A Stokesian Approach for the Comparative Analysis of Satellite Gravity Models and Terrestrial Gravity Data

2014 ◽  
pp. 101-107 ◽  
Author(s):  
Jianliang Huang ◽  
Marc Véronneau
Keyword(s):  
Comparative Analysis ◽  
Gravity Data ◽  
Gravity Models ◽  
Satellite Gravity ◽  
Terrestrial Gravity

Crustal Thickness of Chinese Mainland Inversed by GOCE Satellite Gravity Data

2014 ◽  
Vol 568-570 ◽  
pp. 288-291
Author(s):  
Hai Jun Xu ◽  
Hu Rong Duan ◽  
Jian Ye Zhou
Keyword(s):  
Comparative Analysis ◽  
Gravity Anomaly ◽  
Gravity Data ◽  
Crustal Thickness ◽  
Geoid Height ◽  
Chinese Mainland ◽  
Satellite Gravity ◽  
Inversion Result ◽  
Goce Satellite

GOCE satellite gravity data is often used to compute gravity anomaly and geoid height. In the paper, GOCE gravity data is used to inverse the crustal thickness of Chinese mainland (E70°~130°, N20°~50°) in this paper. In order to test the reliability of the result, the computing result is compared with previous studies. The comparative analysis shows that the inversion result by GOCE gravity data has higher resolution and has good consistence with the previous studies.

scholarly journals Airborne Gravity Across New Zealand - For An Improved Vertical Datum

2021 ◽  
Author(s):  
◽  
Jack McCubbine
Keyword(s):  
New Zealand ◽  
Standard Deviation ◽  
Gravity Anomaly ◽  
Urban Areas ◽  
Gravity Data ◽  
Gravity Models ◽  
Terrestrial Gravity ◽  
Global Gravity ◽  
Vertical Datum ◽  
Gravimetric Quasigeoid

<p>It is important to be able to accurately determine the height of a point on the Earth in terms of the Earth's gravitational potential field. These heights predict how water will flow and so they are vital for engineering and surveying purposes. They are determined using a vertical datum which consists of a specif ed height system and a defined reference surface.  At present, in New Zealand, the o fficial vertical datum is NZVD2009 which uses a normal-orthometric height system and gravimetric quasigeoid, NZGeoid2009, as the reference surface. The aim of this thesis is to develop a more accurate gravimetric quasigeoid than NZGeoid2009, by incorporating new gravity data and utilising a re fined data processing strategy, to establish a better vertical datum for New Zealand.  A new airborne gravimetry data set has been collected which covers the North, South and Stewart Islands of New Zealand with a flight line spacing of 10km. The data were susceptible to short error prone sections of track due to poor (turbulent) flight conditions and mean off sets which separate the recorded gravity data along flight lines by a constant value from neighbouring lines and existing gravity models. The error prone sections of track have been visually identified by assessing the cross track agreement with other flight lines and with the global gravity model EGM2008, and the mean offsets were estimated by a least squares method which takes into consideration the spatially correlated gravity signal.  The repeatability of the data was assessed from data collected from five flights along two separate calibration lines. The mean gravity anomaly pro files calculated along the calibration lines each had a standard deviation of around 2.5 mGal. The internal consistency of the data was assessed by evaluating the diff erence between flight line data at intersection points. This accuracy measure was shown to be influenced by the along track filter, anisotropic topography and the relative flight line elevations. After correcting for all these effects the set of all intersecting differences had a standard deviation of approximately 5.9 mGal.  From an existing terrestrial gravity database, around 40000 observations have been reprocessed to reduce them to Bouguer gravity anomalies, this was done to ensure consistency in the formulas that have been used. A new national 8 m digital elevation model (DEM) was used to calculate terrain corrections and these were carefully compared with terrain corrections estimated from field observations of the topography to reduce any discrepancies in calculating near zone terrain e ffects. The largest source of error in the terrestrial gravity anomaly data is due to inaccurate height estimates of the marks. The height discrepancies have been estimated by comparing the recorded heights in the database to those determined from the 8 m DEM and have been translated into mGal by calculating the propagated effect on the free air and Bouguer slab corrections.  The airborne and terrestrial gravity data, along with a satellite altimetry marine gravity anomaly and existing shipborne gravity data, were assimilated by least squares collocation with a logarithmic covariance function to appropriately deal with the downward continuation of the airborne data, and gridded at 1 arc-minute resolution in the geographical region 25° (S) to 60 ° (S) and 160° (E) to 190° (E). 1 arc-minute block averaged heights were then used to calculate a reverse Bouguer slab correction, which when applied to the gravity data gave a gridded Faye anomaly. Different noise level variances were assigned to the separate data sets to optimally combine them.  Forty six of the most contemporary global gravity models (from 2008 onwards) have each been compared to 1422 leveling and GNSS derived quasigeoid height anomalies. Overall the Eigen-6C4 model fitted the leveling and GNSS derived quasigeoid height anomalies best with a root mean squared error of 5.29cm.  The Eigen-6C4 gravity model was subtracted from the gridded Faye anomaly (remove) and Stokes integral was evaluated on the residual gravity anomaly grid. A, theoretically optimum, modified Stokes kernel has been used and the modification degree L and spherical cap for the integration Ψ₀ were varied over the ranges L = 20; 40; 60; ..., 320 and Ψ₀ = 1° ; 1:5° ; 2° ; 2:5° ; 3° . The Eigen-6C4 geoid undulations were then added back to the residual geoid undulation grids and the primary indirect topographic effect was restored to obtain 80 quasigeoids for each L and Ψ₀ parameter variation.  The optimal parameter choice was determined to be L = 280 and Ψ₀ = 1:5 which had the best agreement with the leveling and GNSS derived quasigeoid height anomalies with a standard deviation of 3.8cm and root mean squared residual of 4.8cm of the differences. This is a 1.25cm improvement on NZGeoid2009. The quasigeoid was also assessed closely in three main urban areas, Auckland, Wellington and Christchurch, where the majority of large scale engineering projects and surveying takes place in New Zealand. Here there were 123, 169 and 125 data points and the standard deviations of the differences were 3.976, 3.385 and 2.071cm and root mean squared differences of 3.58,4.388 and 4.572 cm respectively. This gives an average accuracy of 3.1 cm standard deviation in urban areas which is 1.5 cm better than the average for NZGeoid2009.</p>

