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Konstantinos Patlakis - One of the best experts on this subject based on the ideXlab platform.
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Spectral assessment of isostatic Gravity models against CHAMP, GRACE, GOCE satellite-only and combined Gravity models
Acta Geophysica, 2014Co-Authors: Dimitrios Tsoulis, Konstantinos PatlakisAbstract:The availability of digital elevation databases representing the topographic and bathymetric relief with global homogeneous coverage and increasing resolution permits the computation of crust-related Earth Gravity models, the so-called topographic/isostatic Earth Gravity models (henceforth T/I models). Although expressing the spherical harmonic content of the topographic masses, the interpretation purpose of T/I models has not been given the attention it deserves, apart from the fact that they express some degree of compensation to the observed spectrum of the topographic heights, depending on the kind of the applied compensation mechanism. The present contribution attempts to improve the interpretation aspects of T/I Earth Gravity models. To this end, a rigorous spectral assessment is performed to a standard Airy/Heiskanen T/I model against different CHAllenging Minisatellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), Gravity field and steadystate Ocean Circulation Explorer (GOCE) satellite-only, and combined Gravity models. Different correlation bandwidths emerge for these four groups of satellite-based Gravity models. The band-limited forward computation of the models using these bandwidths reproduces nicely the main features of the applied T/I model.
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A spectral assessment review of current satellite‐only and combined Earth Gravity models
Reviews of Geophysics, 2013Co-Authors: Dimitrios Tsoulis, Konstantinos PatlakisAbstract:[1] The realization over the last decade of dedicated Gravity field satellite missions enabled the production of a series of new satellite-only and combined models for the Earth's Gravity field. Using different sensors, measurement techniques, and algorithmic procedures, the final product in each case is a set of spherical harmonic coefficients representing the series expansion of the gravitational potential up to a certain maximum degree, depending on the mission characteristics and the range of the available data. The present review performs a detailed quantified analysis of a representative selection of currently available CHAMP (Challenging Minisatellite Payload), GRACE (Gravity Recovery and Climate Experiment), GOCE (Gravity Field and Steady-State Ocean Circulation Explorer), and combined Earth Gravity models. In this comparative analysis, we also include the so-called topographic/isostatic Gravity models that represent the contribution of global digital elevation maps for the topography and ocean bathymetry. Applying a range of available spatial and spectral accuracy and assessment measures, such as correlation per degree and order, smoothing per degree and order, signal-to-noise ratio, gain, degree variances, and error degree variances, one gains a quantified “peek” inside the quality of these models spanning over their whole spectrum. The applied error and assessment measures are defined both in an absolute and relative manner with respect to other similar models or some reference Earth Gravity models. Furthermore, the nature of the performed analysis (degree-wise, order-wise, and cumulative) permits the identification of distinct spectral bandwidths in these models, enables the quantification of some standard features of the observed field, such as its “long wavelength”, “short wavelength”, or “very high frequency part”, and specifies the attenuation of the Gravity signal with increasing altitude from the Earth's surface. An examination of the assessment quantities reveals certain bandwidths of these models with characteristic statistical features. A band-limited synthesis of these bandwidths in the space domain quantifies the corresponding contributions in terms of selected Gravity field functionals, including second-order derivatives at GOCE altitude.
Dimitrios Tsoulis - One of the best experts on this subject based on the ideXlab platform.
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Spectral assessment of isostatic Gravity models against CHAMP, GRACE, GOCE satellite-only and combined Gravity models
Acta Geophysica, 2014Co-Authors: Dimitrios Tsoulis, Konstantinos PatlakisAbstract:The availability of digital elevation databases representing the topographic and bathymetric relief with global homogeneous coverage and increasing resolution permits the computation of crust-related Earth Gravity models, the so-called topographic/isostatic Earth Gravity models (henceforth T/I models). Although expressing the spherical harmonic content of the topographic masses, the interpretation purpose of T/I models has not been given the attention it deserves, apart from the fact that they express some degree of compensation to the observed spectrum of the topographic heights, depending on the kind of the applied compensation mechanism. The present contribution attempts to improve the interpretation aspects of T/I Earth Gravity models. To this end, a rigorous spectral assessment is performed to a standard Airy/Heiskanen T/I model against different CHAllenging Minisatellite Payload (CHAMP), Gravity Recovery and Climate Experiment (GRACE), Gravity field and steadystate Ocean Circulation Explorer (GOCE) satellite-only, and combined Gravity models. Different correlation bandwidths emerge for these four groups of satellite-based Gravity models. The band-limited forward computation of the models using these bandwidths reproduces nicely the main features of the applied T/I model.
