Comparison of Global Geoid Models Against the GPS/Levelling-Derived Geoid Heights in Tanzania

Transcription

1 174 Comparson of Global Geod Models Aganst the GPS/LevellngDerved Geod Heghts n Tanzana Method J. Gwaleba Department of Geospatal Scences and Technology, Ardh Unversty, Dar es Salaam, Tanzana Emal: gwalebamj@gmal.com (Receved: Aug 03, 2018; n fnal form: Oct 22, 2018) Abstract: Ths paper compares the geod heghts from the Global Models EGM2008, and EGM1996 aganst the GPS/Levellngderved geod heghts n Tanzana. For the sake of comparson, the exstng Prelmnary Afrcan Geod Model (AGP03) and the Tanzana Geod Model (TZG13) are also tested aganst the GPS/levellng derved geod heghts at 13 benchmarks selected wthn the Tanzana Prmary Levellng Network (). The comparsons of geod heghts obtaned from these geod models aganst the GPS/levellng geod heghts have been performed n absolute sense. Due to the fact that the ellpsodal heghts (h) obtaned from the GPS do not provde the actual postons of ponts on the geod, the orthometrc heghts (H) are needed. Broadly speakng, the orthometrc heghts are obtaned through tradtonal sprt levellng whch s a labour ntensve work. In order to convert the ellpsodal heght (h) determned from GPS applcatons to orthometrc heght, the Geod heghts are needed. The spatal postons of these benchmarks have been recently determned at cmlevel accuracy (wth respect to ITRF2005) through a GPS campagn. The statstcs of the dfferences between GPS/levellngderved geod heghts (N GPS) and the correspondng geod heghts obtaned from the avalable three geod models (N model) suggests that, AGP03 model s the most sutable at ths moment. The Root Mean Square (RMS) ft of the AGP03 geod model aganst the GPS/levellng data s 53.8 cm, whch s a 2 tmes better ft compared to the Global Geopotental Models (EGM08 and EGM96) n the area of nterest. On the other hand, the RMS of the heght dfferences between the TZG13 and the GPS/levelng derved heghts was 74.7cm. The study suggests that AGP03 geod model s closer to the GPS/levellng geod observatons n comparson to EGM08 model n Tanzana. Key words: Geod Models, GPS/Levellng, Geod,, Tanzana 1. Introducton The demand for heght nformaton from the satellte users based postonng technques, mostly Global Postonng System (GPS), has ncreased nterest on determnaton and use of precse geod models. The knowledge of the local geod surface allows the transformaton of ellpsodal heghts to physcally meanngful orthometrc heghts whch are essental n most of the geodetc applcatons. Thus, GPS measurements n combnaton wth a precse geod model are preferred n obtanng orthometrc heghts nstead of sprt levellng measurements, whch s labourntensve and costly (Sders et al., 1992). Normally, for the purpose of GPS/levellng, n the absence of a publcly avalable geod model, t s benefcal to select a Global Geopotental Model (GGM) whch s a best ft to the local gravty feld as the bass for local or regonal geod model (Kamehr and Sjöberg, 2005). The Global models have a long and mportant hstory n the geodetc communty, specfcally as a tool for computng geod heghts. On the other hand, many applcatons n geodesy, geophyscs and engneerng requre physcally defned heghts related to the earth s gravty feld (orthometrc or normal heghts), typcally produced by sprt levelng. Therefore, for the converson and combnaton of these fundamentally dfferent heght systems, the geod must be known wth accuracy comparable to the accuracy of GPS and levelng. Because more Global Geod Models (GGMs) have now been released nto the publc doman, partcularly those ncludng data from the CHAMP and GRACE satelltes dedcated gravmetry mssons, and new gravtyfeldrelated datasets, t s mportant to make valdatons n order to select the most approprate geod model. The development of the Earth Gravtatonal Model 2008 (EGM08) by the US Natonal Geospatal Intellgence Agency (NGA), (Pavls et al., 2008) and other recent models revealed a major achevement n global gravty feld mappng. The model s complete up to degree and order 2159 and contans addtonal sphercal harmonc coeffcents extendng up to degree 2190 and order 2159, respectvely. The EGM08 can provde long and medum wavelength nformaton of the earth s gravty feld to a hgher resoluton of wavelengths