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Guimarães, Gabriel do Nascimento. "A geoid model in the state of São Paulo: an attempt for the evaluation of different methodologies." Universidade de São Paulo, 2013. http://www.teses.usp.br/teses/disponiveis/3/3138/tde-30072013-234021/.
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The purpose of this thesis is to compute and to evaluate the geoid model in the State of São Paulo from two methodologies (Stokes integral through the Fast Fourier Transform - FFT and Least Squares Collocation LSC). Another objective of this study is to verify the potentiality of GOCE-based. Therefore, a brief study about mathematical foundations and fundamentals of Physical Geodesy is carried out. Some features of the Global Geopotential Models (GGMs) are discussed, as well as an overview of the new gravimetric missions. A special attention is given to GOCE mission. The theory related to Stokes integral and Least Squares Collocation is also discussed in this work. The spectral decomposition was employed in the geoid models computation and the long wavelength component was represented by EGM2008 up to degree and order 150 and 360 and GOCE-based models up to 150. The models were compared in terms of geoid height residual and absolute and relative comparisons from GPS/leveling and the results show consistency between them. Also, a comparison in the mountain regions was carried out to verify the methodologies behavior in this area; the results showed that LSC is less consistent than FFT. Regarding GOCE-based models, 13 were tested, besides EGM2008. The evaluation was performed in terms of geoid height comparison obtained by GGMs over GPS/leveling and in terms of gravity disturbance. The evaluation shows that DIR _R3 and TIM_R3 presented more compatible results. The reason for the choice of São Paulo state is that there are a lot of geodetic activities and important engineering works that require the use of a height system. Furthermore, there are a lot of gravity and GPS/leveling data all around the state.Esta tese tem como propósito o cálculo e a avaliação do modelo geoidal no Estado de São Paulo a partir da aplicação de duas metodologias (integral de Stokes por meio da Transformada Rápida de Fourier FFT e a colocação por mínimos quadrados Least Squares Collocation LSC). Outro objetivo deste trabalho é verificar a potencialidade dos mais recentes Modelos Globais do Geopotential (MGGs) baseados nos dados do satélite GOCE. Para tanto, um breve estudo é realizado sobre os fundamentos matemáticos e os da Geodésia Física. Algumas características dos MGGs são discutidas, bem como uma visão global das novas missões gravimétricas. Uma atenção especial é dada a missão do satélite GOCE. A teoria referente à integral de Stokes e a colocação por mínimos quadrados são outros temas discutidos no trabalho. A decomposição espectral foi empregada no cálculo dos modelos geoidais e a componente de longo comprimento de onda foi representada pelo modelo EGM2008 até grau e ordem 150 e 360 e aqueles baseados na missão GOCE até 150. Os modelos foram comparados entre si em termos do resíduo da altura geoidal e na forma absoluta e relativa por meio das estações GPS/RN. Os resultados apontaram consistência entre os modelos em termos de diferença média quadrática. Também foi realizado um estudo na região montanhosa a fim de verificar o comportamento das metodologias; os resultados mostraram que a LSC é menos consistente do que a FFT. No que diz respeito aos modelos baseados na missão GOCE, 13 foram testados, além do EGM2008. A avaliação foi realizada em termos da comparação da altura geoidal obtidas pelos MGGs com as estações GPS/nivelamento e em termos do distúrbio de gravidade. A avaliação mostra que os modelos DIR_R3 e TIM_R3 apresentaram os resultados mais compatíveis. A escolha do estado de São Paulo está relacionada à grande quantidade de trabalhos geodésicos e atividades na área da engenharia e que necessitam da utilização de um sistema altimétrico. Além disso, a grande quantidade de dados gravimétricos e de estações GPS/RN é mais uma justificativa para a realização do trabalho.
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Danila, Uliana. "Mold2012 : a new gravimetric quasigeoid model over Moldova." Licentiate thesis, KTH, Geodesi och geoinformatik, 2012. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-105755.
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In order to be able to use the operational Moldavian GNSS Positioning System MOLDPOS efficiently for the determination of normal heights in surveying engineering, e.g. during the construction of a road, an accurate quasigeoid model is needed. The main goal of this thesis is to present a new gravimetric quasigeoid model for Moldova (Mold2012), which has been determined by applying the Least Squares Modification of Stokes’ formula with Additive corrections (LSMSA), also called the KTH method. Due to limited coverage of gravity data, the integration area is often limited to a small spherical cap around the computation point, which leads to a truncation error for geoid height. Molodensky et al. (1962) showed that the truncation error can be reduced by the modification of Stokes’ formula, where the measured gravity data are combined with the low-frequency component of the geoid from a Global Gravitational Model (GGM). The LSMSA technique combines the GGM and the terrestrial data in an optimum way. In order to find the most suitable modification approach or cap size it is necessary to compare the gravimetric height anomalies with the GPS/levelling derived height anomalies, and for this purpose we use a GPS/levelling dataset that consists of 1042 points with geodetic coordinates in the MOLDREF99 reference system and normal heights at the same points given in the height system Baltic 77. The magnitude of the additive corrections varies within an interval from -0.6 cm to -4.3 cm over the area of Moldova. The quasigeoid model which results from combining the ITG-Grace02s solution (with n = M = 170, ψ0 = 3° and σΔg = 10 mGal) and the solution obtained from the modified Stokes’ formula together with the additive correction gives the best fit for the GPS/levelling data with a standard deviation (STD) of ±7.8 cm. The evaluation of the computed gravimetric quasigeoid is performed by comparing the gravimetric height anomalies with the GPS/levelling derived height anomalies for 1042 points. However, the above heterogeneous data include outliers, and in order to find and eliminate these, a corrector surface model is used. This surface provides a connection to the local vertical when the GNSS technique is used. After the elimination of the suspicious outliers (170 points) according to a 2-RMS test, a new corrective surface was computed based on the remaining 872 GPS/levelling points, and the STD of residuals became ±4.9 cm. The STD value for the residuals according to the order of the levelling network for the Mold2012 fitted to the local vertical datum is 3.8 cm for the I-order, 4.3 cm for the II-order, 4.5 cm for the III-order and 5.0 cm for the IV-order levelling network. But the STD of the residuals for the 18 control points indicates a better result where the STD is 3.6 cm and RMS is 3.9 cm and the min and max value of residuals is -5.3 cm and 9.0 cm, respectively. As the STD of the differences in height anomaly are not just the standard error of the height anomalies (quasigeoid model), but it contains also the standard errors of GPS heights and of normal heights. Assuming that the latter STDs are 3 cm and 3.5 cm, respectively, the STD of Mold2012 is estimated to 1.7 cm.QC 20121127
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Inerbayeva, (Shoganbekova) Daniya. "Determination of a gravimetric geoid model of Kazakhstan using the KTH-method." Thesis, KTH, Geoinformatik och Geodesi, 2010. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-52284.
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This study work deals with the determination of the gravimetric geoid model for Kazakhstan by using the KTH-method. A number of data sets were collected for this work, such as the gravity anomalies, high-resolution Digital Elevation Model (DEM), Global Geopotential Models (GGMs) and GPS/Levelling data. These data has been optimally combined through the KTH approach, developed at the Royal Institute of Technology (KTH) in Stockholm. According to this stochastic method, Stokes’ formula is being used with the original surface gravity anomaly, which combine with a GGM yields approximate geoid heights. The corrected geoid heights are then obtained by adding the topographic, downward continuation, atmospheric and ellipsoidal corrections to the approximate geoid heights. To compute the geoid model for Kazakhstan as accurately as possible with available data set different numerical tests have been performed: Choice of the best fit geopotential model in the computation area Investigations for the best choice of the initial condition for determination of the least-squares parameters Selection of the best parametric model for reducing the effect of the systematic error and data inconsistencies between computed geoid heights and GPS/Levelling heights. Finally, 5'x5' Kazakh gravimetric geoid (KazGM2010) has been modelled.
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Abdalla, Ahmed. "Determination of a gravimetric geoid model of Sudan using the KTH method." Thesis, KTH, Geodesi och satellitpositionering, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-199670.
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The main objective of this study is to compute a new gravimetric geoid model of Sudan using the KTH method based on modification of Stokes’ formula for geoid determination. The modified Stokes’ formula combines regional terrestrial gravity with long-wavelength gravity information provided by the global gravitational model (GGM). The collected datasets for this study contained the terrestrial gravity measurements, digital elevation model (DEM), GPS/levelling data and four global gravitational Models (GGMs), (EGM96, EIGEN-GRACE02S, EIGEN-GL04C and GGM03S). The gravity data underwent cross validation technique for outliers detection, three gridding algorithms (Kriging, Inverse Distance Weighting and Nearest Neighbor) have been tested, thereafter the best interpolation approach has been chosen for gridding the refined gravity data. The GGMs contributions were evaluated with GPS/levelling data to choose the best one to be used in the combined formula. In this study three stochastic modification methods of Stokes’ formula (Optimum, Unbiased and Biased) were performed, hence an approximate geoid height was computed. Thereafter, some additive corrections (Topographic, Downward Continuation, Atmospheric and Ellipsoidal) were added to the approximated geoid height to get corrected geoid height. The new gravimetric geoid model (KTH-SDG08) has been determined over the whole country of Sudan at 5′ x 5′ grid for area ( 4 ). The optimum method provides the best agreement with GPS/levelling estimated to 29 cm while the agreement for the relative geoid heights to 0.493 ppm. A comparison has also been made between the new geoid model and a previous model, determined in 1991 and shows better accuracy. ≤φ ≤ 23 , 22 ≤ λ ≤ 38 Keywords: geoid model, KTH method, stochastic modification methods, modified Stokes’ formula, additive corrections.
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Daras, IIias. "Determination of a gravimetric geoid model of Greece using the method of KTH." Thesis, KTH, Geodesi och satellitpositionering, 2008. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-199682.
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The main purpose of this study is to compute a gravimetric geoid model of Greeceusing the least squares modification method developed at KTH. In regional gravimetricgeoid determination, the modified Stokes’s formula that combines local terrestrial datawith a global geopotential model is often used nowadays.In this study, the optimum modification of Stokes’s formula, introduced by ProfessorSjöberg, is employed so that the expected mean square error (MSE) of all possiblesolutions of the general geoid model is minimized. According to this stochasticmethod, the Stokes’s formula is being used with the original surface gravity anomalywhich combined with a GGM yields an approximate geoid height. The corrected geoidheight is then obtained by adding the topographic, downward continuation,atmospheric and ellipsoidal corrections to the approximate geoid height.The dataset used for the computations, consisted of terrestrial gravimetricmeasurements, a DEM model and GPS/Levelling data for the Greek region. Threeglobal geopotential models (EGM96, EIGEN-GRACE02S, EIGEN-GL04C) weretested for choosing the best GGM to be combined into the final solution. Regarding theevaluation and refinement of the terrestrial gravity measurements, the cross-validationtechnique has been used for detection of outliers.The new Greek gravimetric geoid model was evaluated with 18 GPS/Levelling pointsof the Greek geodetic network. The absolute agreement between the gravimetric andthe GPS/Levelling geoid height was estimated at 27 cm while the relative agreement at0.9 ppm. In a case of study the absolute accuracy of the model was estimated at 14 cm.The geoid model computed in this study was also compared with some previous Greekgeoid models, yielding better external accuracy than them.
