Open AccessInduction in a thin sheet of variable conductance at the surface of a stratified earth – II. Three‐dimensional theory
Author(s) -
McKirdy D. McA,
Weaver J. T.,
Dawson T. W.
Publication year - 1985
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.1985.tb05084.x
Subject(s) - hankel transform , integral equation , mathematical analysis , surface (topology) , electric field integral equation , fourier transform , mathematics , toroid , transfer function , kernel (algebra) , electromagnetic induction , field (mathematics) , physics , geometry , plasma , pure mathematics , engineering , quantum mechanics , electrical engineering , electromagnetic coil
Summary. The algorithm of Dawson & Weaver for modelling electromagnetic induction effects in a thin sheet at the surface of a uniform earth is modified to permit the use of a layered earth model. The theory is developed in Fourier space in terms of the toroidal and poloidal transfer functions instead of with the Green's function approach which was used by Dawson & Weaver. The integral equation for the surface electric field and most of the integral formulae for the derived field components are the same as before, except for the inclusion of additional integral the kernel of which has to be calculated numerically with the aid of fast Hankel transforms. The accuracy of the results is tested by comparing solutions with those obtained from a related 2‐D algorithm and finally an example of 3‐D modelling is presented.