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Until recently, the information about the topographic density distribution has been limited to only certain regions and some countries, while missing in the global context. The UNB_TopoDens is the first model that provides the information about a lateral topographic density globally. The analysis of this model also reveals that the average topographic density for the entire continental landmass (excluding polar glaciers) is 2247 kg m−3. This density differs significantly from the value of 2670 kg m−3 that is typically adopted to represent the continental upper crustal density. In this study, we use the UNB_TopoDens density model to inspect how the topographic density variations affect interpretational properties of Bouguer gravity maps. Since this model provides also the information about density uncertainties of individual lithologies (main rock types), we estimate the corresponding errors in the Bouguer gravity data. Despite a new estimate of the average topographic density corresponds to relative changes of ∼16 per cent in values of the topographic gravity correction, these changes do not affect interpretational properties of Bouguer gravity maps. The anomalous topographic density distribution (taken with respect to the average density of 2247 kg m−3), however, modifies the Bouguer gravity pattern. We demonstrate that the gravitational contribution of anomalous topographic density is globally mostly within ±25 mGal, but much large values are detected in Himalaya, Tibet, central Andes and along the East African Rift System. Our estimates also indicate that errors in the Bouguer gravity data attributed to topographic density uncertainties are mostly less than ±15 mGal, but in mountainous regions could reach large values exceeding even ±50 mGal. Unarguably, the UNB_TopoDens model provides an improved information about the global topographic density variations and their uncertainties. Nevertheless, much more in situ measurements of rock density samples together with detailed 3-D geological models are still necessary to understand better the actual density distribution within the whole topography, particularly to mention a density change with depth. [ABSTRACT FROM AUTHOR]

Four solutions of the spherical gravitational curvature boundary-value problems can be exploited for the determination of the Earth's gravitational potential. In this paper we discuss the combination of simulated satellite gravitational curvatures, that is, components of the third-order gravitational tensor, by merging these solutions using the spectral combination method. For this purpose, integral estimators of biased- and unbiased-types are derived. In numerical studies, we investigate the performance of the developed mathematical models for the gravitational field modelling in the area of Central Europe based on simulated satellite measurements. First, we verify the correctness of the integral estimators for the spectral downward continuation by a closed-loop test. Estimated errors of the combined solution are about eight orders smaller than those from the individual solutions. Second, we perform a numerical experiment by considering the Gaussian noise with the standard deviation of 6.5 × 10−17 m−1 s−2 in the input data at the satellite altitude of 250 km above the mean Earth sphere. This value of standard deviation is equivalent to a signal-to-noise ratio of 10. Superior results with respect to the global geopotential model TIM-r5 (Brockmann et al. 2014) are obtained by the spectral downward continuation of the vertical–vertical–vertical component with the standard deviation of 2.104 m2 s−2, but the root mean square error is the largest and reaches 9.734 m2 s−2. Using the spectral combination of all gravitational curvatures the root mean square error is more than 400 times smaller but the standard deviation reaches 17.234 m2 s−2. The combination of more components decreases the root mean square error of the corresponding solutions while the standard deviations of the combined solutions do not improve as compared to the solution from the vertical–vertical–vertical component. The presented method represents a weight mean in the spectral domain that minimizes the root mean square error of the combined solutions and improves standard deviation of the solution based only on the least accurate components. [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]