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Berntsson, Jenny. "A study on the quality of the NKG2015 geoid model over the Nordic countries." Thesis, Högskolan Väst, Avdelningen för Matematik, Data- och Lantmäteriteknik, 2019. http://urn.kb.se/resolve?urn=urn:nbn:se:hv:diva-13960.
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Geoidmodellen NKG2015 (Nordiska kommissionen för geodesi) är den senaste geoidmodellen över Norden. Det har inte publicerats någon forskning om kvaliteten på den här nya modellen, därför kan den här studien bidra till forskningen inom ämnet. Det är viktigt att vara medveten om begränsningarna och kvaliteten på den geoidmodell som används vid mätning av höjder. Om kvaliteten på geoidmodellen inte är känd så kommer kvaliteten på höjdmätningarna inte heller att vara känd. Detta kan skapa problem när mätningarna används i projekt där precision är viktigt. För att undersöka kvaliteten på geoidmodellen NKG2015 har geoidhöjderna beräknade från modellen jämförts med geoidhöjder som fås från mätning med metoden GNSS (Global Navigation Satellite Systems) /avvägning vid samma punkter. Slutningsfelet mellan geoidhöjderna från geoidmodellen och geoidhöjderna från mätningarna har analyserats med statistiska metoder. Slutningsfelens normalitet testas och analysen utförs på ofiltrerad data samt data som filtrerats med två olika konfidensintervall, 95% och 99,7%. Detta för att filtrera bort eventuella avvikande värden. Eventuella trender i datan jämnas ut med en metod baserad på minsta kvadratmetoden. Studiens resultat visar att filtrering av slutningsfelen generellt gör datan mer normalfördelad, men så är inte fallet för alla länder. I de flesta fall förbättras normaliteten även genom att jämna ut trender i datan. I processen med att jämna ut trender används en korrigerande yta med ett specificerat antal parametrar. Topografin i varje land spelar en stor roll när beslut ska fattas om hur många parametrar som behövs i den korrigerande ytan. Länder med höga berg och stora höjdskillnader så som Norge har en större osäkerhet i datan och kräver fler parametrar i den korrigerande ytan. Danmark är ett land med relativ platt topografi och behöver inte lika många parametrar i den korrigerande ytan som Norge för att effektivt jämna ut trender. Det finns givna värden på felen för datan som är uppmätt med GNSS/avvägning, dessa fel stämmer generellt inte överens med slutningsfelen. För Finland är det givna felet för GNSS/avvägning större än det borde vara medan felen för GNSS/avvägning i de andra länderna är något mindre än vad slutningsfelen antyder. De givna, uppskattade felen för geoidmodellen NKG2015 är 10 mm för Sverige och Danmark, 22 mm för Norge och 12 mm för Finland. Dessa fel är rimliga men stämmer inte helt överens med de givna felen för GNSS/avvägning i relation till slutningsfelen. Under antagandet att de givna felen för GNSS/avvägning är korrekta kan följande konfidensintervall uppskattas för geoidfelen; 06,5mm för Sverige, 1,8-5,2mm för Danmark, 14,8-17,7mm för Norge och 0-0mm för Finland.The NKG2015 (Nordic Geodetic Commission) geoid model is the most recent official geoid model over the Nordic countries. There has been no previous research published on the quality of this model, therefore, this study may be a valuable contribution to the research in this area. It is important to be aware of the limitations and quality of the geoid model used when measuring heights. If the quality of the geoid is not known, the quality of the measured heights will also be uncertain. This might cause problems when the measured heights are used in projects where great precision is vital. Measured GNSS (Global Navigation Satellite Systems)/levelling data has been compared to the computed geoid heights from the NKG2015 geoid model at the corresponding points to investigate the quality of this model. The misclosures between the geoid height, obtained from the GNSS/levelling data and the geoid heights from the NKG2015 geoid model have been analysed by statistical methods. The normality of the misclosures is tested, and the analysis is performed on unfiltered and filtered misclosures with confidence intervals (CIs) of 95% and 99.7% to remove probable outliers. Trends in the misclosures are removed with a least-squares detrending method. The result of the study shows that filtering the misclosures generally makes them more normally distributed, but this is not the case for all countries. Detrending the misclosures improves the normality in most cases. In this process, a corrective surface with a specified number of parameters is fitted to the misclosures to remove trends. The topography of each country is very important when deciding which corrective surface that should be used in the detrending process. Countries with rough topography such as Norway has greater uncertainty in its heights and needs a corrective surface with more parameters than flatter countries such as Denmark. There are some estimates for the errors for the GNSS/levelling data which are not all in agreement with the misclosures. The GNSS/levelling error in Finland is greater than it should be. The given, estimated errors of the NKG2015 geoid model are 10 mm for Sweden and Denmark, 22 mm for Norway and 12 mm for Finland. These errors are reasonable, but not in perfect agreement with the given errors of the GNSS/levelling measurements in relation to the misclosures. Based on the assumption that the GNSS/levelling errors are correct, confidence intervals of the geoid error can be estimated. These estimated intervals are 0-6.5mm for Sweden, 1.8-5.2mm for Denmark, 14.8-17.7mm for Norway and 0-0mm for Finland. The confidence interval for Finland is not realistic because it is based on the assumption that the GNSS/levelling error is correct.
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Nunes, Vagner Conceição. "Testes sobre a eficiência do modelo do geopotencial EGM2008 na cidade de Porto Alegre." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2010. http://hdl.handle.net/10183/26992.
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Este estudo apresenta o teste da eficiência do Earth Global Model 2008 (EGM2008) na geração de um modelo geoidal local, através da compatiblização com a ondulação obtida por posicionamento GPS (Global Positioning System) em 63 Referências de Nível (RN’s) localizadas no município de Porto Alegre, Rio Grande do Sul. O objetivo geral da dissertação foi analisar a exatidão do modelo geoidal gerado a partir dos coeficientes do modelo geopotencial EGM2008 para nivelamento por GPS no município de Porto Alegre e os objetivos específicos foram: a avaliação do modelo na região de Porto Alegre, a comparação das ondulações geoidais do EGM2008 (NEGM2008) com as ondulações geoidais em 63 RN’s (NGPS), o ajustamento da componente sistemática do geoide que é a diferença entre NEGM2008 e NGPS e a geração do modelo geoidal local compatibilizado para Porto Alegre. O método adotado apresenta as seguintes etapas: cálculo das ondulações geoidais nas RN’s; eliminação de erros grosseiros; geração do modelo geoidal através dos dados do EGM2008 com resolução de 7” de arco; cálculo da componente sistemática do geoide; ajustamento da componente sistemática através de transformação por polinômio de 2° grau com seis parâmetros pelo Método dos Mínimos Quadrados (MMQ). Os resultados obtidos foram: os parâmetros que compatibilizam o modelo geoidal global com o local e modelo geoidal local compatibilizado no formato raster, contendo as ondulações geoidais para todo o município. O novo modelo apresentou erro médio de 1,9 cm e desvio padrão de 7,2 cm. Os resultados da dissertação confirmam que é possível reduzir o erro associado ao modelo global através dos procedimentos adotados. Dessa maneira, conclui que o método utilizado reduziu o valor médio da componente sistemática de 15,4 cm para 1,9 cm após o ajustamento.This study presents the Earth Global Model 2008’s (EGM2008) efficiency test on the conception of a local geoid model. The results were acquired through the undulation compatibility obtained by GPS (Global Positioning System) in 63 Bench Mark (BM) located in Porto Alegre, Rio Grande do Sul state, Brazil. The aim of this research was to analyze the accuracy of the geoid model generated from the geopotential model EGM2008’s coefficients to GPS leveling in Porto Alegre. The specific goals were the evaluation of the model in Porto Alegre region’s, the comparison between the EGM2008 (NEGM2008) geoid undulations and the geoid undulations in 63 BM (NGPS), and the adjustment of geoid’s systematic component, that is the difference between NEGM2008 and NGPS and the local geoid model’s conception to Porto Alegre. The method used presents the following steps: geoid undulation on RN’s’s computation; elimination of gross errors; geoid model’s conception through EGM2008’s data with resolution of 7” of arch; geoid’s systematic component computation; adjustment of the systematic component through transformation of 2nd degree polynomial with six parameters by the method of Least Squares. The results were: the parameters that make the models global and local compatible, and local geoid model compatible in raster format, containing the geoid undulations for the entire municipality. The new model showed 1.9 of mean error and 7.2 cm of standard deviation. Through the procedures adopted, the dissertation results’ confirm that it is possible to reduce the error associated of the the global model. Therefore, the conclusion is that the method used reduced the mean error of the systematic component from 15,4 cm to 1.9 cm, after the adjustment.
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Ulotu, Prosper E. "Geoid model of Tanzania from sparse and varying gravity data density by the KTH method /." Stockholm : Skolan för Arkitektur och samhällsbyggnad, Kungliga Tekniska högskolan, 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-10270.
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Ulotu, Prosper. "Geoid Model of Tanzania from Sparse and Varying Gravity Data Density by the KTH method." Doctoral thesis, KTH, Geodesi (stängd 20110301), 2009. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-10270.
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Developed countries are striving to achieve a cm geoid model. Most developing countries/regions think that the situation in their areas does not allow even a few decimetre geoid model. GNSS, which provides us with position, is one of the greatest achievements of the present time. Conversion of ellipsoidal height to orthometric height, which is more useful, requires an accurate geoid model. In spite of the sparse terrestrial gravity data of variable density, distribution and quality (a typical situation in developing countries), this study set out to develop as accurately as possibly achievable, a high quality geoid model of Tanzania. Literature review of three more preferred geoid methods came to a conclusion, that the Royal Institute of Technology of Sweden (KTH) method of least squares modification of Stokes formula (LSMS) with additive corrections (AC) is the most suitable for this research. However, even with a good method, the accuracy and the quality of a geoid model depend much on the quality of the data. In this study, a procedure to create a gravity database (GDB) out of sparse data with varying density, distribution and quality has been developed. This GDB is of high density and full coverage, which ensures presence of high and low gravity frequencies, with medium frequencies ranging between fair and excellent. Also an alternative local/regional Global Gravitational Model (GGM) validation method based on quality terrestrial point surface gravity anomaly has been developed. Validation of a GGM using the new approach of terrestrial point gravity and GPS/Levelling, gave the same results. Once satisfactorily proved, the method has extra advantages. The limits of Tanzania GDB (TGDB) are latitudes 15 ° S to 4 ° N and longitudes 26 ° E to 44 ° E . Cleaning and quality control of the TGDB was based on the cross validation (XV) by the Kriging method and Gaussian distribution of the XV residuals. The data used in the LSMS with AC to develop a new Tanzania gravimetric geoid model 2008, TZG08, are 1′ ×1′ clean and statistically tested surface gravity anomalies. 39,677 point gravity in land and 57,723 in the ocean were utilised. Pure satellite ITGGRACE03S GGM to degree 120 was used to determine modification parameters and long-wavelength component of the geoid model. 3′′ Shuttle Radar Topographic Mission (SRTM) Digital Elevation Model (DEM), ITG-GRACE03S to degree 120 and EIGENCG03C to degree 360 combined GGM qualified to patch the data voids in accordance to the method of this research. TZG08 is referred to Geodetic Reference System 1980 (GRS80), and its extents are latitudes 12 ° S to 1 ° N and longitudes 29 ° E to 41 ° E . 19 GPS/levelling points qualified to assess the overall accuracy of TZG08 as 29.7 cm, and upon approximate removal of GPS and orthometric systematic effects, the accuracy of TZG08 is 27.8 cm. A corrector surface (CS) for conversion of GPS height to orthometric height referred to Tanzania National Height Datum (TNHD) has been created for a part of TZG08. Using the CS and TZG08, orthometric height of Mt. Kilimanjaro is re-established as it was in 1952 to be 5,895 m above the TNHD, which is still the official height of the mountain.QC 20100813
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Ssengendo, Ronald. "A height datum for Uganda based on a gravimetric quasigeoid model and GNSS/levelling." Doctoral thesis, KTH, Geodesi och satellitpositionering, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-172547.
