Open AccessTwo‐dimensional induction in a thin sheet of variable integrated conductivity at the surface of a uniformly conducting earth
Author(s) -
Green V. R.,
Weaver J. T.
Publication year - 1978
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.1978.tb05939.x
Subject(s) - mathematical analysis , conductor , electromagnetic induction , integral equation , electrical conductor , conductivity , polarization (electrochemistry) , surface (topology) , mathematics , physics , geometry , chemistry , quantum mechanics , electromagnetic coil
Summary. The forward solution of the general two‐dimensional problem of induction in a model earth comprising a uniformly conducting half‐space covered by a thin sheet of variable integrated conductivity is obtained. Unlike some previous treatments of similar problems, the method presented here does not require the field to be separated into its normal and anomalous parts. Both the E ‐ and B ‐polarization modes of induction are considered and in each case the solution is expressed in terms of the horizontal component of the electric field satisfying, on the surface of the conductor, a singular integral equation whose kernel is a well‐known analytic function. A recently published solution of the coast effect is included as a special case. The numerical procedure for solving the integral equations is described and some illustrative calculations are presented.