The geodetic and geophysical applications of Earth Gravity Field parameters computed from Global Geopotential Models (GGMs) are quite on the increase despite the inherent commission and omission errors of these models...The geodetic and geophysical applications of Earth Gravity Field parameters computed from Global Geopotential Models (GGMs) are quite on the increase despite the inherent commission and omission errors of these models. In view of this, this study focuses on refining and quantifying terrain-induced effects on Bouguer gravity anomalies computed directly from a total of seven recent GGMs. In the study, the Residual Terrain Model (RTM) technique was used to estimate the residual terrain effects that were added to the GGM-computed Bouguer gravity anomalies at the sixty test points in Enugu State, Nigeria. The computed residual terrain effects range from -24.6 to 37.5 mgal while the percentage of the omission errors of the GGMs based on their Root-Mean-Square (RMS) differences ranges from 7.8% to 44.7%. It can be concluded that GGM-refined Bouguer gravity anomalies are better in accuracy than the unrefined GGM-computed Bouguer gravity anomalies and hence there is need for accurate height information in the development of GGMs. We, therefore, recommend that refined Bouguer gravity anomalies obtained from HUST-Grace2016s, EIGEN-6C4 and GECO that gave best improvement amongst the seven GGMs under consideration should be used to supplement the available terrestrial Bouguer anomalies for geodetic and geophysical applications within the study area.展开更多
Global geopotential models have not included the very high frequencies of the Earth’s external gravity field.This is called omission error.This omission error becomes more important in mountainous areas(areas with hi...Global geopotential models have not included the very high frequencies of the Earth’s external gravity field.This is called omission error.This omission error becomes more important in mountainous areas(areas with highly variable topography).The work reported here consists in reducing the omission error in measurements of Bouguer gravity anomalies,by refining the global geopotential model EGM2008 using the spectral enhancement method.This method consists in computing the residual terrain effects and then coupling them to the gravimetric signal of the global geopotential model.To compute the residual terrain effects,we used the Residual Terrain Model(RTM)technique.To refine it required a reference surface(ETOPO1)developed up to degree 2190(the maximum degree of the EGM2008 model)and a detailed elevation model(AW3D30).Computation was performed with the TC program of the GRAVSOFT package.The topography of the study area was assumed to have a constant density of 2670 kg/m3.For the inner and outer zones,the respective integration radii of 10 km and 200 km have been chosen.We obtained very important RTM values ranging from−53.59 to 34.79 mGal.These values were added to the gravity anomalies grid of the EGM2008 model to improve accuracy at high frequencies.On a part of the Cameroon Volcanic Line and its surroundings(mountainous area),we made a comparison between the residual Bouguer anomalies before and after refinement.We report differences ranging from−37.40 to 26.40 mGal.We conclude that the impact of omission error on gravimetric signatures is observed especially in areas with high variable topography,such as on the Cameroon Volcanic Line and around the localities of Takamanda,Essu,Dumbo,and Ngambe.This finding illustrates the great influence that topography has on accurate measurement of these gravity anomalies,and thus why topography must be taken into account.We can conclude that in preparing a global geopotential model,a high resolution DTM must be used to decrease the omission error:the degree of expansion has to increase in order to take the higher frequencies into account.The refined Bouguer anomalies grid presented here can be used in addition to terrestrial gravity anomalies in the study area,especially in mountainous areas where gravimetric data are very sparse or nonexistent.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
文摘The geodetic and geophysical applications of Earth Gravity Field parameters computed from Global Geopotential Models (GGMs) are quite on the increase despite the inherent commission and omission errors of these models. In view of this, this study focuses on refining and quantifying terrain-induced effects on Bouguer gravity anomalies computed directly from a total of seven recent GGMs. In the study, the Residual Terrain Model (RTM) technique was used to estimate the residual terrain effects that were added to the GGM-computed Bouguer gravity anomalies at the sixty test points in Enugu State, Nigeria. The computed residual terrain effects range from -24.6 to 37.5 mgal while the percentage of the omission errors of the GGMs based on their Root-Mean-Square (RMS) differences ranges from 7.8% to 44.7%. It can be concluded that GGM-refined Bouguer gravity anomalies are better in accuracy than the unrefined GGM-computed Bouguer gravity anomalies and hence there is need for accurate height information in the development of GGMs. We, therefore, recommend that refined Bouguer gravity anomalies obtained from HUST-Grace2016s, EIGEN-6C4 and GECO that gave best improvement amongst the seven GGMs under consideration should be used to supplement the available terrestrial Bouguer anomalies for geodetic and geophysical applications within the study area.
文摘Global geopotential models have not included the very high frequencies of the Earth’s external gravity field.This is called omission error.This omission error becomes more important in mountainous areas(areas with highly variable topography).The work reported here consists in reducing the omission error in measurements of Bouguer gravity anomalies,by refining the global geopotential model EGM2008 using the spectral enhancement method.This method consists in computing the residual terrain effects and then coupling them to the gravimetric signal of the global geopotential model.To compute the residual terrain effects,we used the Residual Terrain Model(RTM)technique.To refine it required a reference surface(ETOPO1)developed up to degree 2190(the maximum degree of the EGM2008 model)and a detailed elevation model(AW3D30).Computation was performed with the TC program of the GRAVSOFT package.The topography of the study area was assumed to have a constant density of 2670 kg/m3.For the inner and outer zones,the respective integration radii of 10 km and 200 km have been chosen.We obtained very important RTM values ranging from−53.59 to 34.79 mGal.These values were added to the gravity anomalies grid of the EGM2008 model to improve accuracy at high frequencies.On a part of the Cameroon Volcanic Line and its surroundings(mountainous area),we made a comparison between the residual Bouguer anomalies before and after refinement.We report differences ranging from−37.40 to 26.40 mGal.We conclude that the impact of omission error on gravimetric signatures is observed especially in areas with high variable topography,such as on the Cameroon Volcanic Line and around the localities of Takamanda,Essu,Dumbo,and Ngambe.This finding illustrates the great influence that topography has on accurate measurement of these gravity anomalies,and thus why topography must be taken into account.We can conclude that in preparing a global geopotential model,a high resolution DTM must be used to decrease the omission error:the degree of expansion has to increase in order to take the higher frequencies into account.The refined Bouguer anomalies grid presented here can be used in addition to terrestrial gravity anomalies in the study area,especially in mountainous areas where gravimetric data are very sparse or nonexistent.
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.