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This study is devoted to the determination of a high resolution gravimetric geoid model for Uganda based on the optimal combination of terrestrial and satellite gravity anomalies using the method of Least Squares Modification of Stokes’ formula with additive corrections. Specifically the study investigates the current status of the existing Uganda Vertical Network relative to the requirements of a modern height datum and includes a detailed evaluation and validation of terrestrial gravity data, several digital elevation models and some recent global geopotential models. Finally a new height datum based on a gravimetric quasigeoid model and Global Navigation Satellite Systems (GNSS)/levelling is proposed. In this thesis, the Uganda Gravimetric Geoid Model 2014 (UGG2014) is computed from several datasets which, include 7839 terrestrial gravity data points from the International Gravimetric Bureau, the 3 arc second Shuttle Radar Topography Mission digital elevation model and a recent Gravity field and steady-state Ocean Circulation Explorer-only global geopotential model. To compensate for the missing gravity data in the target area, the surface gravity anomalies extracted from the World Gravity Map 2012 were used. Outliers in the terrestrial gravity data were detected using the cross-validation technique which, also estimated the accuracy of the remaining terrestrial gravity data as 9 mGal. Based on 12 GNSS/levelling data points distributed over Uganda, the root mean square fit of UGG2014 before and after the 4-parameter fit is 16 cm and 9 cm, respectively. The study has revealed that the heights of the Uganda Vertical Network are normal-orthometric heights for which the quasigeoid is the closest approximation to the zero reference surface. Consequently, the Uganda Gravimetric Quasigeoid Model 2014 (UGQ2014) was derived from the UGG2014 with the quasigeoid-geoid separation computed from the Earth Gravitational Model 2008 complete to degree/order 2160 of spherical harmonics. The root mean square fit of UGQ2014 versus GNSS/levelling is 15 cm and 8 cm before and after the 4-parameter fit, respectively, which shows that the quasigeoid model fits GNSS/levelling better than the geoid model. Thus a new height datum based on UGQ2014 and GNSS/levelling was determined as a practical solution to the determination of heights directly from GNSS. Evaluated with 4 independent GNSS/levelling points, the root mean square fit of the new height datum is 5 cm better than using the quasigeoid model alone. With an average parts-per-million of 29 in the relative test, the new height datum satisfies the precision and accuracy requirements of third order precise levelling. Overall, the results show that UGG2014 and UGQ2014 agree considerably better with GNSS/levelling than any other recent regional/global gravimetric geoid models. Therefore, both gravimetric solutions are a significant step forward in the modelling of a “1-cm geoid” over Uganda given the poor quality and quantity of the terrestrial gravity data used for computation.QC 20150831
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Alves, Alexandre de Paula. "Sobre a técnica Fast Collocation (colocação rápida) na determinação do geóide do estado de São Paulo utilizando dados das missões CHAMP e GRACE." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2007. http://hdl.handle.net/10183/11269.
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Os objetivos deste trabalho são: determinar o geóide do Estado de São Paulo (SP) pela técnica matemática Fast Collocation utilizando o modelo do geopotencial CG01c, derivado das novas missões gravimétricas de satélite CHAMP e GRACE, avaliar esse geóide através de estações com alturas geoidais conhecidas e do geóide calculado por Souza (2002), e apresentar uma nova abordagem que amplia a idéia sobre o sensoriamento remoto. O modelo do geopotencial CG01c, obtido com dados das missões CHAMP, GRACE e dados de superfície, e desenvolvido até o grau e ordem 360, foi utilizado para geração de anomalias gravimétricas, as quais foram subtraídas das anomalias gravimétricas terrestres, gerando as anomalias gravimétricas residuais. Essas anomalias residuais serviram de dados de entrada no programa FASTCOL para gerar as alturas geoidais residuais. A essas alturas geoidais residuais foi adicionado o modelo CG01c, representativo dos longos comprimentos de onda do campo de gravidade terrestre, produzindo-se o modelo geoidal chamado GEÓIDESP_FC_2007. Este geóide foi avaliado e posteriormente comparado com o Modelo Digital do Geóide Regular (MDGR). Ao final, argumentos foram apresentados para justificar o estudo do campo de gravidade da Terra no âmbito do sensoriamento remoto.The objectives of this work are: to determine the geoid of the São Paulo (SP) State applying the mathematical technique so-called Fast Collocation using the CG01c geopotential model, from the new satellite gravity missions CHAMP and GRACE, to evaluate that geoid by stations with known geoidal heights and by the geoid determined by Souza (2002), and to show a new approach that enlarges the idea about the remote sensing. The CG01c geopotential model, obtained from missions CHAMP, GRACE and surface data, and developed up to degree and order 360, it was used to obtain the gravity anomalies, which were subtracted of the terrestrial gravity anomalies, yielding the residuals gravity anomalies. These residuals gravity anomalies it was input to the FASTCOL software to yield the residuals geoidal heights. The CG01c geopotential model, representative of the long wavelengths of the earth gravity field, was added to the residuals geoidal heights, yielding the geoid model so-called GEÓIDESP_FC_2007. This geoid was evaluated and later compared with the Modelo Digital do Geóide Regular (MDGR). At the end, arguments were presented to justify the study of the earth gravity field in the scope of the remote sensing
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Silva, Robert Martins da. "Proposta de metodologia para definição de um modelo digital de elevação para monitoramento de áreas de inundação." Universidade Federal do Pampa, 2017. http://dspace.unipampa.edu.br:8080/jspui/handle/riu/2198.
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O conhecimento do relevo terrestre sempre foi de grande importância para a humanidade, e o modo de sua representação é objeto de constante e múltiplos estudos. Objetivo desse trabalho foi a utilização de métodos geodésicos para eleboração de um modelo digital de elevação integrado com dados hidrológicos para monitoramento das áreas afetadas pelas inundações do Rio Uruguai na cidade de Itaqui, Rio Grande do Sul, que periodicamente sofrem perdas e grandes gastos devido as recorrentes inundações. Para tanto neste trabalho é aplicado uma metodologia baseada na associação de dados provenientes de diferentes fontes (dados de levantamento geodésico, altimétrico, série histórica de dados hidrológicos), e que juntos retornam um produto final preciso e confiável. Para início do trabalho foi realizado a vinculação das cotas do rio ao sistema geodésico brasileiro através do nivelamento geométrico entre uma RN de referência e as réguas linimétricas do rio. Na segunda parte do trabalho foi aplicada técnicas de posicionamento geodésico dentro da região de estudo e posterior processamento e análise dos dados obtidos. Nessa etapa também realizou-se a conversão de altitudes geométricas em ortométricas e sua correção com o uso de um modelo geoidal. A terceira etapa do trabalho consistiu na geração de modelos digitais com diferentes interpoladores em ambiente SIG e posteriormente foi realizada uma análise estatística para validação e classificação dos modelos por meio do Software GeoPec desenvolvido especificamente para avaliação de dados espaciais. E por último a validação do MDE resultante através da comparação com trabalhos já realizados e com uma aplicação direta em um evento ocorrido no ano de 2017. A aplicação dessa metodologia permitiu a obtenção de um modelo digital de elevação preciso e acurado classificado dentro das normativas da cartografia nacional. Tal resultado justifica que a aplicação da metodologia proposta pode ser empregada por toda área urbana do município de Itaqui retornar algum suporte aos gestores visto que a metodologia apresentou resultados satisfatórios, necessitando porém de alguns ajustes e complementos de forma a se tornar mais eficiente.
The knowledge of earthly relief has always been of great importance to mankind, and the mode of its representation is the object of constant and multiple studies.The objective of this work was the use of geodetic methods for the elaboration of a digital elevation model integrated with hydrological data to monitor the areas affected by the Uruguay River floods in the city of Itaqui, Rio Grande do Sul, which periodically suffer losses and large expenses due to recurrent floods. For this purpose, a methodology based on the association of data from different sources (geodetic survey, altimetric data, historical series of hydrological data) is applied, and together they return an accurate and reliable final product. For the beginning of the work the linking of the river quotas to the Brazilian geodetic system was done through the geometric leveling between a reference RN and the linimetric rules of the river. In the second part of the work, geodetic positioning techniques were applied within the region of study and later processing and analysis of the data obtained. In this stage also the conversion of geometric altitudes in ortometric and its correction with the use of a geoidal model was realized. The third stage of the work consisted in the generation of digital models with different interpolators in GIS environment and later a statistical analysis was performed for the validation and classification of the models through the GeoPec Software developed specifically for the evaluation of spatial data. And finally, the validation of the resulting MDE through the comparison with works already carried out and with a direct application in an event occurred in the year 2017. The application of this methodology allowed to obtain a digital model of accurate and accurate elevation classified within the norms of the cartography. This result justifies that the application of the proposed methodology can be used by all urban areas of the municipality of Itaqui to return some support to the managers since the methodology presented satisfactory results, however, requiring some adjustments and complements in order to become more efficient.
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Odera, Patroba Achola. "Precise determination of a local geoid model and a reference height system for the establishment of a modern vertical geodetic datum." 京都大学 (Kyoto University), 2012. http://hdl.handle.net/2433/161036.
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Guimarães, Gabriel do Nascimento. "A altimetria e o modelo geoidal no Estado de São Paulo." Universidade de São Paulo, 2010. http://www.teses.usp.br/teses/disponiveis/3/3138/tde-20102010-170156/.
