Construction of initial national quasi-Geoid model VIGAC2017, first step to national spatial reference system in Vietnam

Vietnam Journal of Earth Sciences 39(2), 155-166, DOI: 10.15625/0866-7187/39/2/9702 155 (VAST) Vietnam Academy of Science and Technology Vietnam Journal of Earth Sciences Construction of initial national quasi-geoid model VIGAC2017, first step to national spatial reference system in Vietnam Ha Minh Hoa Vietnam Institute of Geodesy and Cartography Received 08 March 2017. Accepted 31 March 2017 ABSTRACT Vietnam national WGS-84 reference ellipsoid was obtained in 1999 from results of an orientation of the global WGS-84 reference ellipsoid. However, usage of the broadcast satellite messages doest not give high accuracy in de- termination of national quasi-geoid heights. Based on the determined geopotential of the Hon Dau local geoid and constructed initial mixed quasi-geoid model VIGAC2014, this scientific article presents results of building of initial national quasi-geoid model VIGAC2017. Used data consisting of geodetic coordinates B, L, H of 164 first and se- cond orders benchmarks of the national leveling networks was obtained from GPS data processing in ITRF according to global WGS-84 ellipsoid with satellite ephemeris accuracy at level of ± 2,5 cm, and the initial mixed quasi-geoid model VIGAC2014 was constructed from the EGM2008 model. The orientation of the WGS-84 ellipsoid was ac- complished under conditions of it’s best fitting to the Hon Dau local quasi-geoid and the parallelism of its axes to the corresponding axes of the national WGS-84 reference ellipsoid allows get national quasi-geoid heights  and coor- dinate transformation parameters ,,, 000 dZdYdX that have been used for conversion of the mixed quasi-geoid heights from the VIGAC2014 quasi-geoid model to the initial national quasi-geoid model VIGAC2017. Along withquasi-geoid heights ,* which were obtained from the initial national quasi-geoid model VIGAC2017, an estimation of the accuracy of differences ( *  ) shows that quasi-geoid heights * have the ac- curacy at the level of ± 6,2 cm. Apart from that determination of seven coordinate transformation parameters , , , , , ,0 0 0dX dY dZ mX Y Z    leads to the building of the initial national spatial reference system in Vietnam. Keywords: Global quasi-geoid, local quasi-geoid, mixed quasi-geoid, orientation of ellipsoid. ©2017 Vietnam Academy of Science and Technology 1. Introduction1 In history of construction of national verti- cal reference systems in the world, starting from point of view of German mathematician *Corresponding author, Email: minhhoavigac@gmail.com Carl Friedrich Gauss (1777 - 1855) in 1828 (Gauss C.F., 1828) about a coincidence of the geoid with an undisturbed mean sea level on the oceans and proposal of German mathema- tician Johann Benedict Listing (1808 - 1882) in 1873 (Listing J.B., 1873) about the usage of the geoid for initial surface of the vertical ref- Ha Minh Hoa/Vietnam Journal of Earth Sciences 39 (2017) 156 erence systems, every country or group of different countries used a mean sea level at the zero tide gauge station. In Vietnam, tide gauge station of Hon Dau is used for the con- struction of national or regional vertical refer- ence system. At present, we know that the geoid didn’t coincide with the mean sea level on oceans, geopotential 220 .0,62636856  smW on the surface of the global geoid had been determined by al- timetry data (Bursa M., Kenyon S, et al., 2007)and accepted by IERS (Petit G., Luzum B., 2010). Abovementioned achievement gives ability to determine the geopotential 0W of the local geoid, best fitting to mean sea lev- el at zero tide gauge station. In Vietnam, geo- potential 220 .2911,62636847  smW of the Hon Dau local geoid was announced in (Ha Minh Hoa et al., 2012; Ha Minh Hoa, 2013b; Ha Minh Hoa, 2014b). Because the Hon Dau local quasi-geoid coincides with the Hon Dau local geoid on the sea and it has been used for the initial surface of vertical reference system of Hai Phong 1972 (HP72), the usage of the Hon Dau local quasi-geoid for solving the task of ellipsoid orientation creates important base of construction of the high accurate national quasi-geoid model. In Vietnam GNSS technology is widely used for research of the Earth crustal move- ment or ionosphere disturbances during the magnetic storm (Le Huy Minh et al., 2016; Vy Quoc Hai et al., 2016, Ha Minh Hoa, Dang Hung Vo et al., 2005) proposed the construc- tion of the national dynamic coordinate sys- tem, that in fact is national spatial reference system with the purpose of closely connecting to ITRF. In addition, the construction of the national spatial reference system is the most important content of Development Strategy of Geodesy and Cartography to the 2020 year by Decision No. 33/2008/QĐ-TTg of the prime minister on 27 February 2008. Thanks to GNSS technology, we get high accurate geodetic coordinates B, L in VN2000 2D. However, getting geodetic height H re- quires the high accurate national quasi-geoid model. (Ha Minh Hoa et al., 2012; Ha Minh Hoa, 2014a) analyzed scientific