equvalent to 10 of arc. However, there are varous recent models developed ncludng EIGEN6C2, EIGEN6C4, EIGEN6S4, GGM05C, GECO, GOCO05c etc. whch have hgh precson and spatal resolutons of gravty data (Pal et al., 2016). Ths paper compares EGM2008 and local geod models wth the GPS/levellng observatons n Tanzana. Snce the release of the global geod models ncludng the EGM2018 to the earth scence communty, there has been a strong nterest among the geodessts to quantfy ts actual accuracy wth dfferent valdaton technques and external datasets ndependently of the estmaton and error estmaton procedures that were used for ts development (Ylmaz, and Karaal, 2010). Ylmaz and Karaal attempted over Turkey Landmass/Ocean and observed that the global geod that best fts the GPS/levelng derved geod heghts was EGM08. As currently n Tanzana there s no comprehensve natonal geod model whch has been released for the publc use, several attempts have been done to develop and valdate models that best ft n the Tanzana regon. Mayunga Indan Socety of Geomatcs

2 175 (2016, p. 268, cted n Slyvester, 2013) ndcates the developed model whch was used to compute pont values of a gravmetrc geod usng short wavelength whch later on were compared wth GPS/levelng derved geod heghts. The dfferences obtaned and the bases between the geometrc and gravmetrc geod models were recorded. Ulotu (2009) developed the gravty database usng sparse gravty data wth varyng densty, dstrbuton and qualty. Assessment of ths model was done by usng KHT method and Least Squares Modfcaton of Stokes to compute geod of Tanzana, and the accuracy obtaned was 29.7 cm. In selecton of sutable geod model for applcaton purposes, Kamehr & Sjöberg (2005) cautoned and verfed that publshed error estmates for the geod models, partcularly the global models should not be used drectly to judge the most sutable Global Geopotental Model (GGM) for a certan regonal/local geod model representaton, but rather as performance ndcator. The reason s that such performance evaluatons sometmes tend to be too pessmstc and global statstcs are not necessarly true representatves n a partcular regon. Therefore, the user of a GGM should perform hs own accuracy and precson verfcatons, such as comparng the GGMderved gravty feld quanttes wth local data (Lambeck & Coleman, 1983). The global geod model data have never been valdated n Tanzana for publc purposes. In ths context, there s a need of valdatng the global models so that, t can be used n local areas to serve the communtes. The valdaton process should be done by comparng geod heghts obtaned from the global models aganst the GPS/levellng derved geod heghts. However, t s worth mentonng that though many researchers have revewed the need of Natonal Geod Model n Tanzana, such as Ulotu (2009) and Mayunga (2016), the valdaton context has always remaned a research area of nterest due to lack unfed geodetc network. Ths paper checks the compatblty of the EGM08, EGM96, AGP03 and the TZG13 geod models aganst the exstng GPS/levellng derved geod n Tanzana by usng the weghted mean approach. The purpose of ths paper s to present the global geod (EGM08 and EGM96) and local geod (AGP03 and TZG13) heghts valdaton on a certan part of the Tanzana Prmary levellng Network () by GPS/levelng. 2. Geod, Ellpsod and Orthometrc Heghts: A theoretcal framework 2.1. Geodheght To understand what geod heghts mean, t s mperatve to know what does geod entals. The geod s an equpotental surface of the earth's gravty feld whch, a least square sense concdes wth mean sea surface n the open ocean. It s a best ft mean sea level surface. The geod serves as a reference surface for heght systems such as orthometrc heghts. It s a physcal surface whch represents the sze and shape of the earth, by descrbng orgn surfaces for pont heghts, determnng mean earth ellpsod, determnng the horzontal and vertcal datum of reference systems, examnng changes n the earth and sea surfaces (Ylmaz and Karaal, 2010). In ths context, ts physcal realzaton s usually the mean sea surface as determned by ocean tde gauges (Hofmann and Mortz, 2006). In sum, the geod surface s the closed surface gong under the land whch concdes wth stable sea surface that s free of effects lke temperature, pressure, densty, salnty