scholarly journals Gravimetric Geoid Modeling from the Combination of Satellite Gravity Model, Terrestrial and Airborne Gravity Data: A Case Study in the Mountainous Area, Colorado

2020 ◽  
Author(s):  
Tao Jiang ◽  
Yamin Dang ◽  
Chuanyin Zhang
Keyword(s):  
Standard Deviation ◽  
Gravity Model ◽  
Gravity Data ◽  
Combination Method ◽  
Airborne Gravity ◽  
Mountainous Area ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Satellite Gravity ◽  
Terrestrial Gravity

Abstract Constructing a high precision and high resolution gravimetric geoid model in the mountainous area is a quite challenging task because of the high, rough nature of topography and the geological complexity. One way out is to use as many gravity observations from different sources as possible such as satellite, terrestrial and airborne gravity data, thus the proper combination of heterogeneous gravity datasets is critical. In a rough topographic area in Colorado, we computed a set of gravimetric geoid models based on different combination modes of satellite gravity models, terrestrial and airborne gravity data using the spectral combination method. The gravimetric geoid model obtained from the combination of satellite gravity model GOCO06S and terrestrial gravity data agrees with the GPS leveling measured geoid heights at 194 benchmarks in 5.8 cm in terms of the standard deviation of discrepancies, and the standard deviation reduces to 5.3 cm after including the GRAV-D airborne gravity data collected at ~6.2 km altitude into the data combination. The contributions of airborne gravity data to the signal and accuracy improvements of the geoid models were quantified for different spatial distribution and density of terrestrial gravity data. The results demonstrate that, although the airborne gravity survey was flown at a high altitude, the additions of airborne gravity data improved the accuracies of geoid models by 13.4% - 19.8% in the mountainous area (elevations > 2000 m) and 12.7% - 21% (elevations < 2000 m) in the moderate area in the cases of terrestrial gravity data spacings are larger than 15 km.

scholarly journals Evaluation of GGMs Based on the Terrestrial Gravity Data of Gravity Disturbance and Moho Depthin Afar, Ethiopia

2021 ◽  
Vol 56 (3) ◽  
pp. 78-100
Author(s):  
Eyasu Alemu
Keyword(s):  
Gravity Data ◽  
Gravity Models ◽  
Moho Depth ◽  
Equal Distribution ◽  
Terrestrial Gravity ◽  
Global Gravity ◽  
Gravity Disturbances ◽  
Combined Models ◽  
Global Gravity Models ◽  
Best Fit

