Regional determination of gravity disturbances by inverting satellite gravitational gradients
21/09/2016 | 15:15 | Session 3: Regional and Local Geoid Modelling
Author(s): Martin Pitoňák, Michal Šprlák, Robert Tenzer and Pavel Novák
Martin Pitoňák, Michal Šprlák, Robert Tenzer and Pavel Novák
Several methods exist for reducing the distant-zone effect of the Earth's gravitational field. In this article we apply three of them for solving an inverse problem. We discuss a regional recovery of gravity disturbances at the mean geocentric sphere approximating the Earth over the area of Central Europe from satellite gravitational gradients. For this purpose, we derive integral formulas which allow converting the gravity disturbances onto the disturbing gravitational gradients in local north-oriented frame (LNOF). The derived formulas are free of singularities in case of r is not equal to R. We then investigate three numerical approaches for solving their inverses. In the initial approach, the integral formulas are firstly modified for solving individually the near- and distant-zone contributions. While the effect of the near-zone gravitational gradients is solved as an inverse problem, the effect of the distant-zone gravitational gradients is computed by numerical integration from a global equiangular grid synthesized from the global gravitational model (GGM) TIM-r4. In the second approach, we further elaborate the first scenario by reducing measured gravitational gradients for gravitational effects of topographic masses. In the third approach, we apply additional modification by reducing gravitational gradients for the reference GGM. In all approaches we determine the gravity disturbances from each of the four well-measured gravitational gradients separately as well as from their combination. Our regional gravity field solutions are based on the GOCE EGG TRF 2 gravitational gradients collected within the period from November 1 2009 until January 11 2010. Obtained results are compared with EGM2008, DIR-r1, TIM-r1 and SPW-r1. The best fit, in terms of RMS (2.287 mGal), is achieved for EGM2008 while using a third approach which combine all four well-measured gravitational gradients. This is explained by the fact that a-priori information about Earth's gravitational field up to degree and order 180 was used.