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DISCUSSION ON SOME FFT PROBLEMS TO DETERMINE THE geoid

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Geo-Spatial Information Science 2000年第2期3卷 53-57页

作者： Essam Ghanem LI Jiancheng GPS Center Wuhan Technical University of Surveying and Mapping Wuhan China

The aim of this investigation is to study some FFT problems related to the application of FFT to gravity field convolution *** the others,such as the effect of spectral leakage,edge effects,cyclic convolution and effect of padding,are also discussed.A numerical test for these problems is made.A large area of Western China selected for the test is located between 30°N～36°N and 96°E～102°E and includes 1 858 gravity observations on *** results show that the removal of the bias in the residual gravity anomalies is important to avoid spectral *** hundred percent zero padding is highly recommended for further research of the geoid to remove cyclic convolution errors and edge effects.1_D FFT is recommended for precise local geoid determination because it does not use kernel approximation.

关键词： fast Fourier transformation (FFT) geoid determination

GPS-GRAVIMETRIC geoid DETERMINATION IN EGYPT

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Geo-Spatial Information Science 2001年第1期4卷 19-23页

作者： Essam Ghanem GPS Center Wuhan University Wuhan China

The main objective of this study is to improve the geoid by GPS/leveling data in *** of the gravimetric geoid with GPS/leveling data have been *** the basis of a gravimetric geoid fitted to GPS/leveling by the least square method,a smoothed geoid was obtained.A high_resolution geoid in Egypt was computed with a 2.5′×2.5′ grid by combining the data set of 2 600 original point gravity values,30″×30″ resolution Digital Terrain Model (DTM) grid and the spherical harmonic model *** method of computation involved the strict evaluation of the Stokes integral with 1D_*** standard deviation of the difference between the gravimetric and the GPS/leveling geoid heights is ±0.47 *** standard deviation after fitting of the gravimetric geoid to the GPS/leveling points is better than ±13 *** the future we will try to improve our geoid results in Egypt by increasing the density of gravimetric coverage.

关键词： gravimetric geoid GPS/leveling data fitting

geoid interpolation in Gongzhuling City and the 1cm quasi geoid refinement

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Global Geology 2024年第4期27卷 207-215页

作者： WANG Yongchun ZHONG Linshan ZHAO Han WU Qiong Tianjin Best Marine Geo-Technology Co.Ltd. Tianjin 300457China School of Geodesy and Geomatics Wuhan UniversityWuhan 430079China College of Geo-exploration Science and Technology Jilin UniversityChangchun 130026China

The refinement of the 1cm geoid holds significant importance in engineering applications,where the accuracy of the geoid is frequently constrained by its ***,there has been limited exploration into the specific relationship between geoid resolution and *** article aims to address this gap by thoroughly examining said *** study employs the CapRCR modification to calculate the geoid of Gongzhuling *** findings indicate that the accuracy can be enhanced by 2%to 9%through encryption of the geoid resolution from 2.5′×2.5′to 1.5′×1.5′.Furthermore,this improvement can be augmented by 15%to 21%through encryption of the gravity anomaly to the same *** accuracy of the geoid exhibits a linear relationship with the resolution of gravity *** theoretical accuracy of the geoid,excluding integration errors,is determined to be 1.21 *** engineering applications,opting for a resolution of 30''×30''can result in the geoid containing only an integration error of 2 ***,to attain an accuracy of 1 cm,it becomes imperative to further mitigate data ***,the final refined quasi-geoid accuracy is established at 0.56 mm.

关键词： geoid resolution RCR technique interpolation

Refining geoid and vertical gradient of gravity anomaly

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Geodesy and Geodynamics 2011年第4期2卷 1-9页

作者： Zhang Chijun Bian Shaofeng Yi Zhourun Liu Lingtao Fang Jian Institute of Geodesy and Geophysics Chinese Academy Science Wuhan 430077 China Naval Engineering University Wuhan 430033 China

We have derived and tested several relations between geoid （N） and quasi-geoid （~） with model validation. The elevation correction consists of the first-term （Bouguer anomaly） and second-term （vertical gradient of gravity anomaly）. The vertical gradient was obtained from direct measurement and terrain calcula- tion. The test results demonstrated that the precision of geoid can reach centimeter-level in mountains less than 5000 meters high.

