<abstract xml:lang="en" xmlns="http://www.w3.org/1999/xhtml"><p>The spherical Slepian functions can be used to localize the solutions of the gradiometric boundary value problems on a sphere. These functions involve spatially restricted integral products of scalar, vector and tensor spherical harmonics. This paper formulates these integrals in terms of combinations of the Gaunt coefficients and integrals of associated Legendre functions. The presented formulas for these integrals are useful in recovering the Earth's gravity field locally from the satellite gravity gradiometry data.</p></abstract>

The spherical Slepian functions can be used to localize the solutions of the gradiometric boundary value problems on a sphere. These functions involve spatially restricted integral products of scalar, vector and tensor spherical harmonics. This paper formulates these integrals in terms of combinations of the Gaunt coefficients and integrals of associated Legendre functions. The presented formulas for these integrals are useful in recovering the Earth's gravity field locally from the satellite gravity gradiometry data.

Spatially Restricted Integrals in Gradiometric Boundary Value Problems

Division of Geodesy, Royal Institute of Technology (KTH), Stockholm, Sweden

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{"article-title":"Spatially Restricted Integrals in Gradiometric Boundary Value Problems"}

The spherical Slepian functions can be used to localize the solutions of the gradiometric boundary value problems on a sphere. These functions involve...

Spatially Restricted Integrals in Gradiometric Boundary Value Problems

Published Online: Apr 26, 2010

Page range: 131 - 148

DOI: https://doi.org/10.2478/v10018-009-0025-4

Keywords
Clebsch-Gordan's coefficients, Gaunt's coefficients, harmonic analysis, associated Legendre's function, satellite gravity gradiometry, Slepian's function

This content is open access.

Spatially Restricted Integrals in Gradiometric Boundary Value Problems

Published Online: Apr 26, 2010

Page range: 131 - 148

DOI: https://doi.org/10.2478/v10018-009-0025-4

KeywordsClebsch-Gordan's coefficients, Gaunt's coefficients, harmonic analysis, associated Legendre's function, satellite gravity gradiometry, Slepian's function

This content is open access.

Keywords
Clebsch-Gordan's coefficients, Gaunt's coefficients, harmonic analysis, associated Legendre's function, satellite gravity gradiometry, Slepian's function