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
Different modification methods and software programs were developed to obtain accurate local geoid models in the past two decades.The quantitative effect of the main factors on the accuracy of local geoid modeling is ...Different modification methods and software programs were developed to obtain accurate local geoid models in the past two decades.The quantitative effect of the main factors on the accuracy of local geoid modeling is still ambiguous and has not been clearly diagnosed yet.This study presents efforts to find the most influential factors on the accuracy of the local geoid model,as well as the amount of each factor’s effect quantitatively.The methodology covers extracting the quantitative characteristics of 16 articles regarding local geoid models of different countries.The Statistical Package of Social Sciences(SPSS)software formulated a strong multiple regression model of correlation coefficient r = 0.999 with a high significance coefficient of determination R^2 = 0.997 and adjusted R^2 = 0,98 for the required effective factors.Then,factor analysis is utilized to extract the dominant factors which include:accuracy of gravity data(40%),the density of gravity data(25%)(total gravity factors is 65%),the Digital Elevation Model(DEM)resolution(16%),the accuracy of GPS/leveling points(10%)and the area of the terrain of the country/state under the study(9%).These results of this study will assist in developing more accurate local geoid models.展开更多
Many applications in geodesy, hydrography and engineering require geoid-related heights. Spirit leveling which is the traditional means of obtaining geoid- or mean sea level-related heights is slow, time-consuming and...Many applications in geodesy, hydrography and engineering require geoid-related heights. Spirit leveling which is the traditional means of obtaining geoid- or mean sea level-related heights is slow, time-consuming and costly. Global Navigation Satellite Systems (GNSS) offer faster and relatively cheaper way of obtaining geoid-related heights when geoidal undulation is applied to ellipsoidal heights. However, difficulties involved in determining acceptable geoid height have seriously hampered the application of GNSS for leveling in Rivers State, thus necessitating the need to develop an acceptable geoid model which will serve as a means of conversion of GNSS-delivered ellipsoidal heights to their orthometric heights equivalent. In pursuance of this objective, a detailed gravimetric geoid has been evaluated for Rivers State, Nigeria. The computation of the geoid was carried out by the traditional remove-restore procedure. The Earth Geopotential Model 2008 (EGM08) was applied as the reference field for both the remove and restore parts of the procedures;spherical Fast Fourier Transform (FFT) was employed for the evaluation of the Molodenskii’s integral formula for the height anomaly, (ζ) to yield the quasi-geoid;while the Residual Terrain Modelling (RTM) was done by prism integration. The classical gravimetric geoid over Rivers State was obtained from the rigorously evaluated quasi-geoid by adding the quasi-geoid to geoid (N?- ζ) correction it. The minimum and maximum geoid height values are 18.599 m and 20.114 m respectively with standard deviation of 0.345 m across the study area. Comparison of the gravimetric geoidal heights with the GPS/Leveling-derived geoidal heights of 13 stations across Rivers State, Nigeria showed that the absolute agreement with respect to the GPS/leveling datum is generally better than 7 cm root mean squares (r.m.s) error. Results also showed that combining both GPS heights and the computed Rivers State geoid model can give orthometric heights accurate to 3 cm post-fit using a 4-parameter empirical model. The geoid model can thus serve as a good alternative to traditional leveling when used with GPS leveling, particularly for third order leveling in the study area.展开更多
In this paper, we calculated multi-scale residual geoid anomalies with the method of geoid separation processing, according to EGM2008 ultra-high order gravity field model, remove-restore technique and Stokes integral...In this paper, we calculated multi-scale residual geoid anomalies with the method of geoid separation processing, according to EGM2008 ultra-high order gravity field model, remove-restore technique and Stokes integral. The East Asian continental margin was selected as the study area. The residual geoid anomalies have been calculated by programming. On the basis of residual geoid anomalies at various orders, the interlayer geoid anomalies at different depths were calculated to depict the spatial distribution characteristics of the residual geoid. Finally, we conducted a detailed geophysical interpretation for the study area according to the geoid anomalies in combination with other geophysical datasets. Four conclusions can be outlined as follows: 1) it is impracticable that geoid anomalies are used in the interpretation of the shallow objects due to the influence of the terrain; 2) the anomalies of residual geoid can reflect the intensity of small-scale mantle convection in the asthenosphere; 3) the interlayer geoid anomalies can reflect the magmatic activities associated with the mantle convection and mantle plume in different scales; 4) the study of the geoid may provide an approach for the research of the subduction zone, mantle convection and mantle plume.展开更多
With Chinese latest global gravity field model WDM94, the authors provide the geoid height and mean free air gravity anomaly of Antarctica (The range of latitude is from -60° to -90°). In order to conclude a...With Chinese latest global gravity field model WDM94, the authors provide the geoid height and mean free air gravity anomaly of Antarctica (The range of latitude is from -60° to -90°). In order to conclude and analyze the characters of Antarctic geoid roundly, the authors collect the latest oversea global gravity field model OSU91 (to degree and order 360) and JGMOSU (to degree and order 360), get the corresponding geoid height and mean free air gravity anomaly. The results are compared with the results got from WDM94, thus we get the difference. The standard deviation of geoid height between WDM94 and OSU91 is ±1.90 m;the deviation of geoid between WDM94 and JGMOSU is ±2.09 m. The standard deviation of mean gravity anomaly are ±8.97 mGal and ±9.32 mGal respectively. [WT9.HZ]展开更多
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Different modification methods and software programs were developed to obtain accurate local geoid models in the past two decades.The quantitative effect of the main factors on the accuracy of local geoid modeling is still ambiguous and has not been clearly diagnosed yet.This study presents efforts to find the most influential factors on the accuracy of the local geoid model,as well as the amount of each factor’s effect quantitatively.The methodology covers extracting the quantitative characteristics of 16 articles regarding local geoid models of different countries.The Statistical Package of Social Sciences(SPSS)software formulated a strong multiple regression model of correlation coefficient r = 0.999 with a high significance coefficient of determination R^2 = 0.997 and adjusted R^2 = 0,98 for the required effective factors.Then,factor analysis is utilized to extract the dominant factors which include:accuracy of gravity data(40%),the density of gravity data(25%)(total gravity factors is 65%),the Digital Elevation Model(DEM)resolution(16%),the accuracy of GPS/leveling points(10%)and the area of the terrain of the country/state under the study(9%).These results of this study will assist in developing more accurate local geoid models.