关键词： refine geoid quasi-geoid gravity anomaly vertical gradient

Establishment of a Geometric geoid Model and Evaluation of the EGM2008 and EIGEN-6CA Models over the Dakar-Thies-Mbour Triangle in Senegal

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International Journal of Geosciences 2024年第11期15卷 927-939页

作者： Diogoye Diouf Moustapha Gning Tine Sokhna Mou Mapeinda Gueye Serigne Saliou Fall Unit de Formation et de Recherche Sciences de lIngnieur Universit Iba Der Thiam de This This Senegal

High-accuracy geoid determination is an essential goal that many groups of scientists and countries are striving to achieve. Techniques for determining geoid models have evolved over time. Unfortunately, this all-important determination requires relatively substantial technical and financial resources, depending on the type of geoid to be determined. This situation justifies the inadequacy, and sometimes absence, of accurate geoid models in many countries, despite the new challenges of altimetric positioning using space or satellite positioning techniques. This study focuses on the establishment of a geometric geoid model using simplistic techniques that are accessible and applicable in restricted or wide areas, with or without gravimetric data. The study was applied to the Dakar-Thiès-Mbour triangle, the two regions in the extreme west of Senegal that are home to the most infrastructure projects with the highest socio-economic stakes, as well as mines currently being exploited, and therefore the highest stakes in terms of positioning. This study also enabled us to assess the accuracy of a number of global field models in Senegal, which are used by some professionals for altimetric positioning using Global Positioning Satellite Systems (GNSS) in the absence of a local geoid model. The estimated geoid model is based on the determination of undulation at various sample points in the study area. To this end, a campaign of GNSS observations and direct levelling was carried out on the various points spread across the study area. These measurements were then used to determine the undulation at each point. Bilinear interpolation was used to deduce the undulations throughout the study area, based on the altimeter conversion grid. This grid was evaluated using GPS/level control points.

关键词： Model geoid Geometric Levelling GNSS Undulation EGM2008 EIGEN-6CA

Determination of a Gravimetric geoid Solution for Andalusia (South Spain)

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Engineering（科研） 2010年第3期2卷 160-165页

作者： Francisco Manzano Victor Corchete Mimoun Chourak Gil Manzano 不详

The orthometric heights can be obtained without levelling by means of the ellipsoidal and geoidal heights. For engineering purposes, these orthometric heights must be determined with high accuracy. For this reason, the determination of a high-resolution geoid is necessary. In Andalusia (South Spain) a new geopotential model (EIGEN-GL04C) has been available since the publication of a more recent regional geoid. As a consequence, these new data bring about improvements that ought to be included in a new regional geoid of Andalusia. With this aim in mind, a new gravimetric geoid determination has been carried out, in which these new data have been included. Thus, a new geoid is provided as a data grid distributed for the South Spain area from 36 to 39 degrees of latitude and –7 to –1 degrees of longitude (extending to 3 × 6 degrees), in a 120 × 240 regular grid with a mesh size of 1.5’ × 1.5’ and 28800 points in the GRS80 reference system. This calculated geoid and previous geoids are compared to the geoid undulations obtained for 262 GPS/levelling points, distributed within the study area. The new geoid shows an improvement in accuracy and reliability, fitting the geoidal heights determined for these GPS-levelling points better than any previous geoid.

关键词： Gravity geoid FFT GPS/Levelling Andalusia South Spain

Determination of Antarctic geoid by using global gravity field

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Chinese Journal of Polar Science 2000年第1期11卷 1-8页

作者：陈春明李建成 Antarctic Surveying and Mapping Center of China Wuhan Technical University of Surveying and Mapping.Wuhum 430070 China

With Chinese latest global gravity field model WDM94, the authors provide the geoid height and mean free air gravity anomaly of Antarctica (The range of latitude is from -60° to -90°). In order to conclude and analyze the characters of Antarctic geoid roundly, the authors collect the latest oversea global gravity field model OSU91 (to degree and order 360) and JGMOSU (to degree and order 360), get the corresponding geoid height and mean free air gravity anomaly. The results are compared with the results got from WDM94, thus we get the difference. The standard deviation of geoid height between WDM94 and OSU91 is ±1.90 m;the deviation of geoid between WDM94 and JGMOSU is ±2.09 m. The standard deviation of mean gravity anomaly are ±8.97 mGal and ±9.32 mGal respectively. [***]

关键词： Antarctica geoid gravity anomaly gravity field model.

