B-polarization induction in two thin half-sheets coupled to the mantle by a conducting crust-I. Solution by the Wiener-Hopf technique, with limiting forms

Abstract

S U M M A R YThe Wiener-Hopf technique 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, which is terminated at finite depth by a perfect conductor. The model may be viewed as an idealized local approximation to the Earth, with the half-sheets representing conducting layers (including the oceans) at the surface of the Earth, the conducting layer representing the crust, and the perfect conductor approximating the mantle. The solution may be used to study the behaviour of currents and electromagnetic fields induced in the Earth by ionospheric sheet-current sources flowing perpendicular to the thin-sheet junction. The solution allows for analytical investigation of the behavior of the field components near the thin-sheet junction. It also leads to some additional insight into the adjustment distance question.The model is a generalization of ones considered in three earlier publications by various authors. It is demonstrated that the field solutions for the present model contain those for the three earlier models as limiting cases, when one or more of the thin-sheet integrated conductivities become zero or infinite, or when the mantle depth becomes infinite. Also under appropriate limits, the model may also be viewed as a generalized thin sheet lying on a perfect conductor.

B-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

“…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 to 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.…”

“…In a companion paper (Dawson 1996) (hereafter referred to as Part I), the Wiener-Hopf technique was employed to obtain the analytical B-polarization induction solution for a thinsheet model consisting of two adjacent thin half-sheets of differing finite integrated conductivity, on a uniformly conducting layer, with a perfect conductor at finite depth. This solution includes both the NW and DW models as limiting cases.…”

Modelling of electromagnetic fields in thin heterogeneous layers with application to field generation by volcanoes-theory and example

“…A number of 2‐D algorithms produce consistent results. What is also important is that the 2‐D algorithms can be tested using analytical solutions found by Weidelt (1971) for E ‐polarization, and by Dawson et al (1982) and Dawson (1996) for B ‐polarization. The 2‐D code used in our test was developed by Poll (1994) and based on the scheme by Brewitt‐Taylor & Weaver (1976) and Weaver & Brewitt‐Taylor (1978).…”

“…(71) is that the 2-D algorithms can be tested using analytical solutions found by Weidelt (1971) for E-polarization, and by Owing to the limited values of M x and M y , this function Dawson et al (1982) and Dawson (1996) for B-polarization. is a rather poor approximation to the distribution of the The 2-D code used in our test was developed by Poll (1994) anomalous currents inside area s. On the other hand, it and based on the scheme by Brewitt-Taylor & Weaver (1976) provides a good estimate of the anomalous currents outside and Weaver & Brewitt-Taylor (1978).…”