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EN
Successful development of geodetic satellite missions has aroused new inter-est in determining global and regional gravity field based on satellite data. Satellite altimetry data enable direct determination of the geoid over sea regions. In Egypt, where land and marine geophysical data are inadequate because of rough topography and economic reasons, the use of satellite altimetry data is of special importance. The northern Red Sea region has been selected as a site for case study of the current research, after applying spectral analysis to reveal near-surface structure, the residual geoid of the studied region shows a good correlation with the known geo-logic features. Moreover, satellite-based gravity data enhance small-scale features and agrees well with land and marine gravity data. Thus, geoid undulation and sat-ellite gravity data can be a complementary source of data to determine near-surface and deep structures.
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Content available remote Aktywnie i wirtualnie z geoidą
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EN
Solution of the gradiometric boundary value problems leads to three integral formulas. If we are satisfied with obtaining a smooth solution for the Earth’s gravity field, we can use the formulas in regional gravity field modelling. In such a case, satellite gradiometric data are integrated on a sphere at satellite level and continued downward to the disturbing potential (geoid) at sea level simultaneously. This paper investigates the gravity field modelling from a full tensor of gravity at satellite level. It studies the truncation bias of the integrals as well as the filtering of noise of data. Numerical studies show that by integrating Tzz with 1 mE noise and in a cap size of 7°, the geoid can be recovered with an error of 12 cm after the filtering process. Similarly, the errors of the recovered geoids from Txz,yz and Txx-yy, 2xy are 13 and 21 cm, respectively.
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Content available remote Precise geoid estimation in the Brennero area
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EN
The geoid estimation procedure in the Brennero area was divided in two steps. A data analysis was firstly performed to define possible data onconsistency and deficiencies. Then a gravimetric geoid was estimated according to the well known "remote-restore" procedure. Different techniques to account for the topographic signal were applied and the residual geoid estimate has been computed using Least Squares Collocation (LSC) and Fast Collocation. EGM96 and GPM98CR global geopotential models were also tested to select the one giving the best fit for the long wavelength component of the geopotential field of the area. Geoid undulations were computed on a regular 3`x3` geographical grid in the area 46.25
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Content available remote Mieszanie w układach
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EN
This paper investigates the terrain-aliasing effects on geoid determination using different gravimetric reduction schemes. The high resolution of digital terrain model (DTM), if available, should be used for every gravimetric reduction scheme since it can precisely map the details of the terrain. The reduction methods used in this study are the Rudzki inversion method. Helmert`s second method of condensation, the residual terrain model (RTM) method, and the Pratt-Hayford (PH) topographic-isostatic reduction technique. The effect of using different DTM grid resolutions of 6", 15", 30", 45", 1' d 2' on gravity anomalies and absolute geoid undulations is studied for each of these reduction schemes. A rugged area in the Canadian Rockies bounded by latitude between 49'N and 54'N and longitude between 236'E and 246'E is selected to conduct numerical tests. Our results suggest that a DTM grid resolution of 6" or higher is required for precise geoid determination with an accuracy of a decimetre or higher for any gravimetric reduction method chosen to treat the topographical masses above the geoid in rugged areas. The most precise geoid models obtained in this test are the ones obtained using Rudzki, Helmert, and RTM methods with 6" DTM resolution.
PL
W pracy badany jest wpływ rozdzielczości modelu terenu na wyznaczenie geoidy przy użyciu różnych metod redukcji grawimetrycznych. Numeryczny model terenu umożliwia precyzyjne mapowanie szczegółów terenowych, toteż, w miarę dostępności, powinien być on wykorzystywany w każdej redukcji grawimetrycznej. W badaniach użyto następujących metod redukcji grawimetrycznych: metoda inwersji Rudzkiego, druga metoda kondensacji Helmerta, metoda residualnego modelu terenu (RTM) i metoda topograficzno-izostatycznej redukcji Pratta-Hayforda (PH). Dla każdej z wybranych metod redukcji grawimetrycznej badano wpływ rozdzielczości 6", 15", 30", 45", 1' i 2' modelu terenu na obliczone anomalie grawimetryczne oraz na absolutne undulacje geoidy. Do przeprowadzenia testów numerycznych wybrano silnie pofałdowany obszar w kanadyjskiej części Gór Skalistych pomiędzy równoleżnikami 49'N i 54'N i pomiędzy południkami 236'E i 246'E. Uzyskane wyniki wskazują na to, że do wyznaczenia w terenie górzystym geoidy z dokładnością co najmniej decymetrową konieczne jest, niezależnie od wybranej metody redukcji grawimetrycznej, użycie modelu terenu o rozdzielczości co najmniej 6" w celu uwzględnienia efektów mas topograficznych ponad geoidą. W wyniku przeprowadzonych testów numerycznych najdokładniejsze modele geoidy uzyskano przy zastosowaniu metod Rudzkiego, Helmerta i RTM z użyciem DTM o rozdzielczości 6".