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Esta dissertação tem como objetivo o estudo da altimetria e do modelo geoidal no Estado de São Paulo. Para isso, uma abordagem detalhada do Problema de Valor de Contorno da Geodésia foi realizada. Além disso, são apresentados conceitos relacionados ao sistema de altitudes e a determinação das ondulações geoidais. Uma investigação do movimento e deslocamento vertical da crosta terrestre por meio do processamento preciso por ponto de duas estações de monitoramento contínuo (Cananeia NEIA e Ubatuba UBAT), localizadas no litoral paulista, foi efetuada. Constatou-se uma similaridade nos resultados por meio da comparação com o processamento feito pelo IBGE. A comparação envolvendo o Nível Médio dos Mares de duas estações maregráficas com relação ao nivelamento advindo de Imbituba foi outro estudo executado, onde a diferença após algumas correções foi de 0,34 cm. Uma análise a partir de 199 estações GPS sobre nivelamento foi realizada para comparação da ondulação geoidal com as anomalias de altura. As anomalias foram calculadas a partir dos modelos do geopotencial (EIGEN-GL04, EIGEN-5C e EGM08 para diferentes valores de grau e ordem). Os modelos que apresentaram melhor consistência com as estações GPS sobre nivelamento foram o EIGEN-GL04C e EIGEN-5C grau e ordem 360 e o EGM08 grau e ordem 360 e 2160. O modelo geoidal do Estado de São Paulo foi gerado para um modelo digital de 5. Utilizou-se a integral modificada de Stokes a partir do pacote computacional canadense SHGEO para o cálculo da componente de curto comprimento de onda. Foram empregados dados gravimétricos já existentes e dados advindos dos trabalhos de campo referentes ao Projeto Temático da FAPESP. No cálculo da componente de médio e longo comprimento de onda foi utilizado o modelo do geopotencial EGM08 (grau e ordem 150). A comparação com os dados GPS sobre nivelamento apresentou média de -0,22 m e RMSD 0,21 m. A escolha do Estado de São Paulo está relacionada à grande quantidade de trabalhos geodésicos e atividades na área da engenharia e que necessitam da utilização de um sistema altimétrico. Além disso, a grande quantidade de dados gravimétricos e de estações GPS/RN é mais uma justificativa para a realização do trabalho no Estado.The investigation of the altimetry and the geoid model in São Paulo state is the aim of this dissertation. A detailed study concerning the Geodetic Boundary Value Problem was carried out. Moreover, the concepts related to the height system are presented. The analysis of the crust vertical displacement involving two continuous monitoring GPS stations (Cananeia NEIA and Ubatuba UBAT) in the coast of the state was performed. It was detected similar results between the comparison involved IBGE processing. A comparison involving the mean sea level of two tide gauge stations with respect to levelling from Imbituba was carried out. After some corrections the difference found was 0.34 m. A comparison between height anomalies by the Global Geopotential Models (EIGEN-GL04, EIGEN-5C and EGM08 for different degree and order) and 199 GPS observations on Bench Marks of the spirit leveling network was performed. The Global Geopotential Models that presented consistency with GPS on Bench Marks were: EIGEN-GL04C and EIGEN- 5C degree and order 360 and EGM08 degree and order 2160. São Paulo state geoid model was computed in 5 digital model. The modified Stokes integral by the Canadian package SHGEO to compute the short wavelength component was used, from Helmert gravity anomalies derived. Existing gravity data and data from FAPESP Thematic Project was processed. EGM08 model was used as a reference field restricted to degree and order 150 to obtain the long and medium wavelength components. The comparison with GPS on Bench Marks presented mean -0.22 m and RMSD 0.21 m. The reason for the choice of São Paulo state is that there are a lot of geodetic activities and important engineering works that require the use of a height system. Furthermore, there are a lot of gravimetric and GPS/BM data all around the state.
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Kiamehr, Ramin. "Precise Gravimetric Geoid Model for Iran Based on GRACE and SRTM Data and the Least-Squares Modification of Stokes’ Formula : with Some Geodynamic Interpretations." Doctoral thesis, KTH, Transporter och samhällsekonomi (stängd 20110301), 2006. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-4125.
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Iran is one of the most complicated areas in the world from the view of rough topography, tectonic activity, large lateral density and geoidal height variations. The computation of a regional gravimetric geoid model with high accuracy in mountainous regions, especially with sparse data, is a difficult task that needs a special attention to obtain reliable results which can meet the needs of the today geodetic community. In this research different heterogeneous data has been used, which includes gravity anomalies, the high-resolution SRTM Digital Elevation Model (DEM), recently published GRACE Global Geopotential Models (GGMs), geological maps and GPS/levelling data. The above data has been optimally combined through the least-squares modification of Stokes formula with additive corrections. Regarding the data evaluation and refinement, the cross-validation technique has been used for detection of outliers. Also, several GGMs and DEMs are evaluated with GPS/levelling data. The impact of utilizing a high resolution SRTM DEM to improve the accuracy of the geoid model has been studied. Also, a density variation model has been established, and its effect on the accuracy of the geoid was investigated. Thereafter a new height datum for Iran was established based on the corrective surface idea. Finally, it was found that there is a significant correlation between the lateral geoid slope and the tectonic activities in Iran. We show that our hybrid gravimetric geoid model IRG04 agrees considerably better with GPS/levelling than any of the other recent local geoid models in the area. Its RMS fit with GPS/levelling is 27 cm and 3.8 ppm in the absolute and relative senses, respectively. Moreover, the relative accuracy of the IRG04 geoid model is at least 4 times better than any of the previously published global and regional geoid models in the area. Also, the RMS fit of the combined surface model (IRG04C) versus independent precise GPS/levelling is almost 4 times better compared to the original gravimetric geoid model (IRG04). These achievements clearly show the effect of the new gravity database and the SRTM data for the regional geoid determination in Iran based on the least-squares modification of Stokes’ formula.QC 20100906
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Maia, Túle Cesar Barcelos. "Utilização de redes neurais na determinação de modelos geoidais." Universidade de São Paulo, 2003. http://www.teses.usp.br/teses/disponiveis/18/18137/tde-19122003-185113/.
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A partir de dados obtidos do modelo do geopotencial EGM96, da gravimetria, do GPS e do nivelamento geométrico, e aplicando harmônicos esféricos e FFT como técnicas de determinação geoidal, foram utilizadas neste trabalho redes neurais artificiais como ferramenta alternativa na determinação de um modelo geoidal. Procurou-se uma determinação geoidal de forma mais rápida, com precisão adequada e com menor esforço na determinação de parâmetros importantes na obtenção da referida superfície. Foram utilizados modelos de redes neurais do tipo MLP, algoritmo de treinamento backpropagation, variando o número de camadas, o número de neurônios, a função de ativação, a taxa de aprendizado e o termo momento. Os dados dos modelos mencionados foram tratados de forma a serem utilizados pelos modelos de redes neurais. Foram executadas a normalização, a análise de componentes principais e a definição dos atributos de entrada e saída para treinamento do modelo de rede neural. Foram Realizadas comparações entre os modelos geoidais existentes, os quais foram utilizados nesta pesquisa, com os resultados obtidos pelo modelo de rede neural. Tais comparações resultaram na obtenção dos erros entre as superfícies, justificando dessa forma a possibilidade de uso do referido método, com a conseqüente demonstração de suas vantagens e desvantagens.Applying data from EGM96 geopotential model, gravimetric, GPS and geometric leveling data and using spherical harmonics and FFT as techniques of geoidal determination, this thesis has the goal to find a fast alternative tool to define a geoidal undulation model considering precision and a small effort to estimate important parameters to obtain the mentioned model. MLP neural networks, backpropagation algorithm changing the numbers of layers, neurons numbers, activation function, learning rate and momentum term have been applied. The data of the mentioned models were handling aiming to be used by the neural networks models. Normalization, analysis of the main components, definition of the input and output attributes to training the neural network model, have been also used. Comparison among existing models and the models used in this research with results obtained by the neural network have been done, showing the errors between the created surfaces. At the end, it is presented a positive argument to use the MLP neural network to generate a geoidal model with advantages and disadvantages.
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Velissariou, Vasilia. "Examination of the Barotropic Behavior of the Princeton Coastal Ocean Model in Lake Erie, Using Water Elevations From Gage Stations and Topex/Poseidon Altimeters." The Ohio State University, 2009. http://rave.ohiolink.edu/etdc/view?acc_num=osu1252401353.
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Roussel, Clément. "Expérimentation d’un gravimètre mobile léger et novateur pour la mesure du champ de gravité en fond de mer." Thesis, Paris, CNAM, 2017. http://www.theses.fr/2017CNAM1099/document.
