Abstract
Spatially Restricted Integrals in Gradiometric Boundary Value ProblemsThe 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.
Highlights
A boundary value problem (BVP) is a way of formulating the mathematical problems
The gradiometric BVPs are the special cases of BVPs in which the second-order partial derivatives of the desired function are given on the boundary
The solutions of the gradiometric BVPs are presented by three integral formulas as well
Summary
A boundary value problem (BVP) is a way of formulating the mathematical problems. In BVP a partial differential equation is constructed and solved based on existing values of the desired function on a specific surface, which are called boundary values. In the gradiometric BVP three combinations for the partial secondorder derivatives of geopotential are constructed so that tensor spherical harmonics (SHs) can be used to make some integral formulas for recovering the gravity field; see for instance Rummel (1997), van Gelderen and Rummel (2001) and (2002) and Martinec (2003). Pail et al (2001) used some numerical techniques to orthonormalize the base functions or SHs having a global orthogonality support for local gravity field determination. Another idea which is of interest today is the Slepian method (Slepian 1983). This paper will simplify these SRIs in terms of integral of ALFs and combinations of the Gaunt coefficients
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
