scholarly journals DETERMINATION AND EVALUATION OF THE ESTONIAN FITTED GEOID MODEL EST-GEOID 2003 / ESTIJOS GEOIDO MODELIO EST-GEOID 2003 SUDARYMAS IR VERTINIMAS / СОЗДАНИЕ И ОЦЕНКА МОДЕЛИ ГЕОИДА ЭСТОНИИ EST-GEOID2003

2011 ◽  
Vol 37 (1) ◽  
pp. 15-21
Author(s):  
Harli Jürgenson ◽  
Kristina Türk ◽  
Jüri Randjärv
Keyword(s):  
High Precision ◽  
Gravity Data ◽  
Geodetic Network ◽  
Transformation Model ◽  
Accuracy Evaluation ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Precise Levelling ◽  
Normal Heights ◽  
Gravimetric Data

This paper focuses on issues related to the calculation of a high-precision fitted geoid model on Estonian territory. Model Est-Geoid2003 have been used in Estonia several years in geodesy and other applications. New data from precise levelling, new global models and terrestrial gravity data give plenty of possibilities for updates and accuracy evaluation. The model is based on a gravimetric geoid. From the gravimetric data gathered, a gravimetric geoid for Estonia was calculated as an approximately 3-km net using the FFT method. After including the new gravimetric data gathered, the gravimetric geoid no longer had any significant tilt relative to the height anomalies derived from GPS-levelling points. The standard deviation between the points was 2.7 cm. The surface of the calculated gravimetric geoid was fitted by high-precision GPS-levelling points. As a result, a height transformation model was determined to reflect the differences between the normal heights of BK77 and the ellipsoidal heights of EUREF-EST97 on Estonian territory. The model was originally called Est-Geoid2003 and is part of the official national geodetic system in Estonia. The model is updated and evaluated here using precise GPS-levelling points obtained from different measurement campaigns. In 2008–2010 the preliminary results from the latest precise levelling sessions became available, leading to a significant increase in the number of precise GPS-levelling points. Both networks are part of the Estonian integrated geodetic network. Using very precise levelling connections from new levelling lines, normal heights of several RGP points were calculated additionally. Misclosure of 300 km polygons are less than 2–3 mm normally. Ealier all precisely levelled RGP points were included into fitting points. Now many new points are available for fitting and independent evaluation. However, the use of several benchmarks for the same RGP point sometimes results in a 1–2 cm difference in normal height. This reveals problems with the stability of older wall benchmarks, which are widely used in Estonia. Even we recognized, that 0.5 cm fitted geoid model is not achievable using wall benchmarks. New evaluation of the model Est-Geoid2003 is introduced in the light of preliminary data from new precise levelling. Model accuracy is recognised about 1.2 cm as rms. Santrauka Akcentuojami klausimai, susiję su tiksliausio Estijos geoido modelio skaičiavimu. Šis modelis Estijoje geodezijoje ir kitose mokslo bei technikos šakose taikomas nuo 2003 metų. Nauji precizinės niveliacijos duomenys, nauji globalieji geopotencialo modeliai ir žemyno gravimetriniai duomenys – prielaidos geoido modeliui atnaujinti ir jo tikslumui įvertinti. Modelio pagrindas – gravimetrinis geoidas. Pagal surinktus gravimetrinius duomenis Estijos geoidas buvo apskaičiuotas greitųjų Furjė tranformacijų (FFT) metodu, sukuriant apie 3 km akių tinklą. Įtraukus naujuosius gravimetrinius duomenis, gravimetrinis geoidas daugiau nebeturi aukščių anomalijų. Vidutinė kvadratinė paklaida – 2,7 cm. Apskaičiuoto gravimetrinio geoido paviršius susietas su aukščių sistema pagal GPS niveliacijos taškus. 2008–2010 m. gavus precizinės niveliacijos duomenis, žymiai padidėjo GPS niveliacijos taškų skaičius bei jų tikslumas, nes precizinės niveliacijos poligonų iki 300 km nesąryšiai gauti mažesni nei 2–3 mm. Įvertinus naujo Estijos geoido modelio tikslumą nustatyta 1,2 cm vidutinė kvadratinė paklaida. Резюме Акцентируются вопросы, касающиеся вычисления точной модели геоида Эстонии. Эта модель применяется в Эстонии с 2003 г. в геодезии и других отраслях науки и техники. Новые данные высокоточной нивеляции, новые глобальные модели геопотенциала, а также гравиметрические данные создают предпосылки для обновления модели геоида и оценки его точности. Модель основана на гравиметрическом геоиде. Модель геоида Эстонии была вычислена быстрым методом Фурье с использованием всех гравиметрических данных и созданием сети 3×3 км. После использования новых гравиметрических данных в геоиде не оказалось значительного превышения высот по сравнению с точками, измеренными методом GPS. Среднеквадратическая погрешность составила 2,7 см. Вычисленная модель геоида была соединена с системой высот по точкам GPSнивелирования. Благодаря новым данным по высокоточной нивеляции, полученным в 2008–2010 гг., значительно увеличилось количество точек GPSнивелирования и тем самым увеличилась точность геоида, так как невязки полигонов нивелирования составляют всего 2–3 мм. Оценив точность нового геоида Эстонии, выявлено среднеквадратическое отклонение в 1,2 см.

