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In this article 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 the local north-oriented frame (LNOF). The derived formulas are free of singularities in case of r ≠ 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 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 accurately measured gravitational gradients separately as well as from their combination. Our regional gravitational 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 (2.9 mGal), is achieved for EGM2008 while using the third approach which combine all four well-measured gravitational gradients. This is explained by the fact that a-priori information about the Earth’s gravitational field up to the degree and order 180 was used. [ABSTRACT FROM AUTHOR]

Regional recovery of the disturbing gravitational potential in the area of Central Europe from satellite gravitational gradients data is discussed in this contribution. The disturbing gravitational potential is obtained by inverting surface integral formulas which transform the disturbing gravitational potential onto disturbing gravitational gradients in the spherical local north-oriented frame. Two numerical approaches that solve the inverse problem are considered. In the first approach, the integral formulas are rigorously decomposed into two parts, that is, the effects of the gradient data within near and distant zones. While the effect of the near zone data is sought as an inverse problem, the effect of the distant zone data is synthesized from the global gravitational model GGM05S using spectral weights given by truncation error coefficients up to the degree 150. In the second approach, a reference gravitational field up to the degree 180 is applied to reduce and smooth measured gravitational gradients. In both cases we recovered the disturbing gravitational potential from each of the four well-measured gravitational gradients of the GOCE satellite separately as well as from their combination. Obtained results are compared with the EGM2008, DIR-r2, TIM-r2 and SPW-r2 global gravitational models. The best fit was achieved for EGM2008 and the second approach combining all four well-measured gravitational gradients with rms of 1.231 m2 s-2. [ABSTRACT FROM AUTHOR]

Local gravity field modelling demands high-quality gravity data as well as an appropriate mathematical model. Particularly in coastal areas, there may be different types of gravity observations available, for instance, terrestrial, aerial, marine gravity, and satellite altimetry data. Thus, it is important to develop a proper tool to merge the different data types for local gravity field modelling and determination of the geoid. In this study, radial basis functions, as a commonly useful tool for gravity data integration, are employed to model the gravity potential field of the southern part of Iran using terrestrial gravity anomalies, gravity anomalies derived from re-tracked satellite altimetry, marine gravity anomalies, and gravity anomalies synthesized from an Earth gravity model. Reference GNSS/levelling (geometric) geoidal heights are used to evaluate the accuracy of the estimated local gravity field model. The gravimetric geoidal heights are in acceptable agreement with the geometric ones in terms of the standard deviation and the mean value which are 4.1 and 12 cm, respectively. Besides, the reference benchmark of the national first-order levelling network of Iran is located in the study area. The derived gravity model was used to compute the gravity potential difference at this point and then transformed into a height difference which results in the value of the shift of this benchmark with respect to the geoid. The estimated shift shows a good agreement with previously published studies. [ABSTRACT FROM AUTHOR]