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L’un des défis majeurs relevé par la gravimétrie moderne consiste en la détermination de modèles mathématiques et de cartes numériques du champ de gravité de la Terre dont la fiabilité est identique quelle que soit l’échelle spatiale considérée en domaines terrestre, littoral, marin et sous-marin. Aujourd’hui, les harmoniques de haut degré correspondant aux courtes longueurs d’onde du champ de gravité sont encore affectés de grandes incertitudes de par la diversité et les différences de précision et de résolution des techniques gravimétriques permettant de les atteindre. Le principal obstacle à l’amélioration de la résolution et la précision des modèles vient de ce que les systèmes de gravimétrie et gradiométrie mobiles, seuls instruments qui permettent des acquisitions à précision et à résolution spatiale homogènes, demeurent encore encombrants et gros consommateurs d’énergie, ce qui interdit en particulier leur installation sur des drones terrestres, aériens, navals de surface et sous-marins. L’intérêt de ce type de porteur est de pouvoir opérer des acquisitions très proches des sources ce qui accroît considérablement la restitution des variations locales de la gravité. Le développement d’un nouveau type de capteur gravimétrique à faible encombrement et moindre consommation énergétique apparaît donc indispensable pour répondre à la problématique posée par la mesure des courtes longueurs d’onde du champ de gravité.Dans le cadre de ses activités de recherche en gravimétrie, le Laboratoire de Géomatique et Foncier (Cnam/GeF EA 4630), en collaboration avec le Laboratoire de Recherche en Géodésie (LAREG) de l’Institut National de l’information Géographique et forestière (IGN), le Laboratoire Domaines Océaniques (LDO, UMR CNRS 6538, UBO), l’Institut Français de Recherche pour l’Exploitation de la Mer (IFREMER) et le Service Hydrographique et Océanographique de la Marine (SHOM), développe un instrument novateur qui permet la mesure dynamique du champ de gravité terrestre en fond de mer.Le système baptisé GraviMob (système de Gravimétrie Mobile) ne nécessite pas de plateforme stabilisée et se fixe rigidement dans l’habitacle du véhicule porteur, en l’occurrence, un submersible autonome. Le cœur du système est constitué de triades d’accéléromètres, permettant une mesure vectorielle de l’accélération de pesanteur. Un traitement des mesures par filtrage de Kalman, intégrant les données de position et d’orientation du véhicule porteur, réalise la restitution du champ de pesanteur dans un référentiel adapté à son interprétation et son exploitation. Ce prototype instrumental a été expérimenté en Mer Méditerranée au cours de l’année 2016, à l’aplomb de profils gravimétriques de surface acquis antérieurement par le SHOM. La comparaison du signal gravimétrique obtenu en fond de mer avec les données du SHOM indique une répétabilité de la tendance générale du signal gravimétrique à 5 mGal près.Ce manuscrit aborde successivement, l’établissement de l’équation d’observation du système GraviMob, l’étalonnage et l’orientation des accéléromètres du capteur, la stratégie d’estimation du champ de pesanteur par un filtre de Kalman intégrant un modèle d’évolution des composantes du champ de pesanteur et un modèle d’observation tenant compte du bruit de mesure, le traitement et l’analyse des mesures acquises lors de son expérimentation en Mer Méditerranée, puis la comparaison du signal gravimétrique obtenu avec les données de référenceOne of the major challenges of modern gravimetry consists in determining mathematical models and digital maps of the Earth’s gravity field, the reliability of which is identical whatever the spatial scale considered in terrestrial, coastal, marine and submarine domains. Today, the harmonics of high degree corresponding to the short wavelengths of the gravity field are still affected by great uncertainties due to the diversity and the differences in precision and resolution of the gravimetric techniques making it possible to reach them. The main obstacle to improve the resolution and accuracy of models is that gravimetry and gradiometry mobile devices, the only instruments that allow homogeneous precision and spatial resolution acquisitions, are still bulky and energy-intensive, which prohibits their installation on terrestrial, aerial, surface and submarine drones. The interest of this type of carrier is to make acquisitions very close to the sources which considerably increases the restitution of the local variations of the gravity. The development of a new type of gravimetric sensor with small size and lower energy consumption appears therefore essential to answer the problematic posed by the measurement of the short wavelenghts of the gravity field.As part of its research in gravimetry, the Laboratoire Géomatique et Foncier (Cnam/GeF EA 4630), in collaboration with the Laboratory for Research Geodesy (LAREG) of the National Institute for Geographic and Forest Information (IGN), the Oceanic Domains Laboratory (LDO, UMR, CNRS 6538, UBO), the French Research Institute for the Exploitation of the Sea (IFREMER) and the Marine Hydrographic and Oceanographic Service (SHOM), develops an innovative instrument which allows the dynamic measurement of the Earth’s gravity field in the subsea domain.The system, called GraviMob (Gravimetry Mobile System), does not require a stabilized platform and is rigidly attached to the carrier vehicule, in this case an Autonomous Underwater Vehicule (AUV). The heart of the system consists of triads of accelerometers, allowing a vector measurement of the gravity. A Kalman filter, integrating the position and orientation data of the carrier vehicle, performs the estimation of the gravity field in a frame adapted to its interpretation. This instrumental prototype has been tested in the Mediterranean Sea during the year 2016. The comparison of the gravimetric signal obtained near the seabed with the surface gravimetric profiles, previously acquired by the SHOM, indicates a repeatability of the general trend of the gravimetric signal to within 5 mGal.This manuscript deals successively with the establishment of the observation equation of the GraviMob system, the calibration and orientation of the accelerometers, the gravity field estimation strategy by a Kalman filter, integrating an evolution model of the gravity field components and an observation model taking the measurement noise into account, the processing and analysis of the measurements acquired during its experimentation in the Mediterranean Sea, then the comparison of the gravimetric signal obtained with the reference data
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Silva, Marco Antônio. "Obtenção de um modelo geoidal para o Estado de São Paulo." Universidade de São Paulo, 2002. http://www.teses.usp.br/teses/disponiveis/3/3138/tde-09072003-195706/.
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O sistema GPS tem sido largamente usado para posicionamento. Vislumbra-se o potencial uso deste sistema para determinação de altitudes ortométricas, substituindo o oneroso e demorado processo de nivelamento geométrico. Para isso, um modelo geoidal com precisão absoluta submétrica e precisão relativa da ordem de 2 ppm é necessário. Este modelo pode ser dividido em duas componentes: longo e curto comprimento de onda. O modelo do geopotencial fornece a componente de longo comprimento de onda da altura geoidal, enquanto que a gravimetria associada a um modelo digital do terreno permite calcular a componente de curto comprimento de onda através da integral modificada de Stokes. Algumas das modificações da função de Stokes são comparadas. Dois métodos de avaliação desta integral, integração direta e FFT são mostrados no trabalho. Como resultado dessas comparações, obtém-se um modelo geoidal para o Estado de São PauloThe GPS system has been used broadly for positioning. It is glimpsed the potential use of this system for the determination of orthometric height, substituting the expensive and slow process of geometric leveling. For this propose, it is necessary a geoid model with submetric absolute accuracy and relative accuracy on the order of 2 ppm. This model can be divided in two components: long and short wavelengths. The model of the geopotential supplies the long wavelength component of the geoid height, while gravimetry associated with a digital terrain model, allows the estimation of the short wavelength component, through the modified Stokes´s integral. Comparisons of some of these modifications of the Stokes´s function are carried out. Two methods of evaluation of the integral, numerical integration and FFT are shown in the work. As a result of those comparisons, it is obtained a geoid model for the State of São Paulo
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Ågren, Jonas. "Regional Geoid Determination Methods for the Era of Satellite Gravimetry : Numerical Investigations Using Synthetic Earth Gravity Models." Doctoral thesis, KTH, Infrastructure, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-55.
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It is the purpose of this thesis to investigate different regional geoid determination methods with respect to their feasibility for use with a future GOCE satellite-only Earth Gravity Model (EGM). This includes investigations of various techniques, which involve different approximations, as well as the expected accuracy. Many, but not all, of these tasks are tested by means of Synthetic Earth Gravity Models (SEGMs). The study is limited to remove-compute-restore methods using Helmert condensation and to Sjöberg's combined approach (method with additive corrections).
First, a number of modifications of Stokes' formula are tested with respect to their compatibility with a GOCE EGM having negligible commission error. It is concluded that the least squares modification method should be preferred.
Next, two new point-mass SEGMs are constructed in such a way that the resulting models have degree variances representative for the full and topographically reduced gravity fields, respectively. These SEGMs are then used to test different methods for modified Stokes' integration and downward continuation. It is concluded that the combined method requires dense observations, obtained from the given surface anomalies by interpolation using a reduction for all known density anomalies, most notably the topography. Examples of other conclusions are that the downward continuation method of Sjöberg (2003a) performs well numerically.
To be able to test topographic corrections, another SEGM is constructed starting from the reduced point-mass model, to which the topography, bathymetry and isostatic compensation are added. This model, which is called the Nordic SEGM, is then applied to test one strict and one more approximate approach to Helmert's condensation. One conclusion here is that Helmert's 1st method with the condensation layer 21 km below sea level should be preferred to Helmert's 2nd condensation strategy.
The thesis ends with a number of investigations of Sjöberg's combined approach to geoid determination, which include tests using the Nordic SEGM. It is concluded that the method works well in practice for a region like Scandinavia. It is finally shown how the combined strategy may preferably be used to estimate height anomalies directly.
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Ågren, Jonas. "Regional geoid determination methods for the era of satellite gravimetry : numerical investigations using synthetic earth gravity models /." Stockholm, 2004. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-55.
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Lima, Elen Marten de. "Determinação e avaliação de geoide para o município de Porto Alegre/RS (GEOIDEPOA2016)." reponame:Biblioteca Digital de Teses e Dissertações da UFRGS, 2016. http://hdl.handle.net/10183/150858.
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Conhecer a altitude de um ponto é muito importante em diversas aplicações, como a implantação de uma rede de água ou para determinar se certa área está sujeita à inundação por exemplo. Esta altitude, altitude ortométrica, está referenciada ao nível médio do mar e é determinada a partir do transporte de um ponto com altitude conhecida até o ponto o qual se deseja saber a altitude. O geoide, é a superfície que representa o nível médio do mar e o seu cálculo tem sido objeto dos geodesistas há muito tempo. Devido a irregularidade da forma da Terra, utiliza-se uma figura matemática para representar a Terra, o elipsoide, onde são realizados os cálculos matemáticos. Ao elipsoide está relacionada a altitude geométrica, a qual é determinada utilizando receptores do sistema global de posicionamento por satélite. A altitude ortométrica e a altitude geométrica, relacionam-se através da ondulação geoidal, a qual é a separação geoide-elipsoide. O transporte das altitudes ortométricas exige uma densa rede com altitudes conhecidas, o que é algo difícil de ocorrer em países de dimensões continentais como o Brasil. Uma das soluções encontradas é cálculo de geoides com precisão que atenda as necessidades na determinação da altitude ortométrica. Este trabalho calculou um geoide para o município de Porto Alegre e foi avaliado a partir das alturas geoidais obtidas do posicionamento GNSS sobre referencias de nível (RRNN) as quais possuem precisão milimétrica. No cálculo do geoide utilizou-se o modelo geopotencial global EGM2008 de grau 360, para a representação dos longos comprimentos de onda; e observações gravimétricas terrestres, totalizando 277 pontos distribuídos por todo o munícipio. Para o cálculo do geoide utilizou-se da integral de Stokes, resultando em um geoide com resolução de 3” x 3” e erro médio quadrático de 7,7 centímetros. Em uma segunda fase o geoide (GEOIDEPOA2016) foi avaliado em relação ao modelo de ondulação geoidal oficial do Brasil, o MAPGEO2015 e seu antecessor, o MAPGEO2010, assim como com o modelo de alturas geoidais o qual a prefeitura municipal de Porto Alegre (NPMPA) possui. Os modelos de alturas geoidais que apresentaram melhores resultados para determinar a altitude ortométrica foram o GEOIDEPOA2016 e o NPMPA, com erro médio quadrático de 7,7 e 8,1 centímetros respectivamente.The knowledge of an altitude point is very important in several applications, such as the implantation of a water network or to determine if a certain area is subject to flooding for example. This altitude, ortometric altitude, is referenced to the mean sea level and is determined from the transport of a point with known altitude to the point where the altitude is desired. The geoid is the surface that represents the average level of the sea and its calculation has long been object of the geodesists. Due to the irregularity of the shape of the Earth, a mathematical figure is used to represent the Earth, the ellipsoid, where the mathematical calculations are performed. The ellipsoid is related to geometric altitude, which is determined using receivers of the global satellite positioning system. The orthometric altitude and the geometric altitude are related through the geoidal undulation, which is the geoid-ellipsoid separation. The transportation of orthometric altitudes requires a dense network with known altitudes, which is difficult to achieve in countries with continental dimensions such as Brazil. One of the solutions found is accurately calculating geoids that meet the needs in determining orthometric altitude. This work calculated a geoid for the municipality of Porto Alegre and was evaluated from the geoid heights obtained from the GNSS positioning on level references (RRNN) which have millimetric precision. In the calculation of the geoid, the EGM2008 global geopotential model was used for the representation of the long wavelengths with terrestrial gravimetric observations, totaling 277 points distributed throughout the municipality. For the calculation of the geoid was used of the integral of Stokes, resulting in a geoid with resolution of 3 "x 3" and RMS 7.7 centimeters. In a second phase the geoid (GEOIDEPOA2016) was evaluated in relation to the Brazil official geoidal model, MAPGEO2015 and its predecessor, MAPGEO2010, as well as the geoid heights model, which the municipal government of Porto Alegre (NPMPA) has. The geoid heights models that presented the best results to determine the orthometric altitude were GEOIDEPOA2016 and NPMPA, with a RMS 7.7 and 8.1 cm respectively.