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Content available remote Supergeoida czy kolejny bubel?
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2002
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tom nr 8
41--42
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Spherical harmonic formulation of gravitational potential of the atmosphere depends on the analytical model of the atmospheric density which is used. Exponential and power models are two well-known mathematical tools which are used in atmospheric applications. This paper presents simple formulas for the harmonic coefficients of internal and external types of the atmospheric potential based on these models which can be used in most of the gravimetric aspects. It considers the atmospheric effect on the satellite gravity gradiometry data as an example for numerical investigations. The numerical studies on these data show that the maximum atmospheric effect is about 2 mE over Fennoscandia based on both models, and their differences are less than 0.1 mE. The difference between indirect atmospheric effects reaches 2 cm and 0.02 mGal on the geoid and gravity anomaly, respectively in this region.
EN
Only with satellites it is possible to cover the entire Earth densely with gravity field related measurements of uniform quality within a short period of time. How-ever, due to the altitude of the satellite orbits, the signals of individual local masses are strongly damped. Based on the approach of Petrovskaya and Vershkov we determine the gravity gradient tensor directly from the spherical harmonic coefficients of the recent EIGEN-GL04C combined model of the GRACE satellite mission. Satellite gradiometry can be used as a complementary tool to gravity and geoid information in interpreting the general geophysical and geodynamical features of the Earth. Due to the high altitude of the satellite, the effects of the topography and the internal masses of the Earth are strongly damped. However, the gradiometer data, which are nothing else than the second order spatial derivatives of the gravity potential, efficiently counteract signal attenuation at the low and medium frequencies. In this article we review the procedure for estimating the gravity gradient components directly from spherical harmonics coefficients. Then we apply this method as a case study for the interpretation of possible geophysical or geodynamical patterns in Iran. We found strong correlations between the cross-components of the gravity gradient tensor and the components of the deflection of vertical, and we show that this result agrees with theory. Also, strong correlations of the gravity anomaly, geoid model and a digital elevation model were found with the diagonal elements of the gradient tensor.
EN
GNSS observations carried out in a network of permanent stations are a complex systems which offer post-processing as well as corrections sent in real-time and the creation of so-called virtual observations. Currently, there are several Network-based Real Time Kinematic (NRTK) services around the world. In Poland, such a system has been in operation since June 2008, known as the Polish Active Geodetic Network (ASG-EUPOS). Three real-time correction services and two postprocessing services are currently used by users. NRTK technique uses GNSS observations gathered from a network of Continuously Operating Reference Stations (CORS) in order to generate more reliable error models that can mitigate the distance dependent errors within the area covered by the CORS. This method has been developed and tested considerably by many scientists during recent years. These studies have demonstrated the high centimeter accuracy that can be achieved using NRTK technique. This study analyzed the accuracy of the height determination with NRTK measurements using ASG-EUPOS. The results obtained show that RTK ASG-EUPOS height measurements are characterized by high precision, but the normal height measurements compared to the height measurements obtained from precise leveling, probably due to some systematic errors (the mean of many measurements differs significantly from the actual value) are not so accurate. In this case, fitting NRTK results to a precise leveling network may significantly improve the results. In presented test this resulted in reducing NRTK normal height determination errors by 70 percent.
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Content available remote EGM08 Globalna supergeoida
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EN
Computation of a new gravimetric geoid in Brunei was carried out Rusing terrestrial, airborne and altimetric gravity data and the EGM08 geopotential model by the collocation method. The computations were carried out by the „remove-restore” technique. In order to have better insight in the quality of input data the estimation of accuracy of the gravity data and geoid undulations from GPS/levelling data was carried out using EGM08 geopotential model. It shows a poor quality of GPS/levelling data. Result of the computation is the gravimetric geoid for the territory of Brunei computed by collocation method with an accuracy estimated below of ±0.3 m.
PL
Wyznaczenie przebiegu nowej geoidy na obszarze Brunei zostało zrealizowane z wykorzystaniem lądowych, lotniczych i altimetrycznych danych grawimetrycznych oraz modelu geopotencjału EGM08 metodą kolokacji. Obliczenia zostały przeprowadzone z wykorzystaniem techniki „removerestore”. W celu uzyskania lepszego wglądu, w jakość danych wejściowych oszacowano dokładność danych grawimetrycznych i geometrycznych odstępów geoidy od elipsoidy na punkach sieci GPS wykorzystując do tego celu model geopotencjału EGM08. Z przyprowadzonych oszacowań wynika przede wszystkim niska dokładność danych GPS/niwelacja. Wynikiem przeprowadzonych obliczeń jest grawimetryczna geoida dla obszaru Brunei, obliczona metodą kolokacji, której dokładność szacuje się poniżej ±0.3 m.