dfferences, currents and tdes, and t s defned by ts potental value (Ylmaz and Karaal, 2010). The geods heght, N can therefore be defned as the separaton of the ellpsod surface wth the geod surface measured along the ellpsodal normal as llustrated n Fgure 1. Geod heghts from the Global Geopotental Models (EGM96 and EGM08) are gven as a set of sphercal harmonc coeffcents (Pavls et al, 2008). Dfferent datasets are often used to determne these coeffcents rangng from satellte observatons, whch gve the socalled satellteonly solutons, to data whch ncorporate satellte altmetry and surface gravty data (Rapp, 1996). For the Afrcan Geod Project model (AGP03), geod heght s derved from the combnaton of Stokes s formula and the geopotental coeffcents mpled by EGM96 model (Merry, 2003) Ellpsod heght The ellpsod s a geometrc surface whch approxmates the geod n a least squares sense. For geodetc purposes, the ellpsod of revoluton s produced when an ellpse s rotated about ts sem mnor axs, provdes a welldefned mathematcal surface whose shape and sze are defned by two parameters vz., Sze of a reference ellpsod can be descrbed by semmnor axs, b or semmajor axs, a; Shape of a reference ellpsod can be descrbed by ts flattenng, f or ts eccentrcty, e. The ellpsod surface as a regular surface can be determned mathematcally. It s for ths reason that, as a reference surface, t s wdely used for horzontal coordnate computatons. Nevertheless, t s tradtonally taken to be of lmted use n heghts as t gnores the flow of lquds (Hofmann & Mortz, 2006). The ellpsod, h above the surface of ellpsod s shown n Fgure Orthometrc heght Orthometrc heghts (H) are more desrable, because they better relate to mean sea level n the geophyscal sense. Orthometrc heght refers to a vertcal datum that s usually taken to be a best ft to mean sea level, ether n a global sense or smply adopted from a local tde gage. Such a surface of equal potental of gravty (geopotental) best serves for descrbng heght changes, because water wll flow and selflevel to the lowest geopotental surface (Roman et al., 2010). Theoretcally, both ellpsodal

3 176 Fgure 1: Relatonshp between geod, ellpsod and orthometrc heghts (Source: Roman et al., 2010) heght and orthometrc heghts are measured along the normal to the ellpsod and along the drecton of the plumb lne (vertcal), respectvely. The actual gravty plumb lne (over exaggerated n drawng) along whch H s reckoned s a curved dstance due to effects of drecton of gravty, known as deflecton of the vertcal. For engneerng purposes, the error produced by ths approxmaton can normally be gnored. Fgure 1 provdes the relatonshp between geod, ellpsod and orthometrc heghts. 2.4 Orthometrc heghts The Tanzana Prmary Levellng Network () was desgned n the 1960 and mplemented between 1961 and 1964 (Mayunga, 2016). It s comprsed of 53 fundamental benchmarks (FBM) made up on loops based on local Mean Sea Level. The measurements were made on land n such a way that the msclosures between forward and back levelng between successve benchmarks s less than ± 3mm k where k s the leveled dstance n klometers. The dstrbuton of the msclosures of the levellng data n the loops was done loopwse after the completon of observatons on each loop. At present the consst of eght (8) loops namely, loop A, B, C, D, E, F, G and H. The leveled orthometrc heghts n the are corrected for gravty effects on the bass of the normal gravty computed by means of the Internatonal Gravty Formula, 1930 (Deus, 2007). The establshment of the was referred to tde gauge measurements at the Tanga harbour whose mean sea level was used as a reference. The value for the mean sea level (MSL) at Tanga harbour was deduced from tde gauge readngs taken durng a 28 months perod from August 1962 to November 1964, both months nclusve. The MSL was used to determne the elevaton of the Reference Fundamental Benchmark at Mawen. The other n land benchmarks were connected to the Mawen FBM through the observatons of loop A and the other loops of. 3. Materals and methods The Weghted Mean Method was devoted to valdate the postonal accuracy of the model, the heght accuracy or both postonal and heght accuracy of the models n absolute sense. In order to determne the Global Geod Model that best ft wth the