Open AccessComputation of the Solution of Geomagnetic Induction Problems: a General Method, with Applications
Author(s) -
Hutson V. C. L.,
Kendall P. C.,
Malin S. R. C.
Publication year - 1972
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.1972.tb06144.x
Subject(s) - computation , electromagnetic induction , convergence (economics) , iterative method , mathematics , context (archaeology) , symmetry (geometry) , mathematical analysis , surface (topology) , computer science , mathematical optimization , physics , algorithm , geometry , electromagnetic coil , geology , paleontology , quantum mechanics , economics , economic growth
Summary A general method of computing the solution of a wide class of geomagnetic induction problems is given. The method is based on an integral equation for the electric current J induced in a surface conductor by a time‐varying imposed electromagnetic field. The standard iterative solution of this equation is not convergent for large frequencies. However, an alternative iterative scheme, believed to be new in the context of geomagnetism, is suggested by an analogy from functional analysis, and this formulation allows a rigorous argument for its convergence to be developed. In the special case of axial symmetry the iterative method is shown to lead to a continuous solution for all finite frequencies and conductivities. This appears to clarify a problem which has been much discussed in the literature. Trial calculations are also presented for the case of axial symmetry. In the general case, physical reasoning indicates that the method can be expected to converge. The axisymmetric computations are made in a way which simulate the eventual computation of general problems, showing that the method is feasible. The method also applies to problems in three dimensions and to more general surfaces and surface geometries.