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Content available remote Modernizacja plus
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Content available remote Quasigeoid for the area of Poland computed by least squares collocation
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EN
The quasigeoid models recently computed in Poland e.g. (Łyszkowicz, Kryński 2006) and abroad e.g. (Al Marzooqi et al. 2005) were computed from Stokes'a integral by Fast Fourier Technique (FFT). At present because of significant capability of personal computers and proper strategy of computation more often for geoid/quasigeoid computation the least squares collocation is used. In the present paper is described the first quasigeoid computation by least collocation for the area of Poland. The quasigeoid model was computed in two version, namely from the gravity data only and from the gravity and vertical deflections data simultaneously. The differences between these two versions are small and do not exceed 1-2 mm. In order to evaluate the advantages coming from the collocation the third pure gravimetric model using Stokes'a integral was computed and compared with the gravimetric model computed by collocation. The differences between these versions are significant and at the level of 20 cm, beside the collocation model is better.
PL
Wszystkie ostatnio liczone grawimetryczne modele quasi-geoidy w Polsce (np. Łyszkowicz, Kryński 2006) i na świecie (np. Al Marzooqi et al. 2005) były liczone na podstawie całki Stokesa, do której oszacowania wykorzystywano szybką transformatę Fouriera (FFT). Obecnie ze względu na znaczne możliwości komputerów oraz odpowiednio opracowaną strategię obliczeniową coraz częściej do wyznaczenia przebiegu geoidy/quasi-geoidy wykorzystuje się metodę kolokacji. W pracy przedstawiono pierwsze w Polsce wyznaczenie przebiegu quasi-geoidy metodą kolokacji. Model quasi-geoidy wyznaczono w dwóch wariantach, a mianowicie tylko z danych grawimetrycznych, a następnie łącznie z danych grawimetrycznych i astro-geodezyjnych odchyleń pionu. Różnice między tymi dwoma wariantami są minimalne i wynoszą 1-2 mm. W celu oceny korzyści wynikających z metody kolokacji grawimetryczną quasi-geoidę policzono również metodą FFT i porównano z quasi-geoidą obliczoną metodą kolokacji. Z przeprowadzonego porównania wynika, że rozbieżność między modelami jest rzędu 20 cm, z tym że quasi-geoida kolokacyjna jest lepsza.
EN
The article describes the estimation of covariance parameters in Least Squares Collocation (LSC) by Leave-One-Out (LOO) validation, which is often considered as a kind of cross validation (CV). Two examples of GNSS/leveling (GNSS/lev) geoid data, characterized by different area extent and resolution are applied in the numerical test. A special attention is focused on the noise, which is not correlated in this case. The noise variance is set to be homogeneous for all points. Two parameters in three covariance models are analyzed via LOO, together with a priori noise standard deviation, which is a third parameter. The LOO validation finds individual parameters for different applied functions i.e. different correlation lengths and a priori noise standard deviations. Diverse standard deviations of a priori noise found for individual datasets illustrate a relevance of applying LOO in LSC. Two examples of data representing different spatial resolutions require individual noise covariance matrices to obtain optimal LSC results in terms of RMS in LOO validation. The computation of appropriate a priori noise variance is however difficult via typical covariance function fitting, especially in the case of sparse GNSS/leveling geoid data. Therefore LOO validation may be helpful in describing how the a priori noise parameter may affect LSC result and a posteriori error.
PL
Popularyzacja technik GPS i globalnych układów odniesienia, spowodowała wzrost praktycznego znaczenia łączenia pomiarów satelitarnych z klasycznymi. Dzięki odpowiednio dokładnemu modelowi geoidy, wykorzystanie technik satelitarnych daje możliwość realizacji pomiarów wysokościowych o dokładnościach porównywalnych z niwelacją geometryczną. Niewiele publikacji poświęconych praktycznym aspektom wdrożenia techniki GPS nie sprzyja jej upowszechnieniu w praktyce inżynierskiej. Przedstawione wyniki nawiązań wysokościowych osnów kopalnianych w rejonie Inowrocławia są przykładem potwierdzenia celowości wykorzystania techniki GPS w tego typu pracach, również w aspekcie ekonomicznym.