GPS/Levelng n Tanzana, the geod heghts from EGM08, EGM1996, AGP03 and the TZG13 models were calculated. Generally, the EGM08 model ncorporates satellte data (GRACE), terrestral gravty data and altmetry data (Pavls et al., 2008). The accuracy of the EGM08 equatng to a degree and order 2160 model s clamed to be ± 15 centmeters worldwde. The EGM96 model that ncorporates surface gravty data, altmeterderved free ar gravty anomales from ERS1 and from the GEOSAT Geodetc Msson Global Postonng System (GPS) data, NASA's Trackng and Data Relay Satellte System (TDRSS), the French DORIS system, and the US Navy TRANET Doppler trackng system as well as drect altmeter ranges from TOPEX/POSEIDON (T/P) and the accuracy for the EGM96 geod was ± 50cm worldwde (Lemone et al., 1998; Pavls et al., 2008). The AGP03model ncorporates terrestral gravty data flled at the 5' grd terrestral gravty data set usng gravty anomales mpled by the EGM96 model, wth same accuracy as of EGM96 (Merry, 2003) and the TZG13 that nvolves the use of sphercal harmonc expanson of the Earth s geopotental derved from the GRACE satellte msson (Ulotu, 2009). The TZG13 model has an accuracy of 29.7cm. The EGM08 geod heghts used were obtaned at 5 x 5 grd values for the area of nterest and those computed drectly on benchmarks from the geopotental coeffcents usng software suppled wth the model. The EGM96

4 177 geod heght at each of the 13 benchmarks was obtaned at 5 x 5 grd values by usng NIMA EGM96 calculator program for Wndows 95/NT downloaded from 6/egm96.html. The EGM96 geopotental coeffcents usng sphercal harmonc representatons by the followng expanson that s complete to degree 360 was used to compute the geod heghts. The data fles for the AGP03 geod heghts were downloaded at 5 x 5 grdded free ar gravty anomales Poston of selected benchmarks on part of the GPS observaton was done at 13 benchmarks. The 13 ponts of GPS observaton were made on as possble n accordance wth lattude, longtude and ellpsod heghts as ndcated n Fgure 2. The geodetc coordnates,,h data n ITRF2005 at the 13 benchmarks from the processng of GPS data and the correcton values ( ) were collected as llustrated n Table 1. Table 1: ITRF2005 data based on curvlnear coordnates and ther accuraces wth publshed orthometrc heghts on 13 benchmarks from the Benchmark Name Geodetc coordnates Precson ( ) n meters FBM Dar Lattude: Longtude: Heght: m Heght: m FBM Kwala Lattude: Longtude: Heght:54.951m Heght:79.983m IBM3/54_klosa Lattude: Longtude: Heght:469.00m Heght: m IBM5/47_Dodoma Lattude: Longtude: Heght: m Heght: m FBM Kondoa Lattude: Longtude: Heght: m Heght: m FBM Tabora Lattude: Longtude: Heght: m Heght: m FBM Shnyanga Lattude: Longtude: Heght: m Heght: FBM Mwanza Lattude: Longtude: Heght: m Heght: m FBM Makuyun Lattude: Longtude: Heght: m Heght: IBM A Lattude: /5_Mosh Longtude: Heght: m Heght: m IBM Korogwe Lattude: Longtude: Heght: m Heght: m FBM Mawen Lattude: Longtude: Heght: m Heght:63.237m IBM 15/31_ Wam Lattude: Longtude: Heght: m Heght: m

5 178 Table 2: GPS/levellng derved geod heghts (m) at the selected 13 benchmarks from the GPS measurements. Benchmark Name Heght, h Levelled Heght, H SMD N GPS = h H SMD (m) (m) (m) FBM Dar FBM Kwala IBM3/54_klosa IBM5/47_Dodoma FBM Kondoa FBM Tabora FBM Shnyanga FBM Mwanza FBM Makuyun IBM A 24/51_Mosh IBM Korogwe FBM Mawen IBM 15/31_ Wam data ponts closer to the predcton ponts contrbute to the accuracy of the value of the predcted geod heghts more than the dstant ones. The method has proved to be economcal and suffcently accurate (John and Ulotu 2009, personal communcaton). The predcton s handled accordng to pontwse approach usng the formula: n N W 1 N P. (1) n W 1 The weght W s the recprocal of the dstance between pont P and the corner ponts, N ( = 1, 2, 3, 4) such that: Fgure 2: Selected 13 benchmarks for valdaton of Geod Models from 4. Computatons and dscusson of results 4.1 GPS/Levellngderved geod heghts ( N GPS ) The geod heghts from GPS derved ellpsodal heghts and the orthometrc heghts are referred to as GPS/levellng. The GPS/levellng geod heght results are shown n Table 2. The Profx after a benchmark name ndcates that an auxlary pont had to be establshed to enable GPS observatons Predcton of 5 x 5 geod heghts from geod models