A precise gravimetric geoid model in a mountainous area with scarce gravity data: a case study in central Turkey

2012 ◽  
Vol 56 (4) ◽  
pp. 909-927 ◽  
Author(s):  
Ramazan A. Abbak ◽  
Lars E. Sjöberg ◽  
Artu Ellmann ◽  
Aydin Ustun
Keyword(s):  
Gravity Data ◽  
Mountainous Area ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Central Turkey

scholarly journals Quasi Geoid and Geoid Modeling with the Use of Terrestrial and Airborne Gravity Data by the GGI Method—A Case Study in the Mountainous Area of Colorado

2021 ◽  
Vol 13 (21) ◽  
pp. 4217
Author(s):  
Marek Trojanowicz ◽  
Magdalena Owczarek-Wesołowska ◽  
Yan Ming Wang ◽  
Olgierd Jamroz
Keyword(s):  
Gravity Data ◽  
Research Work ◽  
Airborne Gravity ◽  
Mountainous Area ◽  
Geoid Model ◽  
Data Inversion ◽  
Gravimetric Quasigeoid ◽  
The Mean ◽  
Grid Points

This article concerns the development of gravimetric quasigeoid and geoid models using the geophysical gravity data inversion technique (the GGI method). This research work was carried out on the basis of the data used in the Colorado geoid experiment, and the mean quasigeoid (ζm) and mean geoid (Nm) heights, determined by the approaches used in the Colorado geoid experiment, were used as a reference. Three versions of the quasigeoid GGI models depending on gravity data were analyzed: terrestrial-only, airborne-only, and combined (using airborne and terrestrial datasets). For the combined version, which was the most accurate, a model in the form of a 1′×1′ grid was calculated in the same area as the models determined in the Colorado geoid experiment. For the same grid, the geoid–quasigeoid separation was determined, which was used to build the geoid model. The agreement (in terms of the standard deviation of the differences) of the determined models, with ζm and Nm values for the GSVS17 profile points, was ±0.9 cm for the quasigeoid and ±1.2 cm for the geoid model. The analogous values, determined on the basis of all 1′×1′ grid points, were ±2.3 cm and ±2.6 cm for the quasigeoid and geoid models, respectively.

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

2020 ◽  
Vol 72 (1) ◽  
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

AbstractConstructing 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 Contribution of GRAV-D airborne gravity to improvement of regional gravimetric geoid modelling in Colorado, USA

2021 ◽  
Vol 95 (5) ◽  
Author(s):  
Matej Varga ◽  
Martin Pitoňák ◽  
Pavel Novák ◽  
Tomislav Bašić
Keyword(s):  
Gravity Anomaly ◽  
Gravity Data ◽  
Airborne Gravity ◽  
Mountainous Area ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Terrestrial Gravity ◽  
The Third ◽  
Regional Gravimetric Geoid ◽  
Geoid Computation

AbstractThis paper studies the contribution of airborne gravity data to improvement of gravimetric geoid modelling across the mountainous area in Colorado, USA. First, airborne gravity data was processed, filtered, and downward-continued. Then, three gravity anomaly grids were prepared; the first grid only from the terrestrial gravity data, the second grid only from the downward-continued airborne gravity data, and the third grid from combined downward-continued airborne and terrestrial gravity data. Gravimetric geoid models with the three gravity anomaly grids were determined using the least-squares modification of Stokes’ formula with additive corrections (LSMSA) method. The absolute and relative accuracy of the computed gravimetric geoid models was estimated on GNSS/levelling points. Results exhibit the accuracy improved by 1.1 cm or 20% in terms of standard deviation when airborne and terrestrial gravity data was used for geoid computation, compared to the geoid model computed only from terrestrial gravity data. Finally, the spectral analysis of surface gravity anomaly grids and geoid models was performed, which provided insights into specific wavelength bands in which airborne gravity data contributed and improved the power spectrum.

scholarly journals Performance Comparison of Geoid Refinement between XGM2016 and EGM2008 Based on the KTH and RCR Methods: Jilin Province, China

2020 ◽  
Vol 12 (2) ◽  
pp. 324
Author(s):  
Qiong Wu ◽  
Hongyao Wang ◽  
Bin Wang ◽  
Shengbo Chen ◽  
Hongqing Li
Keyword(s):  
Gravity Field ◽  
Mean Square Error ◽  
Gravity Data ◽  
Jilin Province ◽  
Mountainous Area ◽  
Mean Square ◽  
Geoid Model ◽  
Plain Area ◽  
Gravity Field Models ◽  
Global Mean