Abstract To estimate Moho depth, geoid, gravity anomaly, and other geopotential functionals, gravity data is needed. But, gravity survey was not collected in equal distribution in Ethiopia, as the data forming part of the survey were mainly collected on accessible roads. To determine accurate Moho depth using Global Gravity Models (GGMs) for the study area, evaluation of GGMs is needed based on the available terrestrial gravity data. Moho depth lies between 28 km and 32 km in Afar. Gravity disturbances (GDs) were calculated for the terrestrial gravity data and the recent GGMs for the study area. The model-based GDs were compared with the corresponding GD obtained from the terrestrial gravity data and their differences in terms of statistical comparison parameters for determining the best fit GGM at a local scale in Afar. The largest standard deviation (SD) (36.10 mGal) and root mean square error (RMSE) (39.00 mGal) for residual GD and the lowest correlation with the terrestrial gravity (0.61 mGal) were obtained by the satellite-only model (GO_CONS_GCF_2_DIR_R6). The next largest SD (21.27 mGal) and RMSE (25.65 mGal) for residual GD were obtained by the combined gravity model (XGM2019e_2159), which indicates that it is not the best fit model for the study area as compared with the other two GGMs. In general, the result showed that the combined models are more useful tools for modeling the gravity field in Afar than the satellite-only GGMs. But, the study clearly revealed that for the study area, the best model in comparison with the others is the EGM2008, while the second best model is the EIGEN6C4.

scholarly journals Gravimetric geoid modeling from the combination of satellite gravity model, terrestrial and airborne gravity data: a case study in the mountainous area, Colorado

2020 ◽  
Author(s):  
Tao Jiang ◽  
Yamin Dang ◽  
Chuanyin Zhang
Keyword(s):  
Standard Deviation ◽  
Gravity Model ◽  
Gravity Data ◽  
Combination Method ◽  
Airborne Gravity ◽  
Mountainous Area ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Satellite Gravity ◽  
Terrestrial Gravity

Abstract Constructing a high precision and high resolution gravimetric geoid model in the mountainous area is a quite challenging task because of the the lack of terrestrial gravity observations, rough high, rough nature of topography and the geological complexity. One way out is to use as hight quality and well distributed satellite and airborne gravity data to fill the gravity data gapsmany gravity observations from different sources as possible such as satellite, terrestrial and airborne gravity data, thus the proper combination of heterogeneous gravity datasets is critical. In a rough topographic area in Colorado, we computed a set of gravimetric geoid models based on different combination modes of satellite gravity models, terrestrial and airborne gravity data using the spectral combination method. The gravimetric geoid model obtained from the combination of satellite gravity model GOCO06S and terrestrial gravity data agrees with the GPS leveling measured geoid heights at 194 benchmarks in 5.8 cm in terms of the standard deviation of discrepancies, and the standard deviation reduces to 5.3 cm after including the GRAV-D airborne gravity data collected at ~6.2 km altitude into the data combination. The contributions of airborne gravity data to the signal and accuracy improvements of the geoid models were quantified for different spatial distribution and density of terrestrial gravity data. The results demonstrate that, although the airborne gravity survey was flown at a high altitude, the additions of airborne gravity data improved the accuracies of geoid models by 13.4% - 19.8% in the mountainous area (elevations > 2000 m) and 12.7% - 21% (elevations < 2000 m) in the moderate area in the cases of terrestrial gravity data spacings are larger than 15 km.

scholarly journals Airborne Gravity Across New Zealand - For An Improved Vertical Datum

2021 ◽  
Author(s):  
◽  
Jack McCubbine
Keyword(s):  
New Zealand ◽  
Standard Deviation ◽  
Gravity Anomaly ◽  
Urban Areas ◽  
Gravity Data ◽  
Gravity Models ◽  
Terrestrial Gravity ◽  
Global Gravity ◽  
Vertical Datum ◽  
Gravimetric Quasigeoid