Predctons of geod heghts on the 13 benchmarks by usng Weghted mean Method was done. The Weghted Mean approach s the method that makes the use of the weghted functons whch reflect the fact that W L 1 L (2) x y 2 Where, x and y are the rectangular Cartesan coordnates of pont wth P as the orgn. The predcted geod heghts (N P) from the three geod models denoted as N EGM 08 P, N EGM 96 P and N AGP 03 P were determned respectvely. The gven ponts were geod heghts at 5 x 5 grd coordnates around each benchmark. The scheme for obtanng the geod heght of a benchmark P whch les wthn a 5 x 5 grd cell s depcted n Fgure 3. The symbols N 1, N 2, N 3 and N 4 n Fgure 3 denote geod heghts at the grd ntersectons 1,2,3,4., where

6 179 Fgure 3: Predcton boundares of 5 x 5 geod heght grds at all selected benchmarks usng Weghted Mean Approach. These predcted geod heghts were later denoted as N EGM08, N EGM96, N AGP03 and N TZG13. For the purpose of geod heghts valdaton results, the predcted geod heghts from the EGM08, EGM96, AGP03 and the TZG13 geod models respectvely were computed and the results are shown n Table Computatons and comparson of predcted geod models aganst GPS/levellng geod heghts Computatons of geod heghts from Geod Models were done. The dfferences of geod heghts from the GPS/levellng derved geod heghts and those predcted from the geod models at colocated benchmarks provded dscrete geometrc control valdaton as llustrated n Table Summary of geod heghts dfferences Table 5 shows the summary of the predcted geod heght dfferences results from the four geod models (two beng the global and others beng local) at maxmum, mnmum, mean, root mean square as well as standard devaton respectvely.. Table 3: Predcted geod heghts results from EGM08, EGM96, AGP03 and the NTZG13 Geod Models Benchmark Name Predcted Geod heghts (Unts n meters) N EGM08P N EGM96P N AGP03P N TZG13P FBM Dar FBM Kwala IBM 3/54_Klosa IBM 5/47_Dodoma FBM Kondoa FBM Tabora FBM Shnyanga FBM Mwanza FBM Makuyun IBM A 24/51_Mosh IBM 27/55 Korogwe FBM Mawen IBM Wam

7 180 Table 4: GPS/levellngderved geod heghts aganst the predcted geod heghts from the four Geod Models Benchmark Name Geod Heghts from GPS/Level ng Geod Heghts from Models Dfferences n Geod Heghts NGPS NEGM08 NEGM96 NAGP03 NTZG13 NGPS NGPS NGPS NGPS NEGM08 NEGM96 NAGP03 NTZG13 FBM Dar FBM Kwala IBM 3/54_Klosa FBM Tabora FBM Shnyanga FBM FBM Makuyun IBM /47_Dodoma FBM Kondoa Mwanza IBM A 24/51_Mosh IBM Korogwe FBM Mawen IBM Wam Dscusson The results obtaned n ths research shows that there are dfferences between GPS/levellng derved geod heghts and those obtaned from the four geod models. The geod heght dfferences from the GPS/levellng geod heghts and those from EGM08 model range from m to m. The geod heght dfferences from EGM96 model and GPS/levellng geod heghts ranges from m to m whle the geod heght dfferences from AGP03 model aganst GPS/levellng geod heghts range from m to m. The dfferences from TZG13 model versus GPS/levellng geod heghts range from to m. Fgure 4 depcts graphcally the geod heght dfferences from the geod models based on the standard GPS/levellng derved geod heghts n Tanzana. Table 5 provdes summary of predcted geod heght dfferences. Table 5: Summary of the predcted geod heght dfferences results Geod Models Mn Max Mean RMS SD= s EGM08(Nmax = 2190) ± ± EGM96(Nmax = 360) ± ± AGP ± ± TZG ± ± 0.717

8 Dfferences n Geod Heghts (m) Dar Kwala Klosa Dodoma Kondoa Tabora Shnyanga Mwanza Makuyun Mosh Korogwe Mawen Wam EGM08 EGM96 AGP03 TZG Benchmarks Fgure 4: Comparsons of absolute dfferences of the predcted geod heghts from each model based on GPS/levellng derved geod heghts The mean dfferences are m, m, m and m; the RMS dfferences are ±1.186 m, ±1.530 m, ± m and m; the sample standard devatons are ± m, ± m, ±0.310 m and from EGM08, EGM96, AGP03 and TZG13 respectvely as represented graphcally n Fgure Conclusons The results of these comparsons of the Geod models aganst the GPSLevellng derved geod heghts over 13 benchmark shows that among the developed geod models EGM08, EGM96, AGP03 and the TZG13, the AGP03 model s the best geod model that fts the GPS and levellng data n Tanzana at present. The mean dfferences of m and the RMS of ± m lead to the concluson that the AGP03 geod model s a better model for GPS/Levellng n Tanzana than other three geod models. Thus the EGM08 geod model does not produce geod heghts that are closer to GPS/levellng geod heghts; rather the AGP03 geod model does so. The major contrbuton may however come from the hgher wavelength of 5 whch mproves the consstence Accuracy values Mean RMS STD EGM08 EGM96 AGP03 TZG13 Mean RMS STD Fgure 5: Accuracy evaluaton of geod models due to comparsons at ndependent test benchmarks n the area of nterest

