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Toroidal-Poloidal Decompositions of Electromagnetic Green’s Functions in Geomagnetic Induction

In: Handbook of Geomathematics

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  • Jin Sun

    (ETH Zürich, Institute of Geophysics)

Abstract

In this chapter, we make use of electromagnetic Green’s functions to analyze quasi-static electromagnetic fields outside and inside the domain of external current sources. Scalar potential representation of the magnetic field in a source-free domain is readily derived from the physical currents using Green’s functions. It may be shown that, although the electric field generated by external sources has a poloidal mode component, this component causes no induction inside a conductive ground and vanishes at the surface of a conductive ground in the transverse directions. An effective external current source represented as a toroidal source is thus justified for low-frequency natural source induction such as natural source magnetotellurics and geomagnetic global inductions.

Suggested Citation

  • Jin Sun, 2015. "Toroidal-Poloidal Decompositions of Electromagnetic Green’s Functions in Geomagnetic Induction," Springer Books, in: Willi Freeden & M. Zuhair Nashed & Thomas Sonar (ed.), Handbook of Geomathematics, edition 2, pages 921-938, Springer.
    • Handle: RePEc:spr:sprchp:978-3-642-54551-1_66
    DOI: 10.1007/978-3-642-54551-1_66
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