The selection of an appropriate global gravity field model and refinement method can effectively improve the accuracy of the refined regional geoid model in a certain research area. We analyzed the accuracy of Experimental Geopotential Model (XGM2016) based on the GPS-leveling data and the modification parameters of the global mean square errors in the KTH geoid refinement in Jilin Province, China. The regional geoid was refined based on Earth Gravitational Model (EGM2008) and XGM2016 using both the Helmert condensation method with an RCR procedure and the KTH method. A comparison of the original two gravity field models to the GPS-leveling benchmarks showed that the accuracies of XGM2016 and EGM2008 in the plain area of Jilin Province are similar with a standard deviation (STD) of 5.8 cm, whereas the accuracy of EGM2008 in the high mountainous area is 1.4 cm better than that of XGM2016, which may be attributed to its low resolution. The modification parameters between the two gravity field models showed that the coefficient error of XGM2016 model was lower than that of EGM2008 for the same degree of expansion. The different modification limits and integral radii may produce a centimeter level difference in global mean square error, while the influence of the truncation error caused by the integral was at the millimeter level. The terrestrial gravity data error accounted for the majority of the global mean square error. The optimal least squares modification obtained the minimum global mean square error, and the global mean square error calculated based on XGM2016 model was reduced by about 1~3 cm compared with EGM2008. The refined geoid based on the two gravity field models indicated that both KTH and RCR method can effectively improve the STD of the geoid model from about six to three centimeters. The refined accuracy of EGM2008 model using RCR and KTH methods is slightly better than that of XGM2016 model in the plain and high mountain areas after seven-parameter fitting. EGM2008 based on the KTH method was the most precise at ± 2.0 cm in the plain area and ± 2.4 cm in the mountainous area. Generally, for the refined geoid based on the two Earth gravity models, KTH produced results similar to RCR in the plain area, and had relatively better performance for the mountainous area where terrestrial gravity data is sparse and unevenly distributed.

scholarly journals THE EVALUATION OF THE NEW ZEALAND'S GEOID MODEL USING THE KTH METHOD / NAUJOSIOS ZELANDIJOS GEOIDO MODELIO VERTINIMAS KTH METODU / ОЦЕНКА МОДЕЛИ ГЕОИДА НОВОЙ ЗЕЛАНДИИ С ПРИМЕНЕНИЕМ МЕТОДА КТН

2011 ◽  
Vol 37 (1) ◽  
pp. 5-14 ◽  
Author(s):  
Ahmed Abdalla ◽  
Robert Tenzer
Keyword(s):  
New Zealand ◽  
Least Squares ◽  
Gravity Data ◽  
Spherical Approximation ◽  
Geopotential Model ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Marine Gravity ◽  
Gravity Database ◽  
Stokes Integral

We compile a new geoid model at the computation area of New Zealand and its continental shelf using the method developed at the Royal Institute of Technology (KTH) in Stockholm. This method utilizes the least-squares modification of the Stokes integral for the biased, unbiased, and optimum stochastic solutions. The modified Bruns-Stokes integral combines the regional terrestrial gravity data with a global geopotential model (GGM). Four additive corrections are calculated and applied to the approximate geoid heights in order to obtain the gravimetric geoid. These four additive corrections account for the combined direct and indirect effects of topography and atmosphere, the contribution of the downward continuation reduction, and the formulation of the Stokes problem in the spherical approximation. The gravimetric geoid model is computed using two heterogonous gravity data sets: the altimetry-derived gravity anomalies from the DNSC08 marine gravity database (offshore) and the ground gravity measurements from the GNS Science gravity database (onshore). The GGM coefficients are taken from EIGEN-GRACE02S complete to degree 65 of spherical harmonics. The topographic heights are generated from the 1×1 arc-sec detailed digital terrain model (DTM) of New Zealand and from the 30×30 arc-sec global elevation data of SRTM30_PLUS V5.0. The least-squares analysis is applied to combine the gravity and GPS-levelling data using a 7-parameter model. The fit of the KTH geoid model with GPS-levelling data in New Zealand is 7 cm in terms of the standard deviation (STD) of differences. This STD fit is the same as the STD fit of the NZGeoid2009, which is the currently adopted official quasigeoid model for New Zealand. Santrauka Stokholmo Karališkajame technologijos institute (KTH) sukurtu metodu apskaičiuotas naujas Naujosios Zelandijos ir kontinentinio šelfo geoido modelis. Taikoma Stokso integralo mažiausiųjų kvadratų modifikacija, įvertinant paklaidas ir jų nevertinant bei ieškant optimalių stochastinių sprendinių. Modifikuotas Bruno ir Stokso integralas sieja regioninius žemyninius gravimetrinius duomenis su globaliuoju geopotencialo modeliu (GGM). Gravimetriniam geoidui gauti skaičiuojamos keturios papildomos pataisos: topografinės situacijos ir atmosferos tiesioginės ir netiesioginės įtakos, redukcijos įtakos ir Stokso integralo taikymo sferiniam paviršiui. Gravimetrinis geoido modelis apskaičiuotas pagal du duomenų rinkinius: DNSC08 jūrinių gravimetrinių duomenų bazėje (šelfas) esančias altimetriniu metodu nustatytas sunkio pagreičio anomalijas ir žemyninės dalies gravimetrinių matavimų duomenis iš GNS gravimetrinės duomenų bazės (pakrantė). GGM koeficientai imti iš EIGEN-GRACE02S modelio sferinių iki 65 laipsnio harmonikų. Topografiniai aukščiai sugeneruoti iš Naujosios Zelandijos 1×1 sekundės detaliojo skaitmeninio reljefo modelio ir iš 30×30 sekundžių globaliojo aukščių modelio SRTM30_PLUS V5.0. Gravimetriniams ir GPS niveliacijos duomenims sujungti taikytas mažiausiųjų kvadratų 7 parametrų metodas. KTH metodu sudaryto geoido modelio vidutinė kvadratinė paklaida 7 cm. Tai sutampa su NZGeoid 2009 geoido modelio, taikomo Naujoje Zelandijoje, tikslumu. Резюме Модель геоида континентального шельфа Новой Зеландии построена с применением метода, созданного в Королевском технологическом институте Стокгольма. Данный метод основан на модификации решения интеграла Стокса методом наименьших квадратов с оценкой или без оценки погрешностей и поиском оптимальных статистических решений. Модифицированный интеграл БрунаСтокса объединяет региональные надземные гравиметрические данные с глобальной геопотенциальной моделью (GGM). Для определения гравиметрического геоида вычисляются дополнительные поправки прямого и косвенного влияния топографии и атмосферы, редукции и применения проблемы Стокса для сферической поверхности. Гравиметрическая модель геоида вычисляется на основе двух баз данных: альтиметрическим методом определенных аномалий силы тяжести в базе морских гравиметрических данных DNSC08 (шельф) и надземной части гравиметрических измерений из базы данных GNS. Коэффициенты GGM взяты из сферических гармоник до 65 степени модели EIGENGRACEO2S. Топографические высоты сгенерированы из детальной цифровой модели рельефа Новой Зеландии с сеткой 1×1 секунду и из глобальной модели высот SRTM30_PLUSv5.0 с сеткой 30×30 секунд. Для объединения гравиметрических и GPSнивелирных данных применялся метод наименьших квадратов с 7 параметрами. Среднеквадратическая погрешность модели геоида, созданной по методу КТН, равна 7 см. Точность аналогична точности применяемой в Новой Зеландии модели геоида NZGeoid2009.