文摘Many applications in geodesy, hydrography and engineering require geoid-related heights. Spirit leveling which is the traditional means of obtaining geoid- or mean sea level-related heights is slow, time-consuming and costly. Global Navigation Satellite Systems (GNSS) offer faster and relatively cheaper way of obtaining geoid-related heights when geoidal undulation is applied to ellipsoidal heights. However, difficulties involved in determining acceptable geoid height have seriously hampered the application of GNSS for leveling in Rivers State, thus necessitating the need to develop an acceptable geoid model which will serve as a means of conversion of GNSS-delivered ellipsoidal heights to their orthometric heights equivalent. In pursuance of this objective, a detailed gravimetric geoid has been evaluated for Rivers State, Nigeria. The computation of the geoid was carried out by the traditional remove-restore procedure. The Earth Geopotential Model 2008 (EGM08) was applied as the reference field for both the remove and restore parts of the procedures;spherical Fast Fourier Transform (FFT) was employed for the evaluation of the Molodenskii’s integral formula for the height anomaly, (ζ) to yield the quasi-geoid;while the Residual Terrain Modelling (RTM) was done by prism integration. The classical gravimetric geoid over Rivers State was obtained from the rigorously evaluated quasi-geoid by adding the quasi-geoid to geoid (N?- ζ) correction it. The minimum and maximum geoid height values are 18.599 m and 20.114 m respectively with standard deviation of 0.345 m across the study area. Comparison of the gravimetric geoidal heights with the GPS/Leveling-derived geoidal heights of 13 stations across Rivers State, Nigeria showed that the absolute agreement with respect to the GPS/leveling datum is generally better than 7 cm root mean squares (r.m.s) error. Results also showed that combining both GPS heights and the computed Rivers State geoid model can give orthometric heights accurate to 3 cm post-fit using a 4-parameter empirical model. The geoid model can thus serve as a good alternative to traditional leveling when used with GPS leveling, particularly for third order leveling in the study area.
基金financially supported by the National Natural Science Foundation of China(No.41606044)the Special Fund for Ocean Scientific Research in the Public Interest(No.201305029-02)
文摘In this paper, we calculated multi-scale residual geoid anomalies with the method of geoid separation processing, according to EGM2008 ultra-high order gravity field model, remove-restore technique and Stokes integral. The East Asian continental margin was selected as the study area. The residual geoid anomalies have been calculated by programming. On the basis of residual geoid anomalies at various orders, the interlayer geoid anomalies at different depths were calculated to depict the spatial distribution characteristics of the residual geoid. Finally, we conducted a detailed geophysical interpretation for the study area according to the geoid anomalies in combination with other geophysical datasets. Four conclusions can be outlined as follows: 1) it is impracticable that geoid anomalies are used in the interpretation of the shallow objects due to the influence of the terrain; 2) the anomalies of residual geoid can reflect the intensity of small-scale mantle convection in the asthenosphere; 3) the interlayer geoid anomalies can reflect the magmatic activities associated with the mantle convection and mantle plume in different scales; 4) the study of the geoid may provide an approach for the research of the subduction zone, mantle convection and mantle plume.
文摘With Chinese latest global gravity field model WDM94, the authors provide the geoid height and mean free air gravity anomaly of Antarctica (The range of latitude is from -60° to -90°). In order to conclude and analyze the characters of Antarctic geoid roundly, the authors collect the latest oversea global gravity field model OSU91 (to degree and order 360) and JGMOSU (to degree and order 360), get the corresponding geoid height and mean free air gravity anomaly. The results are compared with the results got from WDM94, thus we get the difference. The standard deviation of geoid height between WDM94 and OSU91 is ±1.90 m;the deviation of geoid between WDM94 and JGMOSU is ±2.09 m. The standard deviation of mean gravity anomaly are ±8.97 mGal and ±9.32 mGal respectively. [WT9.HZ]