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Bärlund, Johnny. "Numerical Investigation on Spherical Harmonic Synthesis and Analysis." Thesis, KTH, Geodesi och satellitpositionering, 2015. http://urn.kb.se/resolve?urn=urn:nbn:se:kth:diva-171779.
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In this thesis work the accuracy of the spherical harmonic synthesis and analysis are investigated, by simulated numerical studies.The main idea is to investigate the loss of accuracy, in the geopotential coeffcients, by the following testing method. We start with a synthesis calculation, using the coefficients(EGM2008), to calculate geoid heights on a regular grid. Those geoid heights are then used in an analysis calculation to obtain a new set of coeffcients, which are in turn used to derive a new set of geoid heights. The difference between those two sets of geoid heights will be analyzed to assess the accuracy of the synthesis and analysis calculations.The tests will be conducted with both point-values and area-means in the blocks in the grid. The area-means are constructed in some different ways and will also be compared to the mean value from 10000 point values as separate tests. Numerical results from this investigation show there are signifi
cant systematic errors in the geoid heights computed by spherical harmonic synthesis and analysis, sometimes reaching as high as several meters. Those big errors are most common at the polar regions and at the mid-latitude regions.
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Jurčík, Josef. "Užití astronomické nivelace pro vytváření modelů kvazigeoidu." Master's thesis, Vysoké učení technické v Brně. Fakulta stavební, 2012. http://www.nusl.cz/ntk/nusl-225611.
Full textAbstract:
My master´s thesis deals with use of astronomical levelling for creation of quasigeoid models. The basic input dates are componets of astronomical-geodetic deflections of the vertical in points, which are determined on AGNES and VEVEŘÍ nets. The dates are adjust for determination of relative quasigeoid. In literature [4], there is simplified solution for adjustment of this dates. The thesis looks for the most comprehensive solutions of adjustment without simplification. The solutions are compared.
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Chu, Chi-Kung, and 儲繼光. "Using B-Spline Surface to Represent and Update Taiwan Geoid Model." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/19337983085237222475.
Full textAbstract:
碩士國立成功大學
測量及空間資訊學系碩博士班
93
ABSTRACT Recently,according to the high precision Taiwan Vertical Datum system had been established at 2001(TWVD2001),the system combined GPS/levelling/geoid height Network adjustments,and used the way of least-square-collocation-with-unknown-parameters to complete the new Taiwan geoid grid data.The research chooses the optimal B-Spline control points and order of B-Spline curve,and uses “Approximation B-Spline”to get the best fitting B-Spline surface model.The model take geoid grid data as an afterward processing,and analyzes the precision of interpolation、 model storage and the results of updating model resolution with new observations. According to the experiment,there is a distinguished improvement when spline interpolation is compared to bilinear interpolation in the infrequent grid data,especially in the mountain area.It can explain that spline interpolation is better than bilinear interpolation in the more flexuous area。Besides,B-Spline model can compress the larger storage capacity grid data like 3"grid data into 25%.On the part of updating with new observations,we can analyze that the update range is in inverse proportion to the precision of interpolation.For considering update range and the precision of interpolation,the update range about 4KM is proper,however,different update range has different improve ratio,the larger update range has smaller improve ratio;on the contrary,the smaller update range considers the local quality and the improve ratio is less obvious.
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Pei-Shan, Lee, and 李佩珊. "An Improved Taiwan Geoid Model And Its Application To DEM Generation." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/36870785035765830992.
Full textAbstract:
碩士國立交通大學
土木工程系所
93
A gravimetric geoid model of Taiwan is computed using remove-compute-restore technique, which divides a geoid model into the long, medium and short wavelength parts. This technique requires a global geopotential model and an elevation model. The residual geoid modeling is done by least-squares collocation. An correction term accounting for the terrain effect is introduced, and it improves greatly the accuracy of modeled geoidal undulations, especially in the high mountain areas. For the long wavelength part, this research experiments with earth gravity models GGM01, GGM02 and EIGEN-CG01C. The combined GGM02C-EGM96 model yields the best result in geoid modeling. The modeled and observed geoidal undulations are compared at four first-order leveling lines, resulting in standard deviations of geoidal differences of less than 10 cm. A refined geoid model is created by applying a harmonic surface of geoidal differences between modeled and observed geoidal undulations at 1920 first-order benchmarks, where GPS-derived ellipsoidal heights are available. The refined geoid model yields standard deviations of geoidal differences of 2 to 3 cm at the same four leveling lines. The refined geoid model is used in the photogrammetry and Lidar methods to generate orthometric heights. In a testing area in Hsinchu County, ellipsoidal heights are first generated by the photogrammetry method, orthometric heights are then computed using the geoid model. Comparing the orthometric heights generated by this approach and the conventional orthometric-height-controlled photogrammetry approach, the standard deviations of height differences range from 11 to 40 cm, depending on the scenarios of the ground control points for the aerial triangulation adjustment. At a testing line in Pintung County, the standard deviation of the differences between Lidar-geoid-derived orthometric height and levelling-derived orthometric heights is 15.8 cm.
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Hsu, Chun-Chia, and 許峻嘉. "The Study of Network RTK Combined with Different Geoid Undulation Model in Taiwan." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/t4267h.
Full textAbstract:
碩士國立宜蘭大學
土木工程學系碩士班
106
Most of Surveying and Mapping industry uses Network RTK to measure the facilities, manhole covers and handhole covers directly. It’s measured the three-dimensional coordinates of the measured points immediately. But elevation value is Ellipsoid Height. It’s still necessary to measure the points of the three-dimensional coordinates and then through Geoid Undulation Model of Taiwan is converted to Orthometric Height. But the current Surveying and Mapping industry or related academic units can only be completed by Ministry of the Interior and National Land Surveying and Mapping Center’s Geoid Undulation Model of Taiwan on 2014 to convert. Before the plan is completed, The Ministry of the Interior in 2002 was first published Geoid Undulation Model of Taiwan. In part of areas, is the Geoid Undulation Model of Taiwan on 2014’s converted result better than Geoid Undulation Model of Taiwan on 2002’s converted result？It's explored the subject for this thesis. In this study, the two experimental areas in Hukou Township, Hsinchu County, and Xincheng Township, Hualien City, Ji’an Township, Shoufeng Township, Fenglin Township, Hualien County, respectively. They were tested the real data. And then the experimental area in the island of Taiwan within range, in accordance with point data using the longitude and latitude of each read gap 30 seconds to build unreal data, and the 2002 edition and the 2014 edition including hybrid and gravity method of the Geoid Undulation Model of Taiwan calculation formula calculates, analysis and calculation of three editions of the program differences. The real data experimental results show, in terms of the experimental area in Hukou Township, Hsinchu County,the difference between 2014 edition including hybrid method of the Geoid Undulation Model of Taiwan and 2002 edition is small, and it still had their own applicable regional location.Hybrid and gravity method’s systematic offset value is between 13 and 17cm. In terms of the experimental area in Hualien County. According to the relevant operational specifications developed by Construction and Planning Agency Ministry of the Interior. Hybrid method’s pass rate is up to 95%, but the 2002 edition’s pass rate is only 67%. And 2014 edition including hybrid method of the Geoid Undulation Model of Taiwan is indeed better than 2002 edition. Hybrid and gravity method’s systematic offset value is between 19 and 26cm.The grid data experimental results show, the precision in the flat area is better than that in the mountain area. In the range of Taiwan island, the differences between 2014 edition including hybrid method and gravity method of the Geoid Undulation Model of Taiwan are the most in the range of 10cm to 30cm, accounting for 90%. In the full range of Taiwan, this is also mentioned previously between the two methods' systematic offset value.
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Shih, Yu-Sheng, and 施煜昇. "A Study of Comparison of Fitting Methods by Terrain Complex Local Geoid Model." Thesis, 2018. http://ndltd.ncl.edu.tw/handle/v7wx8q.
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Liu, Hui-Ching, and 劉蕙菁. "A Study on the Determination of the Best Taiwan Geoid Model Using Gravity Method." Thesis, 2003. http://ndltd.ncl.edu.tw/handle/86247730879748389367.
Full textAbstract:
碩士國立交通大學
土木工程系
91
Due to the rapid development of GPS technique these years, it has been extensively applied to physical geodesy. GPS technique can obtain high-accuracy ellipsoidal heights, and change the face and concept of traditional heighting procedure. However, leveling height is orthometric and GPS height is ellipsoidal, so geoid undulation is essential for relating the two. If we can build up a high-accuracy geoid model, then GPS will be an inexpensive method to measure orthometric. The geoid model has been strictly computed for Taiwan area in this research using Stokes’ formula with two-dimensional plane fast fourier transform (2D Plane FFT), one-dimensional spherical fast fourier transform (1D Spherical FFT) techniques and least square collocation (LSC) methods by remove-compute-restore technique. The computations of geoid undulations were carried out using data from EGM96 spherical harmonic model and residual terrain model for Taiwan. We use some gravity anomaly data, which are measured in different time, different distribution and different density, to compute the best Taiwan geoid model, and checked the accuracy of these models by GPS/Leveling observations. The numerical analysis results show that the result using gravity anomaly collected by Academia Sinica (Yen et al., 1990) is better than other three items. The root mean square of the difference between the geoid undulations computed by gravimetric and GPS/Leveling methods is about 5 cm. According to the results, Stokes’ formula with 1D Spherical FFT is better then 2D Plane FFT method, and LSC is the best one. Moreover, the best Taiwan geoid computed by gravimetric is about 12.993 m to 28.564 m. The maximum, minimum, standard deviation, and root mean square of the difference between the geoid undulations computed by gravimetric and GPS/Leveling methods are 5.8, -9.5, 2.56 and 4.78 cm.
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Chen, Chao-Nan, and 陳昭男. "Performance Analysis of Using Various Geometric Interpolation Methods and Criteria to Determine Local Geoid Model." Thesis, 2019. http://ndltd.ncl.edu.tw/handle/gjghk7.
Full textAbstract:
博士國立中興大學
土木工程學系所
107
How to use GNSS and leveling data with several different geometric interpolation methods and indicators to obtain a better regional earth undulation model, in order to promote the reasonable point precision and its efficiency as the subject of the study. When the fluctuation of the earth''s undulation is considered to be gentle within a certain range, a mathematical function can be used to reflect the change of the spatial distribution, and then the earth fluctuation values of other undetermined unknown points are obtained through interpolation. In this study, if the (1) least squares support vector machine is used in the test area selected in this study, the resulting elevation accuracy can reach ±1.8 cm. (2) Using the particle swarm algorithm, the resulting elevation accuracy can reach ±1.9cm. (3) Using the gene representation planning method, the obtained elevation accuracy can reach ±2.0 cm. (4) Using the WTLS quadric surface method, the obtained elevation accuracy can reach ±1.9 cm. (5) Using the RWTLS quadric surface method, the resulting elevation accuracy can reach ±1.8 cm. Using the regional earth undulation mode established by these several methods, the root mean square error of the checkpoints is within ±5 cm of the engineering measurement standard. Five kinds of indicators were used to evaluate the six preferred regional undulation models, which were judged by the sensitivity and stability of the index values. The comprehensive conclusion in this study is that the "confidence index (C)" evaluation index has the best stability. It is concluded how to choose the best regional earth undulation model for various mapping applications.