<p>It is important to be able to accurately determine the height of a point on the Earth in terms of the Earth's gravitational potential field. These heights predict how water will flow and so they are vital for engineering and surveying purposes. They are determined using a vertical datum which consists of a specif ed height system and a defined reference surface.  At present, in New Zealand, the o fficial vertical datum is NZVD2009 which uses a normal-orthometric height system and gravimetric quasigeoid, NZGeoid2009, as the reference surface. The aim of this thesis is to develop a more accurate gravimetric quasigeoid than NZGeoid2009, by incorporating new gravity data and utilising a re fined data processing strategy, to establish a better vertical datum for New Zealand.  A new airborne gravimetry data set has been collected which covers the North, South and Stewart Islands of New Zealand with a flight line spacing of 10km. The data were susceptible to short error prone sections of track due to poor (turbulent) flight conditions and mean off sets which separate the recorded gravity data along flight lines by a constant value from neighbouring lines and existing gravity models. The error prone sections of track have been visually identified by assessing the cross track agreement with other flight lines and with the global gravity model EGM2008, and the mean offsets were estimated by a least squares method which takes into consideration the spatially correlated gravity signal.  The repeatability of the data was assessed from data collected from five flights along two separate calibration lines. The mean gravity anomaly pro files calculated along the calibration lines each had a standard deviation of around 2.5 mGal. The internal consistency of the data was assessed by evaluating the diff erence between flight line data at intersection points. This accuracy measure was shown to be influenced by the along track filter, anisotropic topography and the relative flight line elevations. After correcting for all these effects the set of all intersecting differences had a standard deviation of approximately 5.9 mGal.  From an existing terrestrial gravity database, around 40000 observations have been reprocessed to reduce them to Bouguer gravity anomalies, this was done to ensure consistency in the formulas that have been used. A new national 8 m digital elevation model (DEM) was used to calculate terrain corrections and these were carefully compared with terrain corrections estimated from field observations of the topography to reduce any discrepancies in calculating near zone terrain e ffects. The largest source of error in the terrestrial gravity anomaly data is due to inaccurate height estimates of the marks. The height discrepancies have been estimated by comparing the recorded heights in the database to those determined from the 8 m DEM and have been translated into mGal by calculating the propagated effect on the free air and Bouguer slab corrections.  The airborne and terrestrial gravity data, along with a satellite altimetry marine gravity anomaly and existing shipborne gravity data, were assimilated by least squares collocation with a logarithmic covariance function to appropriately deal with the downward continuation of the airborne data, and gridded at 1 arc-minute resolution in the geographical region 25° (S) to 60 ° (S) and 160° (E) to 190° (E). 1 arc-minute block averaged heights were then used to calculate a reverse Bouguer slab correction, which when applied to the gravity data gave a gridded Faye anomaly. Different noise level variances were assigned to the separate data sets to optimally combine them.  Forty six of the most contemporary global gravity models (from 2008 onwards) have each been compared to 1422 leveling and GNSS derived quasigeoid height anomalies. Overall the Eigen-6C4 model fitted the leveling and GNSS derived quasigeoid height anomalies best with a root mean squared error of 5.29cm.  The Eigen-6C4 gravity model was subtracted from the gridded Faye anomaly (remove) and Stokes integral was evaluated on the residual gravity anomaly grid. A, theoretically optimum, modified Stokes kernel has been used and the modification degree L and spherical cap for the integration Ψ₀ were varied over the ranges L = 20; 40; 60; ..., 320 and Ψ₀ = 1° ; 1:5° ; 2° ; 2:5° ; 3° . The Eigen-6C4 geoid undulations were then added back to the residual geoid undulation grids and the primary indirect topographic effect was restored to obtain 80 quasigeoids for each L and Ψ₀ parameter variation.  The optimal parameter choice was determined to be L = 280 and Ψ₀ = 1:5 which had the best agreement with the leveling and GNSS derived quasigeoid height anomalies with a standard deviation of 3.8cm and root mean squared residual of 4.8cm of the differences. This is a 1.25cm improvement on NZGeoid2009. The quasigeoid was also assessed closely in three main urban areas, Auckland, Wellington and Christchurch, where the majority of large scale engineering projects and surveying takes place in New Zealand. Here there were 123, 169 and 125 data points and the standard deviations of the differences were 3.976, 3.385 and 2.071cm and root mean squared differences of 3.58,4.388 and 4.572 cm respectively. This gives an average accuracy of 3.1 cm standard deviation in urban areas which is 1.5 cm better than the average for NZGeoid2009.</p>

Quantifying the contribution of airborne gravity data for geoid modeling: two case studies

2020 ◽  
Author(s):  
Tao Jiang ◽  
Yamin Dang ◽  
Chuanyin Zhang
Keyword(s):  
Large Scale ◽  
Gravity Data ◽  
Airborne Gravity ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Satellite Gravity ◽  
Terrestrial Gravity ◽  
Modeling Experiment ◽  
The Usa ◽  
Gps Leveling