scholarly journals Gravity data requirements for decimetre accuracy regional geoid using Stokes' Remove Compute Restore technique in Nigeria

2020 ◽  
Vol 50 (3) ◽  
pp. 325-346
Author(s):  
Joseph Olayemi ODUMOSU ◽  
Victor Chukwuemeka NNAM
Keyword(s):  
Spatial Resolution ◽  
Gravity Data ◽  
Data Accuracy ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Solution Approach ◽  
Test Region ◽  
Error Propagation Analysis ◽  
Gravimetric Data ◽  
Observational Errors

The need for dense and accurate gravity data cannot be overemphasised in the development of a precise gravimetric geoid model. Unfortunately, the field observations required are costly, and labour-intensive hence the need to ascertain via numerical simulations the appropriate field specifications before embarking on them. This paper presents an experimental study on the gravimetric data specifications (spatial resolution and data accuracy) required for achieving decimetre-level accuracy geoid using the conventional Stokes' Remove Compute Restore (RCR) method in Nigeria. A two-step solution approach was used in this study. The steps were determination of the (i) effect of data spacing by a comparative assessment of computation results obtained by using gravity data at four user determined intervals and (ii) effect of observation accuracy by numerical simulation using error propagation analysis. The data intervals (3′×3′, 5′×5′, 10′×10′ and 20′×20′) were selected from a combination of 1815 terrestrial FA anomaly points merged with EGM2008 derived FA anomaly covering the study area. Also, observational errors investigated were 0 mGal, 0.1 mGal, 0.5 mGal, 1 mGal and 5 mGal. The study was conducted in Nigeria having a total land area of approximately 923,768 km2. The study established that gravimetric geoid accuracy improves substantially as the spatial resolution and accuracy of the gravity data improves. Also, the study identified that data spacing contributes more to the overall geoid error than data accuracy. In addition, the study observed that hilly regions should have denser data spacing than plain areas. Within the test region, a data spacing of 3′×3′ with gravity observational errors 5 mGal was found to produce an acceptable gravimetric geoid. The produced gravimetric geoid had a pre-fit Root Mean Square Error (RMSE) of 15.6 cm when compared with GNSS-Levelling data at 27 stations located evenly across the study area.

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.

scholarly journals The Uganda Gravimetric Geoid Model 2014 Computed by The KTH Method

2015 ◽  
Vol 5 (1) ◽  
Author(s):  
L. E. Sjöberg ◽  
A. Gidudu ◽  
R. Ssengendo
Keyword(s):  
Gravity Field ◽  
Gravity Data ◽  
Geoid Determination ◽  
Geopotential Model ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Satellite Mission ◽  
Terrestrial Gravity ◽  
Gravity Field Recovery ◽  
Goce Satellite

AbstractFor many developing countries such as Uganda, precise gravimetric geoid determination is hindered by the low quantity and quality of the terrestrial gravity data. With only one gravity data point per 65 km2, gravimetric geoid determination in Uganda appears an impossible task. However, recent advances in geoid modelling techniques coupled with the gravity-field anomalies from the Gravity Field and Steady-State Ocean Circulation Explorer (GOCE) satellite mission have opened new avenues for geoid determination especially for areas with sparse terrestrial gravity. The present study therefore investigates the computation of a gravimetric geoid model overUganda (UGG2014) using the Least Squares Modification of Stokes formula with additive corrections. UGG2014 was derived from sparse terrestrial gravity data from the International Gravimetric Bureau, the 3 arc second SRTM ver4.1 Digital Elevation Model from CGIAR-CSI and the GOCE-only global geopotential model GO_CONS_GCF_2_TIM_R5. To compensate for the missing gravity data in the target area, we used the surface gravity anomalies extracted from the World Gravity Map 2012. Using 10 Global Navigation Satellite System (GNSS)/levelling data points distributed over Uganda, the RMS fit of the gravimetric geoid model before and after a 4-parameter fit is 11 cm and 7 cm respectively. These results show that UGG2014 agrees considerably better with GNSS/levelling than any other recent regional/ global gravimetric geoid model. The results also emphasize the significant contribution of the GOCE satellite mission to the gravity field recovery, especially for areas with very limited terrestrial gravity data.With an RMS of 7 cm, UGG2014 is a significant step forward in the modelling of a “1-cm geoid” over Uganda despite the poor quality and quantity of the terrestrial gravity data used for its computation.

