Spherical harmonic modeling of the geomagnetic field using the fast Fourier transform

Details Spherical harmonic modeling of the geomagnetic field using the fast Fourier transform Spherical harmonic modeling of the geomagnetic field using the fast Fourier transform

Oct 1987

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1987pepi...48..206q&link_type=abstract

Physics of the Earth and Planetary Interiors, Volume 48, Issue 3-4, p. 206-220.

Physics

2

Scientific paper

The Dilts method for computing spherical harmonic expansion coefficients of a surface function ƒ;(θ, ϕ) is adapted to the inverse and forward problems of geomagnetic main-field modeling. This method, which takes full advantage of the intrinsic speed of the fast Fourier transform (FFT), can compute the coefficients of a typical degree and order 12 model in just a few seconds on most main-frame computers and therefore seems optimally suited to perform high-degree and order modeling of the Earth's crustal magnetic anomalies. Execution of the method requires the construction of an equiangular grid of geomagnetic data over the entire surface of a sphere. This is a weak point of the method since a subset of data observations must be judiciously selected from the available data to form a very thin shell that encloses the spherical surface. The data in this shell must then be very carefully averaged and interpolated to form the necessary grid. The Gauss coefficients are quite sensitive to errors in this gridding process. Satellite observations appear to be the most appropriate data source for spherical harmonic FFT modeling due to the uniform quality and global coverage that such data provide.

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