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pure and applied geophysics

, Volume 131, Issue 3, pp 357–370 | Cite as

Least squares and integral methods for the spherical harmonic analysis of theSq-field

  • Koji Kawasaki
  • S. Matsushita
  • J. C. Cain
Article

Abstract

Spherical harmonic coefficients (SHCs) for the daily magnetic variation fields (solar and lunar) and the main field of the earth are usually estimated by the method of least squares applied to a truncated spherical harmonic series. In this paper, an integral method for computing the SHCs for the solar quiet daily magnetic variation fieldSq is described and applied toSq data for May and June 1965. TheSq SHCs thus derived are then compared with the results obtained using both unweighted and weighted versions of the least squares method. The weighting used tends to orthogonalize the least squares terms. The integral and weighted least squares results agree closely for terms up to order 4 and degree 30, but both disagree considerably for the higher degree terms with the results of the unweighted least squares. Errors introduced by the numerical integration can be shown to be small, hence the disagreement between integral and unweighted least squares coefficient sets arises from improper weighting. Also, it is concluded that discrepancies between the geomagnetic northward and eastward component-derived coefficient sets arise from either time-dependent external sources that produce non-local-time, based fields or nonpotential sources and not from truncation of the spherical harmonic series as has previously been suggested.

Key words

Spherical harmonic analysis Sq 

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Copyright information

© Birkhäuser Verlag 1989

Authors and Affiliations

  • Koji Kawasaki
    • 1
  • S. Matsushita
    • 2
  • J. C. Cain
    • 3
  1. 1.Geophysical InstituteUniversity of AlaskaFairbanksUSA
  2. 2.High Altitude ObservatoryNational Center for Atmospheric ResearchBoulderUSA
  3. 3.Department of GeologyFlorida State UniversityTallahasseeUSA

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