&lt;p&gt;Airborne gravimetry has become increasingly important for geoid modeling because of its capability of collecting large scale gravity data over difficult areas. In order to quantify the contribution of airborne gravity data for geoid determination, two regions with distinct topographical condition, a hilly desert area in Mu Us of China and a mountainous region in Colorado of the USA were selected for gravimetric geoid modeling experiment. The gravimetric geoid model computed by combining satellite gravity model, terrestrial and airborne gravity data fits with GPS leveling data to 0.8 cm for Mu Us case and 5.3 cm for Colorado case. The contribution of airborne gravity data to the signal and accuracy improvement of the geoid was quantitatively evaluated for different spatial distribution and density of terrestrial gravity data. The results demonstrate that in the cases of the spacing of terrestrial gravity points exceeds 15 km, the additions of airborne gravity data improve the accuracies of gravimetric geoid models by 11.1%~48.3% for Mu Us case and 13%~20% for Colorado case.&lt;/p&gt;

scholarly journals Gravimetric geoid modeling from the combination of satellite gravity model, terrestrial and airborne gravity data: a case study in the mountainous area, Colorado

2020 ◽  
Author(s):  
Tao Jiang ◽  
Yamin Dang ◽  
Chuanyin Zhang
Keyword(s):  
Standard Deviation ◽  
Gravity Model ◽  
Gravity Data ◽  
Combination Method ◽  
Airborne Gravity ◽  
Mountainous Area ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Satellite Gravity ◽  
Terrestrial Gravity

Abstract Constructing a high precision and high resolution gravimetric geoid model in the mountainous area is a quite challenging task because of the lack of terrestrial gravity observations, rough topography and the geological complexity. One way out is to use high quality and well distributed satellite and airborne gravity data to fill the gravity data gaps, thus the proper combination of heterogeneous gravity datasets is critical. In a rough topographic area in Colorado, we computed a set of gravimetric geoid models based on different combination modes of satellite gravity models, terrestrial and airborne gravity data using the spectral combination method. The gravimetric geoid model obtained from the combination of satellite gravity model GOCO06S and terrestrial gravity data agrees with the GPS leveling measured geoid heights at 194 benchmarks in 5.8 cm in terms of the standard deviation of discrepancies, and the standard deviation reduces to 5.3 cm after including the GRAV-D airborne gravity data collected at ~6.2 km altitude into the data combination. The contributions of airborne gravity data to the signal and accuracy improvements of the geoid models were quantified for different spatial distribution and density of terrestrial gravity data. The results demonstrate that, although the airborne gravity survey was flown at a high altitude, the additions of airborne gravity data improved the accuracies of geoid models by 13.4% - 19.8% in the mountainous area (elevations > 2000 m) and 12.7% - 21% (elevations < 2000 m) in the moderate area in the cases of terrestrial gravity data spacings are larger than 15 km.

scholarly journals LOCAL EVALUATION OF EARTH GRAVITATIONAL MODELS, CASE STUDY: IRAN

2017 ◽  
Vol 43 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Ismael FOROUGHI ◽  
Yosra AFRASTEH ◽  
Sabah RAMOUZ ◽  
Abdolreza SAFARI
Keyword(s):  
Gravity Data ◽  
Low Frequency ◽  
Gravity Anomalies ◽  
Gravity Models ◽  
Data Sets ◽  
Observation Data ◽  
Satellite Gravity ◽  
Global Gravity ◽  
Marine Gravity ◽  
Global Gravity Models

Global gravity models are being developed according to new data sets available from satellite gravity missions and terrestrial/marine gravity data which are provided by different countries. Some countries do not provide all their available data and the global gravity models have many vague computational methods. Therefore, the models need to be evaluated locally before using. It is generally understood that the accuracy of global gravity models is enough for local (civil, mining, construction, etc.) projects, however, our results in Iran show that the differences between synthesized values and observation data reach up to ∼300 mGal for gravity anomalies and ∼2 m for geoid heights. Even by applying the residual topographical correction to synthetized gravity anomalies, the differences are still notable. The accuracy of global gravity models for predicting marine gravity anomalies is also investigated in Persian Gulf and the results show differences of ∼140 mGal in coastal areas. The results of evaluating selected global gravity models in Iran indicate that the EIGEN-6C4 achieves the lowest RMS for estimating the geoid heights. EGM08 predicts the closest results to terrestrial gravity anomalies. DIR-R5 GOCE satellite-only model estimates the low-frequency part of gravity field more accurately. The best prediction of marine gravity anomalies is also achieved by EGM08.

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