Toroidal-Poloidal Decompositions of Electromagnetic Green’s Functions in Geomagnetic Induction
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.
KeywordsTransverse Electric Toroidal Field Poloidal Field Spherical Harmonic Degree Helmholtz Decomposition
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