Utilizing the adopted average topographic density of 2670 kg/m^(3)in the reduction of gravity anomalies introduces errors attributed to topographic density variations,which consequently affect geoid modeling accuracy....Utilizing the adopted average topographic density of 2670 kg/m^(3)in the reduction of gravity anomalies introduces errors attributed to topographic density variations,which consequently affect geoid modeling accuracy.Furthermore,the mean gravity along the plumbline within the topography in the definition of Helmert orthometric heights is computed approximately by applying the Poincar e-Prey gravity reduction where the topographic density variations are disregarded.The Helmert orthometric heights of benchmarks are then affected by errors.These errors could be random or systematic depending on the specific geological setting of the region where the leveling network is physically established and/or the geoid model is determined.An example of systematic errors in orthometric heights can be given for large regions characterized by sediment or volcanic deposits,the density of which is substantially lower than the adopted topographic density used in Helmert's definition of heights.The same applies to geoid modeling errors.In this study,we investigate these errors in the Hong Kong territory,where topographic density is about 20%lower than the density of 2670 kg/m^(3).We use the digital rock density model to estimate the effect of topographic density variations on the geoid and orthometric heights.Our results show that this effect on the geoid and Helmert orthometric heights reach maxima of about 2.1 and 0.5 cm,respectively.Both results provide clear evidence that rock density models are essential in physical geodesy applications involving gravimetric geoid modeling and orthometric height determination despite some criticism that could be raised regarding the reliability of these density models.However,in regions dominated by sedimentary and igneous rocks,the geological information is essential in these applications because topographic densities are substantially lower than the average density of 2670 kg/m^(3),thus introducing large systematic errors in geoid and orthometric heights.展开更多
At present,one of the methods used to determine the height of points on the Earth’s surface is Global Navigation Satellite System(GNSS)leveling.It is possible to determine the orthometric or normal height by this met...At present,one of the methods used to determine the height of points on the Earth’s surface is Global Navigation Satellite System(GNSS)leveling.It is possible to determine the orthometric or normal height by this method only if there is a geoid or quasi-geoid height model available.This paper proposes the methodology for local correction of the heights of high-order global geoid models such as EGM08,EIGEN-6C4,GECO,and XGM2019e_2159.This methodology was tested in different areas of the research field,covering various relief forms.The dependence of the change in corrected height accuracy on the input data was analyzed,and the correction was also conducted for model heights in three tidal systems:"tide free","mean tide",and"zero tide".The results show that the heights of EIGEN-6C4 model can be corrected with an accuracy of up to 1 cm for flat and foothill terrains with the dimensionality of 1°×1°,2°×2°,and 3°×3°.The EGM08 model presents an almost identical result.The EIGEN-6C4 model is best suited for mountainous relief and provides an accuracy of 1.5 cm on the 1°×1°area.The height correction accuracy of GECO and XGM2019e_2159 models is slightly poor,which has fuzziness in terms of numerical fluctuation.展开更多
Different methods have been deployed to compute the geoid, the altimetry reference for surveying applications. One of their main goals is to allow the use of GPS (Global Positioning System) or GNSS heights, which are ...Different methods have been deployed to compute the geoid, the altimetry reference for surveying applications. One of their main goals is to allow the use of GPS (Global Positioning System) or GNSS heights, which are related to an ellipsoid and therefore must be corrected. Some of these methods are accurate but quite heavy as developed by [1], but one of them is easy to use while giving very good results in a local system: some mm for a 10 × 10 km2 area developed by [2] [3]. In our study, we have used software called “Géoide Program”, previously used at the CERN in Switzerland and set up by [4], which they complete this software allowing a parameterization of general data to provide results in a general system. Then, tests have shown the way to optimize computations without any loss of accuracy. For our computations we use gridded of geodetic heights, from Lambert or WGS 84 datum’s, DTM (Digital Terrain Model) and leveled GPS points. To obtain these results, components of the vertical deflection are computed for every point on the grid, deduced from the attraction exerted by the mass Model. Then, geodetic heights are computed by an incremental way from an arbitrary reference. Once the calculation is performed, the geodetic height of any point located in the modelled area can be interpolated. The variations of parameters (mainly size and increments of the DTM and of the modeled area, and ground density) have shown that they do not play a significant role although DTM must be large enough to take into account an important area around a selected zone. However, the choice of the levelled GPS points is primordial. We have performed tests with real data concerning Mejez El Bab zone, in north of Tunisia. Nevertheless, for a few hundreds of square kilometers area, and just by using a DTM and a few levelled GPS points, this method provides results that look extremely promising, at least for surveying activities, as it shows a good possibility to use GPS for coarse precision levelling, and as DTM are now widely available in many countries.展开更多
The Global Navigation Satellite System(GNSS)positioning method has been significantly developed in geodetic surveying.However,the height obtained through GNSS observations is given in a geodetic height system that nee...The Global Navigation Satellite System(GNSS)positioning method has been significantly developed in geodetic surveying.However,the height obtained through GNSS observations is given in a geodetic height system that needs to be converted to orthometric height for engineering applications.Information on geoid height,which can be calculated using the global geopotential mode,is required to convert such GNSS observations into orthometric height.However,its accuracy is still insufficient for most engineering purposes.Therefore,a reliable geoid model is essential,especially in areas growing fast,e.g.,the central part of Java,Indonesia.In this study,we modeled the local geoid model in the central part of Java,Indonesia,using terrestrial-based gravity observations.The Stokes'formula with the second Helmert's condensation method under the Remove-Compute-Restore approach was implemented to model the geoid.The comparison between our best-performing geoid model and GNSS/leveling observations showed that the standard deviation of the geoid height differences was estimated to be 4.4 cm.This geoid result outperformed the commonly adopted global model of EGM2008 with the estimated standard deviation of geoid height differences of 10.7 cm.展开更多