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Degree-wise validation of satellite-only and combined Earth Gravity models in the frame of an orbit propagation scheme applied to a short GOCE arc
Acta Geodaetica et Geophysica, 2013Co-Authors: Dimitrios Tsoulis, Thomas PapanikolaouAbstract:The procedure of satellite orbit analysis apart from its significance in orbit dynamics can be also used as an independent assessment tool for the available Earth Gravity models. The contribution of these models, which represent the main gravitational component in dynamic orbit computations, can be performed in a degree-wise cumulative sense, thus quantifying the band-limited performance of the individual models at satellite altitude. In order to demonstrate such a procedure, which can be applied as a closed assessment tool for any Low Earth Orbiter (LEO), we apply it in the frame of orbit propagation of the GOCE (Gravity Field and Steady-State Ocean Circulation) satellite. Differences of the obtained GOCE orbits are compared with the corresponding Rapid Science Orbit (RSO) data. For the contribution of the dynamic component we used the Gravity models EGM2008, EIGEN-5C, GGM03S, ITG-Grace2010s and AIUB-CHAMP03S. The actual calculation of the orbit is based on the numerical integration of the equation of motion according to an 8th order Gauss-Jackson multi-step method using the predictor-corrector algorithm. The proposed scheme leads to a validation of the different Gravity models, providing an insight to the effect of the gravitational counterpart to the geometry of the orbit by referring explicitly all computations to the three components of the orbital frame.
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A spectral assessment review of current satellite‐only and combined Earth Gravity models
Reviews of Geophysics, 2013Co-Authors: Dimitrios Tsoulis, Konstantinos PatlakisAbstract:[1] The realization over the last decade of dedicated Gravity field satellite missions enabled the production of a series of new satellite-only and combined models for the Earth's Gravity field. Using different sensors, measurement techniques, and algorithmic procedures, the final product in each case is a set of spherical harmonic coefficients representing the series expansion of the gravitational potential up to a certain maximum degree, depending on the mission characteristics and the range of the available data. The present review performs a detailed quantified analysis of a representative selection of currently available CHAMP (Challenging Minisatellite Payload), GRACE (Gravity Recovery and Climate Experiment), GOCE (Gravity Field and Steady-State Ocean Circulation Explorer), and combined Earth Gravity models. In this comparative analysis, we also include the so-called topographic/isostatic Gravity models that represent the contribution of global digital elevation maps for the topography and ocean bathymetry. Applying a range of available spatial and spectral accuracy and assessment measures, such as correlation per degree and order, smoothing per degree and order, signal-to-noise ratio, gain, degree variances, and error degree variances, one gains a quantified “peek” inside the quality of these models spanning over their whole spectrum. The applied error and assessment measures are defined both in an absolute and relative manner with respect to other similar models or some reference Earth Gravity models. Furthermore, the nature of the performed analysis (degree-wise, order-wise, and cumulative) permits the identification of distinct spectral bandwidths in these models, enables the quantification of some standard features of the observed field, such as its “long wavelength”, “short wavelength”, or “very high frequency part”, and specifies the attenuation of the Gravity signal with increasing altitude from the Earth's surface. An examination of the assessment quantities reveals certain bandwidths of these models with characteristic statistical features. A band-limited synthesis of these bandwidths in the space domain quantifies the corresponding contributions in terms of selected Gravity field functionals, including second-order derivatives at GOCE altitude.
Lars E Sjoberg - One of the best experts on this subject based on the ideXlab platform.
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A synthetic Earth Gravity model based on a topographic-isostatic model
Studia Geophysica et Geodaetica, 2012Co-Authors: Mohammad Bagherbandi, Lars E SjobergAbstract:The Earth’s Gravity field is related to the topographic potential in medium and higher degrees, which is isostatically compensated. Hence, the topographic-isostatic (TI) data are indispensable for extending an available Earth Gravitational Model (EGM) to higher degrees. Here we use TI harmonic coefficients to construct a Synthetic Earth Gravitational Model (SEGM) to extend the EGMs to higher degrees. To achieve a high-quality SEGM, a global geopotential model (EGM96) is used to describe the low degrees, whereas the medium and high degrees are obtained from the TI or topographic potential. This study differes from others in that it uses a new gravimetric-isostatic model for determining the TI potential. We test different alternatives based on TI or only topographic data to determine the SEGM. Although the topography is isostatically compensated only to about degree 40–60, our study shows that using a compensation model improves the SEGM in comparison with using only topographic data for higher degree harmonics. This is because the TI data better adjust the applied Butterworth filter, which bridges the known EGM and the new high-degree potential field than the topographic data alone.
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least squares modification of stokes formula vs remove compute restore technique
The EGU General Assembly, 2009Co-Authors: Lars E Sjoberg, Ramin Kiamehr, Jonas AgrenAbstract:Today's applications of Stokes' formula combine the classical formula with an Earth Gravity model (EGM). In the remove-compute-restore technique this is performed by removing the EGM from the gravi ...
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Further studies on the Fennoscandian Gravity field versus the Moho depth and land uplift
Journal of Geodesy, 1994Co-Authors: Lars E Sjoberg, Tomas NordAbstract:Whether post-glacial rebound or/and crustal variation contributes to the pattern of the Fennoscandian Gravity field has been of great interest to geoscientists. Previous numerical studies are based on different Moho maps, different global Earth Gravity models and different isostatic models of Pratt type, resulting in quite different conclusions.
