Open AccessB‐polarization induction in two thin half‐sheets coupled to the mantle by a conducting crust—II. Solution by the mode‐matching method, the fields above the conductors, and example results
Author(s) -
Dawson T. W.
Publication year - 1996
Publication title -
geophysical journal international
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.302
H-Index - 168
eISSN - 1365-246X
pISSN - 0956-540X
DOI - 10.1111/j.1365-246x.1996.tb07038.x
Subject(s) - dimensionless quantity , electrical conductor , conductor , polarization (electrochemistry) , mantle (geology) , geology , crust , geophysics , mathematical analysis , mechanics , physics , geometry , mathematics , chemistry , quantum mechanics
The mode‐matching method is used to obtain an exact analytical solution to the problem of B ‐polarization induction in two adjacent thin half‐sheets, lying on a conducting layer that is terminated by a perfect conductor at finite depth. These components of the model represent, respectively, the Earth's conducting surface layers, crust, and mantle. In dimensionless variables, the model has three independent parameters, these being the two thin‐sheet conductances and the layer thickness. The mode‐matching solution obtained in this paper is shown to be identical lo that derived via the Wiener‐Hopf method in a companion paper (Dawson 1996), and so provides additional verification of that solution. As was shown in the companion paper, the solution for the present model contains, as special limiting cases, those for three models considered earlier by various authors. The second part of the present paper addresses the solutions for the electric fields in the non‐conducting half‐space above the conductors, which represents the atmosphere. In the final part, sample numerical calculations are presented to illustrate the solution.