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Chang, Sheng-Hsiung, and 張勝雄. "Monitoring Strata Variation in Taiwan Area by GPS/GLONASS Multi-Satellite signals, Groundwater Method and Geoid Model." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/10276421635307107788.
Full textAbstract:
碩士國防大學理工學院
空間科學碩士班
99
The purpose of this study is verifying the feasibility of GPS/GLONASS integrated satellite system, groundwater method and geoid model used to monitor changes of strata variation in Taiwan area. First, GPS/GLONASS integrated satellite systems were used for baseline observation for 24 hours on CCIT’s (Chung Cheng Institute of Technology) G002 and G007 control points with Bernese 5.0 GPS software. Data from GPS-only and both integrated satellites systems were divided in each second and 15 seconds. Results show that baseline observations of GPS/GLONASS compared with those of GPS systems increase up to 34% ~ 81% in each 15 seconds and increase up to 94.56% to 95.93% in every 1 second. As cycle ambiguity resolutions of GPS/GLONASS compared with those of GPS increase up to 16% to 64% in each 15 seconds and increase up to 22% ~ 67% in every 1 second. The results indicate that compared GPS/GLONASS systems with GPS-only system in calculation not only reduce time of consuming but also improve accuracy of computing. Second, by collecting of three years’ GPS and GLONASS’s satellite tracking data, Kimnen point was selected in center of star –net for computing 22 points’ ellipsoid heights, and Geoid Model for determining geoid undulations of values on same points. 22 Groundwaters of the Water Resources Agency which closed to previous observed points monitor heights of water level. It is indicated that three kinds of height values at 8 locations within almost 2 km from the groundwater show a linear relationship, and the changes of Taiwan area’s strata variation can be presented effectively.
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Chien, Zih-Ling, and 簡子淩. "A Study of Fitting Local Geoid Model by Gene Expression Programming - A Case Study of Taichung Area." Thesis, 2012. http://ndltd.ncl.edu.tw/handle/27223674572598085063.
Full textAbstract:
碩士國立中興大學
土木工程學系所
100
In recent years, with the vigorous development of the Global Positioning System(GPS), GPS has become even more widely used in Surveying, and the traditional measurement has been gradually replaced by GPS measurements in the horizontal control surveys. However, the accuracy of GPS measurements in vertical control surveys is not sufficient. The elevation value of coordinate is generally still use the leveling to measure, but spend a lot of human resources, operating times and costs, so how to use the high efficiency GPS measurements to obtain the elevation accuracy that meets the engineering specifications is worth exploring. The accuracy of GPS measurements in vertical control surveys is not sufficient, because the surveying engineering mainly in use is orthometric height, and the height that GPS measured is ellipsoidal height, not the orthometric height, it must be transformed by geoid model, in this process, the resulting error will reduce the accuracy, therefore fitting the high-accuracy geoid model is the key of use GPS measurements to replace the leveling. In the study, we will use the Gene Expression Programming(GEP) to fitting different terrain geoid models in Taichung area by GPS and leveling data, and analyze the results. According to the experimental, the best accuracy of the Taichung Basin(north) is ±0.933 cm, Taichung Basin(south) is ±2.164 cm, Dadu Tableland is ±0.961 cm, Takeng Toukoshan Hill is ±1.702 cm, and not only using less than half of the region points to fitting model, but also meet the surveying engineering specifications on the accuracy of the height. Prove that GEP in the basins, hills, tablelands and different terrain all can be fitted to high-accuracy geoid model. Compared with the previous reference, GEP''s accuracy is better than Least Squares Support Vector Machine(LSSVM) that is currently the highest accuracy in the previous reference. Increase the possibility of use GPS measurement to replace the leveling and provide a possible reference program for surveying engineering in future.
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Wang, Wen-An, and 王文安. "A Study of Using Different Methods to Determine Local Geoid Model─A Case Study of Taichung City." Thesis, 2005. http://ndltd.ncl.edu.tw/handle/37346740358468010417.
Full textAbstract:
碩士國立中興大學
土木工程學系
93
Abstract Currently, the research area of most of the Geoid Model building in Taiwan area covers the entire Taiwan and usually the research method is the gravity measurement. However, because the gravity measurement data is difficult to obtain, and needs a great deal of manpower and working-hour, as well as the reason of the special terrain of Taiwan, the representation of the result is not good enough, and is not totally suitable for the precision requirement in small area. Therefore, this research utilizes GPS technique, the data from leveling, and different computation to calculate regional geodetic undulation. It is anticipated that the results must be under a specified precision. No matter on academic or practicality domain of engineering surveying, it should be a topic worthy of further study. The research adopts the GPS points with known 1st order leveling data, acquiring the coordinate and the ellipsoid height by RTK, computing by 2nd curve surface fitting, and discussing on the integrality and the localization, with the changing of quantity of the referencing points, to achieve the best solution. At the same time, the BP Artificial Neural Network is adopted, implementing tests aiming to random point selecting, best fitting point and different training functions and concealed level nodes, to decide regional geoid precisely. According to this research, the root mean square could achieve and by adopting the curve surface fitting and BP Artificial Neural Network to build the geoid model. It fulfills the standard of engineering survey. Finally, compared with the program developed by Ministry of Interior and Taichung city government, then we found it could be applied for a better solution for the elevation measurement of GPS surveying, and could be the reference for future engineering survey.
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Chen, Kwo-Hwa, and 陳國華. "Improving Local Geoid Model of Taiwan Using TWVD2001 Leveling and GPS Data with Application to GPS Heighting." Thesis, 2004. http://ndltd.ncl.edu.tw/handle/87558398455111584678.
Full textAbstract:
博士國立成功大學
測量工程學系碩博士班
92
Developments in Global Positioning System(GPS), which can be applied to the cm-level ellipsoidal height, have reached a mature stage in recent years. In comparison with conventional leveling technique, GPS heighting has the advantages of saving time and cost while doing field surveying. However, the accuracy of an orthometric height by GPS heighting is subjected to the existing Taiwan geoid model, which can’t reach to the cm-level. To solve this problem, we use Taiwan Vertical Datum 2001(TWVD2001) instead, which was established through the calculation of 1010 first-order first-class leveling lines. Based on it, they finished further the calculation of 1055 first-order second-class leveling lines. Thus, we obtained 2065 observations of geodetic leveling, GPS and surface gravity. If we can get highly accurate orthometric and ellipsoidal height by using this 2065 data, we will be able to improve the accuracy of Taiwan local geoid model by least-squares collocation(LSC) technique. The major themes of this research are:(1)Using leveling data to analyze the systematic error-correction parameters in the leveling networks; (2)Analyzing the accuracy of leveling data by using Generalized Gauss-Markoff Model; (3)Using the multistation-multisession GPS geodetic network adjustment model to analyze the accuracy of GPS data; (4)Combining the leveling and GPS data to improve the accuracy of Taiwan local geoid model by using two different LSC techniques. This thesis has obtained conclusions as follows: (1)The posteriori accuracy of unit weight of the leveling observations is ~ . The average accuracy of the orthometric height is ±8.9 mm, and all the accuracy of the orthometric height are smaller than ±10 mm in the mountain area. (2)The average accuracy of ellipsoidal height is ±3.6 cm in the first-order first-class network, and ± 2.5 cm in the first-order second-class network. (3)In comparison with the 24 hours GPS data result, we find that the accuracy of ellipsoidal height within the mountain area is weaker than the plane area in 2 ~ 3 orders. (4)The improvement of the local geoid accuracy is 74 % by using the additional parameters LSC adjustment model, and 69 % in none additional parameter one. (5)The results are then compared with the independent leveling and GPS data obtained from 16 monitoring points. Comparison results show that the accuracy of the improved model has reached ± 3.4 cm in the test area, where a worse level of ± 13.5 cm is obtained from the existing model.
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Shen, Yu-Ting, and 沈昱廷. "A Study of Fitting Local Geoid Model by Least Squares Support Vector Machine─A Case Study of Taichung Area." Thesis, 2011. http://ndltd.ncl.edu.tw/handle/94712598541681838676.
Full textAbstract:
碩士中興大學
土木工程學系所
99
GPS has been used widely in all kinds of engineering, the traditional measurement of plane surveying has been replaced, but datum of leveling is restricted the inconsistency between the two elevations, GPS technique, which obtains ellipsoidal heights, can not be directly used in the leveling height system, it must be transformed by appropriate geoid model, and then can be used in engineering survey. Therefore, researchers have been so far devoting themselves to geoid study in domestic and abroad. Due to geographical environment''s impact in Taiwan, gravity and leveling are not easy to survey, hence a lack of reliable data. The representation of the result is poor in geoid model of Taiwan, all the results are fit to large area, but small area are not. The geoid, which can be used to reflect the circumstances of its spatial distribution by mathematical functions, is changed unobviously in a specific area, it obtained other by interpolating. A local geoid model is established by the study, which is based on GPS and leveling data with least squares support vector machine. According to the experiment, the result of using LS-SVM with Radial Basis Function (RBF) kernel and the third-order polynomial kernel computed that the accuracy is about ±1.4 cm, it could satisfy the requirements of elevation in engineering survey. Comparing with the results by zoning, RBF kernel is better than others. The obtained results from this study would be a great help in improving spirit leveling in the future, as well as enhance GPS technique.
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Huang, Chun-Jia, and 黃春嘉. "A Study of Fitting Local Geoid Model by Weighted Total Least Squares Method-A Case Study of Taichung Area." Thesis, 2016. http://ndltd.ncl.edu.tw/handle/x6k62s.
Full textAbstract:
碩士國立中興大學
土木工程學系所
104
The aim of the study is to explore how to use the measurements of GPS to obtain the elevation precision that meets the engineering specifications.In this study, we adopt the orthometric heights of first-order leveling data and the ellipsoidal heights that are measured by GPS to fit the local geoid model. Traditionally, the fitting method adopts surface curve fitting method is calculated by least-squares to get the geoid value. Nevertheless, least-squares method can’t deal with the problems which exist in random errors of data in coefficient matrix. Thus, the purpose of this study is to improve the precision of traditional surface curve fitting. We apply both total least-squares and weighted total least-squares which also combined with quadratic polynomial surface curve fitting to improve the random errors of data in coefficient matrix and find the local geoid value with better precision. Combining traditional leveling control points with adjustment in number of fitting points, we obtain an ideal optimal local geoid model that is developed into the elevation precision of ±1.38cm. This study provides not only a fast practical method in getting orthometric heights but also academic references for a different method to fit the local geoid model.
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Chung, Chih-Wei, and 鍾智偉. "A Study of Different Multisurface Functions to Improve the Determined Local Geoid Model-A Case Study of Taichung City." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/11301615624780499799.