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 Geoid Modelling of Kalimantan Island using Airborne Gravity Data and Global Geoid Model (EGM2008)

2021 ◽  
Vol 936 (1) ◽  
pp. 012029
Author(s):  
Zahroh Arsy Udama ◽  
Ira Mutiara Anjasmara ◽  
Arisauna Maulidyan Pahlevi ◽  
Anas Sharafeldin Mohamed Osman
Keyword(s):  
Standard Deviation ◽  
Gravity Anomaly ◽  
Gravity Data ◽  
Airborne Gravity ◽  
Gravimetric Geoid ◽  
Wave Component ◽  
Geoid Model ◽  
Free Air ◽  
Free Air Gravity ◽  
Local Geoid

Abstract The availability of geoids, especially in survey and mapping activities, is useful for transforming the geometric heights obtained from observations of the Global Navigation Satellite System (GNSS) into orthometric heights that have real physical meanings such as those obtained from waterpass measurements. If a geoid is available, the orthometric heights of points on earth can be determined using the GNSS heighting method. The use of modern survey and mapping instruments based on satellite observations such as GNSS is more efficient in terms of time, effort, and cost compared to the accurate waterpass method. According to the Indonesian Geospatial Information Agency (BIG) it is stated that the application of geoid as a national Vertical Geospatial Reference System has an adequate and ideal category if the accuracy is higher than 15 cm. Recent studies have shown that it is possible to generate local geoid models with centimetre accuracy by utilizing airborne gravity data. We calculate free-air gravity anomaly data is calculated by processing airborne gravity and GNSS data using the Stokes Integral method on AGR software. Next a geoid model is created by calculating the contribution of three components, namely the long wave component represented by the EGM2008 global geoid data model, the shortwave component represented by the Shuttle Radar Topography Mission (SRTM) data and the medium wave component represented by the free-air gravity anomaly data. The geoid model validation was carried out using the geoid fitting method for geoid accuracy by calculating the difference between the gravimetric geoid and the geometric geoid and comparing it with the global geoid model EGM2008 degrees 2190. As a result, the total geoid model accuracy value was determined to be 49.4 cm on gravimetric geoid undulations with a standard deviation of 7.1 cm. Meanwhile, the results of the EGM2008 geoid undulation accuracy test at 2190 degrees resulted in an accuracy of 51.9 cm with a standard deviation of 9.9 cm. These results indicate that the local geoid model from airborne gravity measurement data produces a geoid model with a higher accuracy than the global geoid model EGM2008 degrees 2190. However, the accuracy of the resulting data is still below the BIG standard of 15 cm, so further research is needed to produce a geoid model which conforms to the standard.

scholarly journals Verification of the Jakarta Geoid Model from the Gravity Data of 2.5 km Resolution with Gravimetric Geoid

2021 ◽  
Vol 873 (1) ◽  
pp. 012045
Author(s):  
D Ramdani ◽  
A N Safi’i ◽  
P Hartanto ◽  
N Oktaviani ◽  
M I Hariyono
Keyword(s):  
Gravity Data ◽  
Geoid Undulation ◽  
Satellite System ◽  
Orthometric Height ◽  
Geopotential Model ◽  
Gravimetric Geoid ◽  
Geoid Model ◽  
Speed Up ◽  
Global Navigation Satellite ◽  
Stokes Kernel

Abstract To use the Global Navigation Satellite System (GNSS) correctly, the height information should be transformed into orthometric height by subtracting geoid undulation from it. This orthometric height is commonly used for practical purposes. In 2015 geoid of Jakarta has been produced, and it has an accuracy of 0.076 m. In the year 2019, airborne gravimetry has been done for the entire Java Island. The area of DKI Province cannot be measured because there is inhibition from Airnav. For this reason, terrestrial gravimetric measurements are carried out in this region by adding points outside the previously measured area. To compute the geoid in the Jakarta region is needed the Global Geopotential Model (GGM). In this paper, the GMM used is gif48. The “remove and restore” method will be used in calculating the geoid in this Jakarta region. Besides that in this geoid calculation also uses Stokes kernel and FFT to speed up the calculation. The verification of the resulting geoid is carried with 11 points in DKI Jakarta Province. This verification produces a standard deviation of 0.116 m and a root mean square of 0.411 m.

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.

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