EN
The popularization of GPS technique and global positioning system has led to increase practical importance of satellite and classic survey combination. Thanks to adequately accurate geoid model advantages of satellite techniques proves execution of height measurements with accuracy that equals classic spirit levelling. The most discussions about GPS techniques concern reference system or geoid models. The small number of papers dealing with the problem of practical uses resulting from application of GPS technique to engineering practice (in the range of height measurements) does not allow to their dissemination (what implies economical effect as well). Presented paper discusses results of height measurements on Inowrocław region (reference measurements for mines' networks) and it is an example proving utility of GPS measurements in such works.
EN
The main theme of this paper is to study two important aspects of precise geoid determination using Helmert's second method of condensation. This work illustrates via numerical investigations the importance of using actual density information of topographical bulk and the effects that different gravimetric reductions have on gravity interpolation in Helmert geoid computational process, in addition to the commonly used Bouguer scheme. A rugged area in the Canadian Rockies bounded by latitude between 49'N and 54'N and longitude between 236'E and 246'E is selected to carry out numerical investigations. The lateral density information is used in all steps of the Helmert geoid computational process. The Bouguer and residual terrain modelling (RTM) topographic reductions, the Rudzki inversion scheme, and the topographic-isostatic reductions of Pratt-Hayford (PH) and Airy-Heiskanen (AH) are for gravity interpolation. Results show that the density information should be applied in all steps of the Helmert geoid computational process and that the topographic-isostatics gravimetric reduction schemes like the PH or AH models or the RTM reduction, should be applied for smooth gravity interpolation instead of the commonly used Bouguer reduction scheme for precise Helmert geoid determination.
PL
Tematem pracy jest badanie dwóch istotnych aspektów wyznaczania geoidy przy zastosowaniu drugiej metody kondensacji Helmerta. Przy użyciu badań numerycznych zilustrowane zostało w pracy znaczenie wykorzystania aktualnej informacji o gęstości topografii terenu oraz efektów różnych rodzajów redukcji grawimetrycznych na interpolację przyspieszenia siły ciężkości w procesie obliczania geoidy Helmerta, uzupełniających powszechnie stosowaną procedurę opartą na anomaliach Bougera. Do przeprowadzenia testów numerycznych wybrano silnie pofałdowany obszar w kanadyjskiej części Gór Skalistych pomiędzy równoleżnikami 49'N i 54'N i pomiędzy południkami 236'E i 246'E. We wszystkich krokach procesu obliczania geoidy Helmerta używano informacji o rozkładzie gęstości warstwy topografii nad poziomem morza. Do interpolacji przyspieszenia siły ciężkości wykorzystano anomalie Bougerta, redukcje topograficzne w oparciu o residualny model terenu (RTM), redukcje Rudzkiego, redukcje topograficzno-izostatyczne Pratta-Hayforda (PH) i Airy-Heiskanena (AH). Uzyskane wyniki wskazują na to, że informacja o gęstości topografii powinna być używana we wszystkich krokach procesu obliczania geoidy Helmerta oraz, że topograficzno-izostatyczna redukcja grawimetryczna, taka jak PH, AH lub RTM, wygładzająca interpolację przyspieszenia siły ciężkości powinna byś stosowana do precyzyjnego wyznaczania geoidy Helmerta zamiast powszechnie stosowanej metody opartej na anomaliach Bouguera.
EN
Temporal mass variations in the Earth system, which can be detected from the Gravity Recovery and Climate Experiment (GRACE) mission data, cause temporal variations of geoid heights. The main objective of this contribution is to analyze temporal variations of geoid heights over the area of Poland using global geopotential models (GGMs) developed on the basis of GRACE mission data. Time series of geoid height variations were calculated for the chosen subareas of the aforementioned area using those GGMs. Thereafter, these variations were analyzed using two different methods. On the basis of the analysis results, models of temporal geoid height variations were developed and discussed. The possibility of prediction of geoid height variations using GRACE mission data over the area of Poland was also investigated. The main findings reveal that the geoid height over the area of Poland vary within 1.1 cm which should be considered when defining the geoid model of 1 cm accuracy for this area.
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Content available Gravity field modelling and gravimetry
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EN
The summary of research activities concerning gravity field modelling and gravimetric works performed in Poland in the period of 2011-2014 is presented. It contains the results of research on geoid modelling in Poland and other countries, evaluation of global geopotential models, determination of temporal variations of the gravity field with the use of data from satellite gravity space missions, absolute gravity surveys for the maintenance and modernization of the gravity control in Poland and overseas, metrological aspects in gravimetry, maintenance of gravimetric calibration baselines, and investigations of the nontidal gravity changes. The bibliography of the related works is given in references.
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