathematics , geology , optics , quantum mechanics , seismology , surface wave , tectonics , evolutionary biology , biology , electromagnetic coil
Summary . Using a variational formulation for the response function V ( r ), commonly used in the inversion of electromagnetic induction data for a spherically symmetric earth, a number of independent expressions for the total variation of this response function with respect to perturbations in the (electrical) conductivity S o have been derived. These results have been used to indicate: (1) How the boundary constraints contained in the expressions for the total variation of V ( r ) affect any computational implementation. (2) How refinement modelling for the inversion of electromagnetic induction data can be implemented iteratively without the use of linearization. In addition, these results have been used to examine the validity of Parker's linearization proposal by showing that his results depend heavily on the exclusion of certain boundary constraints, and the choice of the L 2 norm as the norm to use.