Comment on ``Error Made in Reports of Main Field Decay''

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Forum, Geomagnetism And Paleomagnetism: Reference Fields (Regional, Global), Geomagnetism And Paleomagnetism: Spatial Variations (All Harmonics And Anomalies)

Scientific paper

As the International Association of Geomagnetism and Aeronomy (IAGA) Working Group on Geomagnetic Field Modeling (http://www.ngdc.noaa.gov/IAGA/vmod/), responsible for the International Geomagnetic Reference Field (IGRF), we would like to comment on the Forum article with the title ``Error made in reports of main field decay'' by Wallace H. Campbell (Eos, 85(16), 20 April 2004). Campbell claims that reports of dipole decay at a special session held at the AGU 2003 Fall Meeting were misleading due to an incorrect choice of the coordinate system for the spherical harmonic analysis (SHA) of the geomagnetic field used for the IGRF, the model on which the decay calculation was based. Campbell alleges that the dipole moment of a spherical harmonic expansion depends on the choice of the origin of the coordinate system. In his textbook on geomagnetism, Campbell goes one step further in asserting that, without changing the origin, the process of ``tilting the analysis axis to align with the geomagnetic axis... would enhance the dipole term at the expense of the higher multipoles''. Remembering that (because of the absence of magnetic monopoles) the magnetic dipole vector moment is physically invariant, and also some basic properties about orthogonal functions, many readers must have been puzzled by these statements. In fact, these statements are incorrect, as the dipole coefficients (G1,0, G1,1, and H1,1) are invariant under displacements of the origin and the dipole moment is independent of the orientation of the coordinate system.

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