Modelling Orthometric Heights from a Combination of Ellipsoidal Heights and Gravimetric geoid Model in Rivers State, Nigeria

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International Journal of Geosciences 2020年第4期11卷 184-196页

作者： Kurotamuno P. Jackson Elochukwu C. Moka Department of Surveying and Geomatics Rivers State University Port Harcourt Port Harcourt Nigeria Department of Geoinformatics and Surveying University of Nigeria Enugu Campus Enugu Nigeria

Many applications in geodesy, hydrography and engineering require geoid-related heights. Spirit leveling which is the traditional means of obtaining geoid- or mean sea level-related heights is slow, time-consuming and costly. Global Navigation Satellite Systems (GNSS) offer faster and relatively cheaper way of obtaining geoid-related heights when geoidal undulation is applied to ellipsoidal heights. However, difficulties involved in determining acceptable geoid height have seriously hampered the application of GNSS for leveling in Rivers State, thus necessitating the need to develop an acceptable geoid model which will serve as a means of conversion of GNSS-delivered ellipsoidal heights to their orthometric heights equivalent. In pursuance of this objective, a detailed gravimetric geoid has been evaluated for Rivers State, Nigeria. The computation of the geoid was carried out by the traditional remove-restore procedure. The Earth Geopotential Model 2008 (EGM08) was applied as the reference field for both the remove and restore parts of the procedures;spherical Fast Fourier Transform (FFT) was employed for the evaluation of the Molodenskii’s integral formula for the height anomaly, (ζ) to yield the quasi-geoid;while the Residual Terrain Modelling (RTM) was done by prism integration. The classical gravimetric geoid over Rivers State was obtained from the rigorously evaluated quasi-geoid by adding the quasi-geoid to geoid (N?- ζ) correction it. The minimum and maximum geoid height values are 18.599 m and 20.114 m respectively with standard deviation of 0.345 m across the study area. Comparison of the gravimetric geoidal heights with the GPS/Leveling-derived geoidal heights of 13 stations across Rivers State, Nigeria showed that the absolute agreement with respect to the GPS/leveling datum is generally better than 7 cm root mean squares (r.m.s) error. Results also showed that combining both GPS heights and the computed Rivers State geoid model can give orthometric heigh

关键词： geoid Modelling Remove-Compute-Restore Fast Fourier Transform Residual Terrain Model Ellipsoidal Heights Orthometric Heights

Modeling a Local geoid: Application in Thies, Senegal

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International Journal of Geosciences 2024年第11期15卷 940-956页

作者： Mouhamadou Moustapha Mbacké Ndour Papa Matar Sylla Babacar Faye Moussa Mbacké Ndour UFR-SI University of Iba Der Thiam Thies Senegal Holding Gueye Dakar Senegal Simon & Christiansen Afrique (S.C.A) Dakar Senegal

Many applications in geodesy, hydrography and engineering require determining heights linked to the geoid. Direct leveling, which is the traditional method of obtaining these elevations, is slow, time consuming and expensive. The contribution of space techniques can make it possible to overcome these constraints provided that we have a precision geoid model compatible with that obtained by the GNSS method. There are today relatively precise regional geoid models, at least outside of mountain ranges, in all developed countries, which is not yet the case in developing countries like Senegal. An alternative is to use local models restricted to a small area. Thus, this study aims to produce a geoid model by combining multi-source data for the city of Thies intended mainly to support leveling operations by GNSS. To achieve this objective, direct precision leveling and GNSS leveling (static mode) were carried out covering the study area. The reference points used are, among others, those of the RRS04 (Reference Network of Senegal 2004) and the NGAO53 (General Leveling of West Africa 1953). Additionally, gravimetric measurements were conducted using the Sensor Play-Data Recorder application. The calculation of the model was carried out by the SRBF (Spherical Radial Basis Function) method using the PAGravf4.5 software. The SRBF method uses EGM08 to first calculate height and gravity anomalies. These are then compared with the raw data in order to determine the residuals which will allow the model to be refined. In order to validate our model, control points (GNSS/leveled) were chosen based on a homogeneous geographical distribution in the area in order to evaluate their altitude. An accuracy of less than 2 cm was obtained. Comparing our model with the existing local model GGSV12v1 shows that our model is more accurate.

关键词： geoid Direct Leveling GNSS Gravity PAGravf4.5 SRBF Thies