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Further studies on the Fennoscandian Gravity field versus the Moho depth and land uplift
Bulletin géodésique, 1994Co-Authors: Lars E Sjoberg, Tomas NordAbstract:Whether post-glacial rebound or/and crustal variation contributes to the pattern of the Fennoscandian Gravity field has been of great interest to geoscientists. Previous numerical studies are based on different Moho maps, different global Earth Gravity models and different isostatic models of Pratt type, resulting in quite different conclusions. In this study, we use the improved Moho depth map of Korja et al. (1993), the OSU91A Earth Gravity model and a refined modeling of the Moho depth contribution. We conclude that not more than about 40% and 30% of the Fennoscandian geoid and Gravity depressions of the orders of -12m and -40 mGal might be caused by crustal thickening, leaving at least -6 m and -28 mGal to be adjusted in accordance with post-glacial rebound.
P. Vaníček - One of the best experts on this subject based on the ideXlab platform.
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A synthetic Earth Gravity Model Designed Specifically for Testing Regional Gravimetric Geoid Determination Algorithms
Journal of Geodesy, 2006Co-Authors: I. Baran, M. Kuhn, S. J. Claessens, W. E. Featherstone, S. A. Holmes, P. VaníčekAbstract:A synthetic [simulated] Earth Gravity model (SEGM) of the geoid, Gravity and topography has been constructed over Australia specifically for validating regional gravimetric geoid determination theories, techniques and computer software. This regional high-resolution (1-arc-min by 1-arc-min) Australian SEGM (AusSEGM) is a combined source and effect model. The long-wavelength effect part (up to and including spherical harmonic degree and order 360) is taken from an assumed errorless EGM96 global geopotential model. Using forward modelling via numerical Newtonian integration, the short-wavelength source part is computed from a high-resolution (3-arc-sec by 3-arc-sec) synthetic digital elevation model (SDEM), which is a fractal surface based on the GLOBE v1 DEM. All topographic masses are modelled with a constant mass-density of 2,670 kg/m^3. Based on these input data, Gravity values on the synthetic topography (on a grid and at arbitrarily distributed discrete points) and consistent geoidal heights at regular 1-arc-min geographical grid nodes have been computed. The precision of the synthetic Gravity and geoid data (after a first iteration) is estimated to be better than 30 μ Gal and 3 mm, respectively, which reduces to 1 μ Gal and 1 mm after a second iteration. The second iteration accounts for the changes in the geoid due to the superposed synthetic topographic mass distribution. The first iteration of AusSEGM is compared with Australian Gravity and GPS-levelling data to verify that it gives a realistic representation of the Earth’s Gravity field. As a by-product of this comparison, AusSEGM gives further evidence of the north–south-trending error in the Australian Height Datum. The freely available AusSEGM-derived Gravity and SDEM data, included as Electronic Supplementary Material (ESM) with this paper, can be used to compute a geoid model that, if correct, will agree to in 3 mm with the AusSEGM geoidal heights, thus offering independent verification of theories and numerical techniques used for regional geoid modelling.
H. Nahavandchi - One of the best experts on this subject based on the ideXlab platform.
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two different methods of geoidal height determinations using a spherical harmonic representation of the geopotential topographic corrections and the height anomaly geoidal height difference
Journal of Geodesy, 2002Co-Authors: H. NahavandchiAbstract:It is suggested that a spherical harmonic representation of the geoidal heights using global Earth Gravity models (EGM) might be accurate enough for many applications, although we know that some short-wavelength signals are missing in a potential coefficient model. A `direct' method of geoidal height determination from a global Earth Gravity model coefficient alone and an `indirect' approach of geoidal height determination through height anomaly computed from a global Gravity model are investigated. In both methods, suitable correction terms are applied. The results of computations in two test areas show that the direct and indirect approaches of geoid height determination yield good agreement with the classical gravimetric geoidal heights which are determined from Stokes' formula. Surprisingly, the results of the indirect method of geoidal height determination yield better agreement with the global positioning system (GPS)-levelling derived geoid heights, which are used to demonstrate such improvements, than the results of gravimetric geoid heights at to the same GPS stations. It has been demonstrated that the application of correction terms in both methods improves the agreement of geoidal heights at GPS-levelling stations. It is also found that the correction terms in the direct method of geoidal height determination are mostly similar to the correction terms used for the indirect determination of geoidal heights from height anomalies.
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Terrain corrections to power 3 in gravimetric geoid determination
Journal of Geodesy, 1998Co-Authors: H. Nahavandchi, L.e. SjöbergAbstract:In precise geoid determination by Stokes formula, direct and primary and secondary indirect terrain effects are applied for removing and restoring the terrain masses. We use Helmert's second condensation method to derive the sum of these effects, together called the total terrain effect for geoid. We develop the total terrain effect to third power of elevation H in the original Stokes formula, Earth Gravity model and modified Stokes formula. It is shown that the original Stokes formula, Earth Gravity model and modified Stokes formula all theoretically experience different total terrain effects. Numerical results indicate that the total terrain effect is very significant for moderate topographies and mountainous regions. Absolute global mean values of 5–10 cm can be reached for harmonic expansions of the terrain to degree and order 360. In another experiment, we conclude that the most important part of the total terrain effect is the contribution from the second power of H, while the contribution from the third power term is within 9 cm.
