Spherical integral formulas for upward/downward continuation of gravitational gradients onto gravitational gradients
Abstract
New integral formulas for upward/downward continuation of gravitational gradients onto gravitational gradients are derived in this article. They provide more options for continuation of gravitational gradient combinations and extend available mathematical apparatus formulated for this purpose up to now. The starting point represents the analytical solution of the spherical gradiometric boundary value problem in the spatial domain. Applying corresponding differential operators on the analytical solution of the spherical gradiometric boundary value problem, a total of 18 integral formulas are provided. Spatial and spectral forms of isotropic kernels are given and their behaviour for parameters of a GOCElike satellite is investigated. Correctness of the new integral formulas and the isotropic kernels is tested in a closedloop simulation. The derived integral formulas and the isotropic kernels form a theoretical basis for validation purposes and geophysical applications of satellite gradiometric data as provided currently by the GOCE mission. They also extend the wellknown Meissl scheme.
 Publication:

Journal of Geodesy
 Pub Date:
 February 2014
 DOI:
 10.1007/s0019001306766
 Bibcode:
 2014JGeod..88..179S
 Keywords:

 GOCE;
 Gravitational gradient;
 Integral equation;
 Meissl scheme;
 Satellite gradiometry