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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]

We investigate a numerical performance of four different schemes applied to a regional recovery of the gravity anomalies from the third-order gravitational tensor components (assumed to be observable in the future) synthetized at the satellite altitude of 200 km above the mean sphere. The first approach is based on applying a regional inversion without modelling the far-zone contribution or long-wavelength support. In the second approach we separate integral formulas into two parts, that is, the effects of the third-order disturbing tensor data within near and far zones. Whereas the far-zone contribution is evaluated by using existing global geopotential model (GGM) with spectral weights given by truncation error coefficients, the near-zone contribution is solved by applying a regional inversion. We then extend this approach for a smoothing procedure, in which we remove the gravitational contributions of the topographic-isostatic and atmospheric masses. Finally, we apply the remove-compute-restore (r-c-r) scheme in order to reduce the far-zone contribution by subtracting the reference (long-wavelength) gravity field, which is computed for maximum degree 80. We apply these four numerical schemes to a regional recovery of the gravity anomalies from individual components of the third-order gravitational tensor as well as from their combinations, while applying two different levels of a white noise. We validated our results with respect to gravity anomalies evaluated at the mean sphere from EGM2008 up to the degree 250. Not surprisingly, better fit in terms of standard deviation (STD) was attained using lower level of noise. The worst results were gained applying classical approach, STD values of our solution from Tzzz are 1.705 mGal (noise value with a standard deviation 0.01 x 10 -15m-1s-2) and 2.005 mGal (noise value with a standard deviation 0.05 x 10-15m-1s-2), while the superior from r-c-r up to the degree 80, STD fit of gravity anomalies from Tzzz with respect to the same counterpart from EGM2008 is 0.510 mGal (noise value with a standard deviation 0.01 x 10-15m-1s-2) and 1.190 mGal (noise value with a standard deviation 0.05 x 10-15m-1s-2). [ABSTRACT FROM AUTHOR]

In context of the vertical datum unification, the geoid-to-quasi-geoid separation has been of significant interest in recent years, because most of existing local vertical datums are realized in the system of either normal or orthometric heights. Nevertheless, the normal-orthometric heights are still used in many other countries where the normal gravity values along leveling lines were adopted instead of the observed gravity. Whereas the conversion between the orthometric and normal heights is defined by means of the mean gravity disturbances (i.e. differences between the mean values of the actual and normal gravity) along the plumbline within the topography, differences between the normal and normal-orthometric heights can be described by means of the surface gravity disturbances. Since the normal gravity field does not reflect the topographic masses and actual mass density distribution inside the Earth, the definition of gravity represents a principal aspect for a realization of particular vertical datum. To address this issue in this study, we investigate effects of the Earth's inner density structure on the surface and mean gravity disturbances, and discuss their impact on the vertical datum realization. These two gravity field quantities are computed globally with a spectral resolution complete to a spherical harmonic degree 2160 using the global gravity, terrain, ice-thickness, inland bathymetry and crustal structure models. Our results reveal that both, the surface and mean gravity disturbances mostly comprise the gravitational signal of topography and masses distributed below the geoid surface. Moreover, in polar areas, a significant contribution comes from large glaciers. In contrast, the contributions of anomalous density distribution within the topography attributed to major lakes, sediments and bedrock density variations are much less pronounced. We also demonstrate that the mean gravity disturbances within the topography are significantly modified compared to the corresponding surface values mainly due to topographic elevation and terrain geometry as well as the presence of large glaciers in polar regions. Changes of the vertical gravity gradient within the topography attributed to the masses distributed below the geoid (dominated mainly by the isostatic signature and the long-wavelength gravitational signature of deep mantle density heterogeneities) are, on the other hand, relatively small. Despite differences between the normal and normal-orthometric heights could directly be assessed from the surface gravity disturbances only when taken along leveling lines with information about the spirit leveling height differences, our results indicate that differences between these two height systems can be significant. [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]