Open AccessH ‐polarization induction in two thin half‐sheets
Author(s) -
Dawson T. W.,
Weaver J. T.
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.tb00175.x
Subject(s) - classification of discontinuities , electromagnetic induction , geophysics , earth's magnetic field , source field , polarization (electrochemistry) , electric field , geology , electromagnetic field , discontinuity (linguistics) , half space , geometry , magnetic field , physics , mechanics , mathematical analysis , mathematics , near and far field , optics , electromagnetic coil , chemistry , quantum mechanics
Summary The Wiener—Hopf technique is used to solve the problem of electromagnetic induction in two adjacent half‐sheets underlain by a uniform conducting half‐space. The If‐polarization mode is considered in which the inducing magnetic field is assumed to be uniform and horizontal in space and directed parallel to the boundary between the two sheets. The solution, which complements one for E ‐polarization induction in two half‐sheets obtained previously by Weidelt, is of geophysical interest in describing the change in apparent resistivity across a conductivity discontinuity near the Earth's surface and also in explaining the coast effect on geomagnetic variations recorded on the ocean‐floor. The analysis shows that the horizontal electric field has a finite jump discontinuity where the two sheets meet and that the vertical electric field on the underside of the sheets has a logarithmic singularity there. Algebraic singularities occur in both components of the electric field when only one half‐sheet is present. The surface electromagnetic field is calculated for two specific models, one of which represents a coastal region, and the results are compared with those obtained by a recently published numerical method. The pattern of induced current‐flow associated with the coast effect is illustrated.