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Conventional spherical harmonic analysis for regional modelling of the geomagnetic field
Author(s) -
De Santis Angelo
Publication year - 1992
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1029/92gl01068
Subject(s) - spherical harmonics , zonal spherical harmonics , spin weighted spherical harmonics , spherical cap , earth's magnetic field , harmonic analysis , computation , harmonic , harmonics , legendre polynomials , solid harmonics , mathematics , mathematical analysis , vector spherical harmonics , physics , magnetic field , geometry , algorithm , acoustics , quantum mechanics , voltage
Spherical Harmonic Analysis (SHA) is normally used to model the three‐dimensional global geomagnetic field. To address the same problem in regional modelling, Haines (1985) proposed Spherical Cap Harmonic Analysis (SCHA). This regional technique involves the computation of more complex Legendre functions with real (generally non‐integer) harmonic degree. Here a new more practical technique is described; it is called Adjusted Spherical Harmonic Analysis (ASHA) because it is based on the expansion of conventional spherical harmonics after the colatitude interval is adjusted to that of a hemisphere. This kind of analysis can also be applied to modelling general two‐dimensional functions.