9 182 between the AGP03 and the GPS/levellng geod heghts such that ts shorter wavelength of 5 durng ts computatons and the fact that Stoke s formula s more senstve to short wavelength components of geod heghts than the hgher degree (> 360) sphercal harmoncs n the EGM08. Thus, the results obtaned from pontwse valdaton have revealed that the AGP03 geod model performs exceedngly better than other models over the area of nterest. The TZG13 whch was expected to be the best model as tested n the 13 benchmarks, does not provde the best accuracy as compared to AGP03. Acknowledgement I would lke to express my grattude to the Survey and Mappng Dvson of the Mnstry of Lands, Housng and Human Settlements Development, especally Mr. Shja Wachawandeka for provdng me the orthometrc heghts as well as the GPS observaton data of the benchmarks coverng the study area. I am also grateful for the unlmted support from Prof. Peter Morgan (the tme when he was workng for establshng the Tanzana Geodetc Network) for a free computaton of the geod heghts from EGM08 model wthout whch access to the EGM08 datasets would be very dffcult durng the study. Also, I thank Dr. Ulotu Prosper for provdng me geod heghts from the TZG13 model for the 13 benchmarks. Eventually, many thanks are extended to the revewers of ths study. References Deus, D. (2007). Determnaton of transformaton parameters between the Tanzana natonal levellng datum and the geod. Master s Thess, Ardh Unversty. Dar es salaam, Tanzana. Hofmann, B and H. Mortz (2006). Physcal Geodesy, Second corrected edton, Sprnger Wen New York. John, S and P.E. Ulotu (2000). Earth s gravty feld and ts applcaton n Geodesy, Lecture Notes, Ardh Unversty, Tanzana. Kamehr, R and L.E. Sjöberg (2005). Comparson of the qualtes of recent global and local gravmetrc geod models n Iran, Royal Insttute of Technology, Geodesy Group, SE Stockholm, Sweden. Lambeck, K and R. Coleman. (1983). The Earth s shape and gravty feld: A report of progress from 1958 to Geophyscal Journal of the Royal Astronomcal socety, 74, Lemone, F.G., S.C. Kenyon, J.K. Factor, R.G. Trmmer, N.K. Pavls, D.S. Chnn, C.M. Cox, S.M. Klosko, S.B. Luthcke, M.H. Torrence, Y.M. Wang, R.G. Wllamson, E.C. Pavls, R.H. Rapp and T.R Olson (1998). The development of the jont NASA GSFC and the Natonal Imagery and Mappng Agency (NIMA) geopotental model EGM96, NASA/TP Mayunga, S. (2016). Towards a New Geod Model of Tanzana Usng Precse Gravty Data, Journal of Envronmental Scence and Engneerng, A (5), Merry, C.L. (2003). The Afrcan Geod model Project and ts relevance to the unfcaton of Afrcan vertcal reference frames (AFREF). 2nd FIG Regonal conference, Marrakech, Morocco, December 25, Roman, D., Y.M. Wang, J. Saleh and X. L (2010). Geodesy, Geods and Vertcal Datums: A Perspectve from the U. S Natonal Geodetc Survey. FIG Congress Sdney, Australa. Pal, S., S. Narayan, T.J. Majumdar and U. Kumar. (2016). Structural mappng over the 85 E Rdge and surroundngs usng EIGEN6C4 hghresoluton global combned gravty feld model:an ntegrated approach. Mar Geophys Res. DOI /s Pavls, N.K., S.A. Holmes, S.C Kenyon and J.K. Factor (2008). An Earth Gravtatonal Model to degree 2160: EGM2008, presented at the 2008 general assembly of the European Geoscences Unon, Venna, Austra, Aprl 13 18, Rapp, R.H. (1996). Use of potental coeffcent models for geod undulaton determnatons usng a sphercal harmonc representaton of the heght anomaly/geod undulaton dfference, Journal of Geodesy, 71, Ulotu, P.E. (2009). Geod Model of Tanzana from sparse and varyng gravty data densty by the KTH method, Doctoral Dssertaton n Geodesy PhD Thess, Dvson of Geodesy, KTH Stockholm Sweden. Ylmaz, N and C. Karaal (2010). Comparson of global and local gravmetrc geod models n Turkey, Scentfc Research and Essays, 5(14),