Full textAbstract:
碩士國立中興大學
土木工程學系所
96
Currently, the researches of the geoid undulation in Taiwan usually use gravity equation or gravity model to calculate the geoid undulation value. However, because the terrain of Taiwan is very special, the representation of the gravity model is not good enough to be used in engineering measurement. Although there are different methods of the geoid undulation calculation, the research area covers entire Taiwan. Therefore, this research takes a small area of Taiwan, and using different mathematical models to calculate regional geodetic undulation. It is anticipated that the results must be under a specified precision. The researches of the calculation bases on Multisurface Function and chooses Taichung city as testing area. Through adjustment, fitting, and comparing with three different calculation of kernel function which are hyperbolic mode, three times of the distance mode and distance square model. It is anticipated that people can use GPS surveying with direct leveling to save working-hour, and the terrain of difficult Measurement (such as Taichung Tai Hang mountain area) can be a breakthrough. According to this research, the root mean square error could achieve ±1.156cm, ±1.253cm and ±1.376cm by adopting hyperbolic mode, three times of the distance mode and distance square model. Its precision is good enough for engineering measurement. It provides not only the quicker methods to measure the orthometric height on survey engineer, but also a academic reference on regional geoid model
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Yeh, Han-Chun, and 葉漢軍. "A Study of Fitting Local Geoid Model by Robust Weighted Total Least Squares Method -A Case Study of Taichung Area." Thesis, 2017. http://ndltd.ncl.edu.tw/handle/48876762392689670067.
Full textAbstract:
碩士國立中興大學
土木工程學系所
105
The objective of this study involved using global navigation satellite system (GNSS) data to achieve reasonable point height accuracy. In this study, the orthometric heights of benchmarks were obtained from first order leveling of Taichung city and GNSS measurements of ellipsoid heights underwent fitting. A traditional fitting method was adopted, in which geoid height was built using generalized least squares combined with a curved surface fitting method. However, because generalized least square calculations do not take into consideration random errors that exist in coefficient matrices and observation vectors, weighted total generalized least square-based calculations were performed to solve these problems. In this study, the combination of weighted total generalized least squares and the quadratic curved surface fitting method improved on the traditional method by considering the covariance matrices of coefficient vectors and observation vectors. The solutions of the new model were subsequently analyzed, elevating point height accuracy to ±1.401 cm. The new method satisfies height accuracy requirements demanded in engineering surveys and provides valuable information for regional geoid height research.
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Lee, Shang-Hsun, and 李尚訓. "A Study of Using Support Vector Machine （SVM） Method to Determine Local Geoid Model─A Case Study of Taichung Area." Thesis, 2010. http://ndltd.ncl.edu.tw/handle/6asuff.
Full textAbstract:
碩士國立中興大學
土木工程學系所
98
The elevation data is used to be acquired by spirit leveling method in Taiwan nowadays. It is worthy, from either academic or practical point of view in engineering survey, to study if GPS-RTK technology can be applied to fast get accurate enough elevation data. The key issue here is geoidal undulation. Most domestic researches of geoid model cover the whole Taiwan area by using gravity surveying data which is relatively difficult to be obtained, time-consuming and much labored while the results are not fit well to some local terrain. In this research all GPS control points with known first-order orthometric heights as well as ellipsoid heights obtained by RTK in Taichung city are used while plane fitting and second-order curve surface fitting methods are also applied to calculate the local geoidal undulation model. In order to get the best solution, issues like data integrality and localization are also considered by changing the quantity and distribution of reference points. At the same time, both randomly selected points and reference points are tested by Support Vector Machine（SVM）method to accurately determine the local geoidal undulation model. The results show that local geoidal undulation models built by each of three methods above meet accuracy requirements of engineering surveying standards ±5 cm. This study provides a fast practical method in getting orthometric heights, meanwhile it can also be used as an academic reference for local geoid model researches.
40
Richards, Mark Alan. "Dynamical Models for the Earth's Geoid." Thesis, 1986. https://thesis.library.caltech.edu/9559/8/Richards_ma_1986.pdf.
Full textAbstract:
The Earth's largest geoid anomalies occur at the lowest spherical harmonic degrees, or longest wavelengths, and are primarily the result of mantle convection. Thermal density contrasts due to convection are partially compensated by boundary deformations due to viscous flow whose effects must be included in order to obtain a dynamically consistent model for the geoid. These deformations occur rapidly with respect to the timescale for convection, and we have analytically calculated geoid response kernels for steady-state, viscous, incompressible, self-gravitating, layered Earth models which include the deformation of boundaries due to internal loads. Both the sign and magnitude of geoid anomalies depend strongly upon the viscosity structure of the mantle as well as the possible presence of chemical layering.
Correlations of various global geophysical data sets with the observed geoid can be used to construct theoretical geoid models which constrain the dynamics of mantle convection. Surface features such as topography and plate velocities are not obviously related to the low-degree geoid, with the exception of subduction zones which are characterized by geoid highs (degrees 4-9). Recent models for seismic heterogeneity in the mantle provide additional constraints, and much of the low-degree (2-3) geoid can be attributed to seismically inferred density anomalies in the lower mantle. The Earth's largest geoid highs are underlain by low density material in the lower mantle, thus requiring compensating deformations of the Earth's surface. A dynamical model for whole mantle convection with a low viscosity upper mantle can explain these observations and successfully predicts more than 80% of the observed geoid variance.
Temperature variations associated with density anomalies in the man tie cause lateral viscosity variations whose effects are not included in the analytical models. However, perturbation theory and numerical tests show that broad-scale lateral viscosity variations are much less important than radial variations; in this respect, geoid models, which depend upon steady-state surface deformations, may provide more reliable constraints on mantle structure than inferences from transient phenomena such as postglacial rebound. Stronger, smaller-scale viscosity variations associated with mantle plumes and subducting slabs may be more important. On the basis of numerical modelling of low viscosity plumes, we conclude that the global association of geoid highs (after slab effects are removed) with hotspots and, perhaps, mantle plumes, is the result of hot, upwelling material in the lower mantle; this conclusion does not depend strongly upon plume rheology. The global distribution of hotspots and the dominant, low-degree geoid highs may correspond to a dominant mode of convection stabilized by the ancient Pangean continental assemblage.
41
Huang, Jing-Yao, and 黃敬堯. "The Verification of GOCE Geoid Models Using GPS/Leveling in Taiwan." Thesis, 2013. http://ndltd.ncl.edu.tw/handle/42779950320948700049.
Full textAbstract:
碩士國立中正大學
應用地球物理研究所
101
The GOCE (Gravity field and steady-state Ocean Circulation Explorer) Mission of the European Space Agency (ESA) is currently the only one using the satellite gravity gradiometry (SGG) technique for exploring the Earth¡¦s gravity. The satellite-observed gravity data is combined to the surface gravity measurements (on land, airborne or shipborne) in order to form a precise model with high-spatial resolution. One of the goals of the GOCE Mission is to provide 1-cm accuracy geoid with the spatial resolution of about 100 km. Hence, we attempted to verify the geoid model derived from GOCE and other gravity missions, such as GRACE (Gravity Recovery and Climate Experiment), CHAMP (CHAllenging Minisatellite Payload), EGM2008 (Earth Gravitational Model 2008), and a local geoid model with the geoid undulation observed at about 2,000 benchmarks in Taiwan by GPS leveling. The objective of this study is to analyze the models and find the best one that one could work with in GPS leveling work in Taiwan. We have categorized the entire Taiwan island into 5 different regions based on their geological settings in order to test the models. The result indicates the local geoid model released by the Ministry of the Interior, the so-called Hwang’s model, is the best choice due to its consistent datum with GPS and the inclusion of very dense surface, shipborne and airborne gravity measurements. The discrepancy of Hwang’s model to the GPS leveling is around 5-10 cm, whereas that of EGM2008 is around 30 cm, that of GOCE is 30-100 cm.
42
HUANG, LI-XIN, and 黃立信. "Using GPS method and high-degree gravitational coefficient' models to study geoid undulation." Thesis, 1992. http://ndltd.ncl.edu.tw/handle/54662770783282215018.
Full text
43
鄭志毅. "A Study for Estimating the Precision of Local Geoid Models determined by using GPS RTK data ─A Case Study of Taichung Monitoring Network." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/94541355440847945015.
Full textAbstract:
碩士國立中興大學
土木工程學系所
96
People usually measure the elevation by direct leveling in Taiwan now,and it will be a great improvement if we could measure the elevation with the precision we except using GPS-RTK technology instantly. And the key-point is how to determinate the geoid undulation value. Currently, the research area of most of the Geoid Model building in Taiwan area covers the entire Taiwan and usually the research method is the gravity measurement. However, because the gravity measurement data is difficult to obtain, and needs a great deal of manpower and working-hour, as well as the reason of the special terrain of Taiwan, the representation of the result is not good enough, and is not totally suitable for the precision requirement in small area. The research adopts the GPS points with known 1st order leveling data, acquiring the coordinate and the ellipsoid height by RTK, computing by plane surface fitting method, Shepard’s 2nd curve surface fitting method and X 3 fitting method, and discussing on the integrality and the localization, with the changing of quantity and distribution of the referencing points, fitting radius and fitting degree to achieve the best solution. According to this research, the root mean square error could achieve ± 1.3cm , ± 1.4cm and ± 1.5cm by adopting plane surface fitting method, Shepard’s 2nd curve surface fitting method and X 3 fitting method to build the geoid model. It fulfills the standard of engineering survey. It provides not only the quicker way to measure the orthometric height on survey engineer, but also a academic reference focus on localized geoid model.
44
Cheng, Chih-I., and 鄭志毅. "A Study for Estimating the Precision of Local Geoid Models determined by using GPS RTK data─A Case Study of Taichung Monitoring Network." Thesis, 2008. http://ndltd.ncl.edu.tw/handle/03558764004041844100.
Full textAbstract:
碩士國立中興大學
土木工程學系所
96
People usually measure the elevation by direct leveling in Taiwan now, and it will be a great improvement if we could measure the elevation with the precision we except using GPS-RTK technology instantly. And the key-point is how to determinate the geoid undulation value. Currently, the research area of most of the Geoid Model building in Taiwan area covers the entire Taiwan and usually the research method is the gravity measurement. However, because the gravity measurement data is difficult to obtain, and needs a great deal of manpower and working-hour, as well as the reason of the special terrain of Taiwan, the representation of the result is not good enough, and is not totally suitable for the precision requirement in small area. The research adopts the GPS points with known 1st order leveling data, acquiring the coordinate and the ellipsoid height by RTK, computing by plane surface fitting method, Shepard’s 2nd curve surface fitting method and fitting method, and discussing on the integrality and the localization, with the changing of quantity and distribution of the referencing points, fitting radius and fitting degree to achieve the best solution. According to this research, the root mean square error could achieve , and by adopting plane surface fitting method, Shepard’s 2nd curve surface fitting method and fitting method to build the geoid model. It fulfills the standard of engineering survey. It provides not only the quicker way to measure the orthometric height on survey engineer, but also a academic reference focus on localized geoid model.