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1992•Geophysical Research LettersRequires access

Conventional spherical harmonic analysis for regional modelling of the geomagnetic field

Angelo De Santis

Open publisher page 48 citations

Abstract

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.

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What this paper is about

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.

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Available abstract

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.

Key concepts: Spherical harmonics, Zonal spherical harmonics, Spin-weighted spherical harmonics, Spherical cap, Earth's magnetic field, Harmonic analysis, Computation, Harmonic

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