基金supported by the Hong Kong GRF RGC project 15217222:“Modernization of the leveling network in the Hong Kong territories”。
文摘Utilizing the adopted average topographic density of 2670 kg/m^(3)in the reduction of gravity anomalies introduces errors attributed to topographic density variations,which consequently affect geoid modeling accuracy.Furthermore,the mean gravity along the plumbline within the topography in the definition of Helmert orthometric heights is computed approximately by applying the Poincar e-Prey gravity reduction where the topographic density variations are disregarded.The Helmert orthometric heights of benchmarks are then affected by errors.These errors could be random or systematic depending on the specific geological setting of the region where the leveling network is physically established and/or the geoid model is determined.An example of systematic errors in orthometric heights can be given for large regions characterized by sediment or volcanic deposits,the density of which is substantially lower than the adopted topographic density used in Helmert's definition of heights.The same applies to geoid modeling errors.In this study,we investigate these errors in the Hong Kong territory,where topographic density is about 20%lower than the density of 2670 kg/m^(3).We use the digital rock density model to estimate the effect of topographic density variations on the geoid and orthometric heights.Our results show that this effect on the geoid and Helmert orthometric heights reach maxima of about 2.1 and 0.5 cm,respectively.Both results provide clear evidence that rock density models are essential in physical geodesy applications involving gravimetric geoid modeling and orthometric height determination despite some criticism that could be raised regarding the reliability of these density models.However,in regions dominated by sedimentary and igneous rocks,the geological information is essential in these applications because topographic densities are substantially lower than the average density of 2670 kg/m^(3),thus introducing large systematic errors in geoid and orthometric heights.
基金the International Center for Global Earth Models(ICGEM)for the height anomaly and gravity anomaly data and Bureau Gravimetrique International(BGI)for free-air gravity anomaly data from the World Gravity Map project(WGM2012)The authors are grateful to Głowny Urza˛d Geodezji i Kartografii of Poland for the height anomaly data of the quasi-geoid PL-geoid2021.
文摘At present,one of the methods used to determine the height of points on the Earth’s surface is Global Navigation Satellite System(GNSS)leveling.It is possible to determine the orthometric or normal height by this method only if there is a geoid or quasi-geoid height model available.This paper proposes the methodology for local correction of the heights of high-order global geoid models such as EGM08,EIGEN-6C4,GECO,and XGM2019e_2159.This methodology was tested in different areas of the research field,covering various relief forms.The dependence of the change in corrected height accuracy on the input data was analyzed,and the correction was also conducted for model heights in three tidal systems:"tide free","mean tide",and"zero tide".The results show that the heights of EIGEN-6C4 model can be corrected with an accuracy of up to 1 cm for flat and foothill terrains with the dimensionality of 1°×1°,2°×2°,and 3°×3°.The EGM08 model presents an almost identical result.The EIGEN-6C4 model is best suited for mountainous relief and provides an accuracy of 1.5 cm on the 1°×1°area.The height correction accuracy of GECO and XGM2019e_2159 models is slightly poor,which has fuzziness in terms of numerical fluctuation.
文摘Different methods have been deployed to compute the geoid, the altimetry reference for surveying applications. One of their main goals is to allow the use of GPS (Global Positioning System) or GNSS heights, which are related to an ellipsoid and therefore must be corrected. Some of these methods are accurate but quite heavy as developed by [1], but one of them is easy to use while giving very good results in a local system: some mm for a 10 × 10 km2 area developed by [2] [3]. In our study, we have used software called “Géoide Program”, previously used at the CERN in Switzerland and set up by [4], which they complete this software allowing a parameterization of general data to provide results in a general system. Then, tests have shown the way to optimize computations without any loss of accuracy. For our computations we use gridded of geodetic heights, from Lambert or WGS 84 datum’s, DTM (Digital Terrain Model) and leveled GPS points. To obtain these results, components of the vertical deflection are computed for every point on the grid, deduced from the attraction exerted by the mass Model. Then, geodetic heights are computed by an incremental way from an arbitrary reference. Once the calculation is performed, the geodetic height of any point located in the modelled area can be interpolated. The variations of parameters (mainly size and increments of the DTM and of the modeled area, and ground density) have shown that they do not play a significant role although DTM must be large enough to take into account an important area around a selected zone. However, the choice of the levelled GPS points is primordial. We have performed tests with real data concerning Mejez El Bab zone, in north of Tunisia. Nevertheless, for a few hundreds of square kilometers area, and just by using a DTM and a few levelled GPS points, this method provides results that look extremely promising, at least for surveying activities, as it shows a good possibility to use GPS for coarse precision levelling, and as DTM are now widely available in many countries.
文摘The Global Navigation Satellite System(GNSS)positioning method has been significantly developed in geodetic surveying.However,the height obtained through GNSS observations is given in a geodetic height system that needs to be converted to orthometric height for engineering applications.Information on geoid height,which can be calculated using the global geopotential mode,is required to convert such GNSS observations into orthometric height.However,its accuracy is still insufficient for most engineering purposes.Therefore,a reliable geoid model is essential,especially in areas growing fast,e.g.,the central part of Java,Indonesia.In this study,we modeled the local geoid model in the central part of Java,Indonesia,using terrestrial-based gravity observations.The Stokes'formula with the second Helmert's condensation method under the Remove-Compute-Restore approach was implemented to model the geoid.The comparison between our best-performing geoid model and GNSS/leveling observations showed that the standard deviation of the geoid height differences was estimated to be 4.4 cm.This geoid result outperformed the commonly adopted global model of EGM2008 with the estimated standard deviation of geoid height differences of 10.7 cm.