scholarly journals GRAVIMETRIC GEOID MODELLING OVER PENINSULAR MALAYSIA USING TWO DIFFERENT GRIDDING APPROACHES FOR COMBINING FREE AIR ANOMALY

2019 ◽  
Vol XLII-4/W16 ◽  
pp. 515-522
Author(s):  
M. F. Pa’suya ◽  
A. H. M. Din ◽  
J. C. McCubbine ◽  
A. H. Omar ◽  
Z. M. Amin ◽  
...  
Keyword(s):  
Gravity Data ◽  
Reference Signal ◽  
Digital Terrain Model ◽  
Peninsular Malaysia ◽  
Airborne Gravity ◽  
Geopotential Model ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Free Air ◽  
Free Air Anomaly

Abstract. We investigate the use of the KTH Method to compute gravimetric geoid models of Malaysian Peninsular and the effect of two differing strategies to combine and interpolate terrestrial, marine DTU17 free air gravity anomaly data at regular grid nodes. Gravimetric geoid models were produced for both free air anomaly grids using the GOCE-only geopotential model GGM GO_CONS_GCF_2_SPW_R4 as the long wavelength reference signal and high-resolution TanDEM-X global digital terrain model. The geoid models were analyzed to assess how the different gridding strategies impact the gravimetric geoid over Malaysian Peninsular by comparing themto 172 GNSS-levelling derived geoid undulations. The RMSE of the two sets of gravimetric geoid model / GNSS-levelling residuals differed by approx. 26.2 mm. When a 4-parameter fit is used, the difference between the RMSE of the residuals reduced to 8 mm. The geoid models shown here do not include the latest airborne gravity data used in the computation of the official gravimetric geoid for the Malaysian Peninsular, for this reason they are not as precise.

scholarly journals Implementation of a rigorous least-squares modification of Stokes’ formula to compute a gravimetric geoid model over Saudi Arabia (SAGEO13)

2015 ◽  
Vol 52 (10) ◽  
pp. 823-832 ◽  
Author(s):  
Ahmed Abdalla ◽  
Saad Mogren
Keyword(s):  
Saudi Arabia ◽  
Least Squares ◽  
Gravity Data ◽  
Computational Method ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Geopotential Models ◽  
Digital Elevation ◽  
Stokes Formula ◽  
Elevation Model

A gravimetric geoid model (SAGEO13) is computed for the Kingdom of Saudi Arabia using a rigorous stochastic computational method. The computational methodology is based on a combination of least-squares (LS) modification of Stokes’ formula and the additive corrections for topographic, ellipsoidal, atmospheric, and downward continuation effects on the geoid solution. In this study, we used terrestrial gravity data, a digital elevation model (SRTM3), and seven global geopotential models (GGMs) to compute a new geoid model for Saudi Arabia. The least-squares coefficients are derived based on the optimisation of the input modification parameters. The gravimetric solution and its additive corrections are computed based on the optimum LS coefficients. Compared to GPS-levelling data, SAGEO13 shows a fit of 18 cm (RMS) after using a 4-parameter fitting model.

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