An application of the Wiener-Hopf technique to the solution of H-polarization induction over a coastline
Date
1976
Authors
Nicoll, Martin Adrian
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Abstract
The Wiener-Hopf technique uses results from complex analysis to obtain analytic solutions to differential equations with mixed boundary conditions. This type of problem arises frequently in geomagnetic induction models.
In this thesis the technique is applied to two models with magnetic polarized fields over an ocean edge. The earth's properties were assumed to be constant in the direction parallel to the coastline resulting in a two dimensional mathematical problem. In both models the crust was assumed to have a small conductivity to allow current flow. The difference between the models is that the first assumes the depth to the mantle is infinite while the second has a mantle of infinite conductivity at a finite depth.
The solution of the second model demonstrates the existence of current loops flowing from the sea through the crust and returning via the mantle.