Authors: Oliver Baur Nico Sneeuw Erik W Grafarend
Publish Date: 2007/08/04
Volume: 82, Issue: 4-5, Pages: 279-293
Abstract
Although its use is widespread in several other scientific disciplines the theory of tensor invariants is only marginally adopted in gravity field modeling We aim to close this gap by developing and applying the invariants approach for geopotential recovery Gravitational tensor invariants are deduced from products of secondorder derivatives of the gravitational potential The benefit of the method presented arises from its independence of the gradiometer instrument’s orientation in space Thus we refrain from the classical methods for satellite gravity gradiometry analysis ie in terms of individual gravity gradients in favor of the alternative invariants approach The invariants approach requires a tailored processing strategy Firstly the nonlinear functionals with regard to the potential series expansion in spherical harmonics necessitates the linearization and iterative solution of the resulting leastsquares problem From the computational point of view efficient linearization by means of perturbation theory has been adopted It only requires the computation of reference gravity gradients Secondly the deduced pseudoobservations are composed of all the gravitational tensor elements all of which require a comparable level of accuracy Additionally implementation of the invariants method for large data sets is a challenging task We show the fundamentals of tensor invariants theory adapted to satellite gradiometry With regard to the GOCE Gravity field and steadystate Ocean Circulation Explorer satellite gradiometry mission we demonstrate that the iterative parameter estimation process converges within only two iterations Additionally for the GOCE configuration we show the invariants approach to be insensitive to the synthesis of unobserved gravity gradients
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