base for the construction of the national dynamic coordi- nate system, in which the most important task is a creation of the high accurate national qua- si-geoid model with accuracy more than ±4 cm to get spatial coordinates of geodetic points with relative accuracy at level 10-9 by international regulation. For that, we must return to solve the task of the orientation of global WGS-84 ellipsoid best fitting to the Hon Dau local quasi-geoid. Solving above-mentioned task, we will get coordinate transformation ,,, 000 dZdYdX which are spatial coordinates of the center of the WGS-84 global reference ellipsoid ac- cording to the center of the WGS-84 national (local) reference ellipsoid. Hence we will ob- tain two types of data: - Data of type 1: Geodetic coordinates HLB ,, of GNSS points, with being used for solving the task of the orientation of ellip- soid in the national spatial reference system VN2000 - 3D. Global WGS-84 reference el- lipsoid oriented under the condition of the best fitting to the Hon Dau local quasi-geoid will become the WGS-84 national (local) ref- erence ellipsoid (Figure 1); - Data of type 2: National quasi-geoid heights  of GNSS points. For the purpose of construction of the high accurate national quasi-geoid model, we are only interested in data of type 2. Thus, the high accurate national quasi-geoid model is the model of quasi-geoid heights  of specif-ic points on the surface of the Hon Dau local quasi-geoid according to the surface of the WGS-84 national reference ellipsoid. For solving the task of orientation of ellip- soid, we must create a GNSS network on whole territory of Vietnam and accomplish Vietnam Journal of Earth Sciences 39(2), 155-166 157 processing of GNSS data in ITRF on base of the using of satellite ephemeris with accuracy at the level ± 2,5 cm, which allows getting global geodetic H (Figure 1) with accuracy at the level ± 1,4 cm. After processing of GNSS data in ITRF, we obtain spatial coordi- nates , ,X Y Z and global geodetic coordi- nates , ,B L H of GNSS points according to the WGS-84 global reference ellipsoid. Apart from that, GNSS points have national normal heights H obtained by first and second or- ders differential leveling from first and second orders national benchmarks and determined from the surface of the Hon Dau local quasi- geoid (Figure 1). Aforementioned GNSS points have been called as orientation points. Figure 1. Relationships between local quasi-geoid, global quasi-geoid, local ellipsoid and global ellipsoid The national quasi-geoid model is the model of heights of points M1 on the surface of the Hon Dau local quasi-geoid according to the surface of the WGS-84 national reference ellipsoid, in addition, points M1 corresponds to points M on the Earth’s physical (Figure 1). In Figure 1, we symbolize as local quasi- geoid height (national quasi-geoid height) of point M and is equal to segment M1M3, as mixed quasi-geoid height of point M and is equal to segment M1Q0, as global quasi- geoid height of point M and is equal to seg- ment M2Q0, 210 MMD  as height of point M1 on the Hon Dau national (local) quasi- geoid according to the global quasi-geoid. Result of the orientation of the global el- lipsoid under the condition of best it’s fitting to the Hon Dau national quasi-geoid allows obtaining the national quasi-geoid height (lo- cal quasi-geoid height)  and the local geo- detic height H of GNSS point so that .  HH High accurate national quasi-geoid heights  of GNSS points are very pre- cious data for serving the construction of the high accurate national quasi-geoid model and the determination of the 07 coordinate trans- formation parameters from ITRF to national spatial reference system VN2000 - 3D by formula of Bursa - Wolf with the purpose of a close connection between two those spatial reference systems. The results of solving tasks of the orientation of the WGS-84 global refer- Earth’s physical surface M Local (national) quasi-geoid Global quasi-geoid Local (national) reference ellipsoid M1 M2 M3 Global reference ellipsoid Ha Minh Hoa/Vietnam Journal of Earth Sciences 39 (2017) 158 ence ellipsoid under the condition of the best it’s fitting to the Hon Dau local quasi-geoid, the construction of the high accurate national quasi-geoid model and the determination of the 07 coordinate transformation parameters from ITRF to national spatial reference sys- tem VN2000 - 3D by formula of Bursa - Wolf will be presented in this scientific article. It is necessary to underline that it was seen in 1999 the accomplished orientation of the WGS - 84 global reference ellipsoid under the condition of the best fitting to the Hon Dau local quasi-geoid in the proves of the con- struction of the plane coordinate reference system VN2000-2D based on the GPS data of the 25 GPS points. However, in that period, the GPS data has not been processed in ITRF with the using of satellite ephemeris with ac- curacy at level ±2,5 cm by software Bernese, rather being processed in WGS-84 with the usage of broadcast satellite message by soft- ware GPSuvey. Because global geodetic co- ordinates , ,B L H of GPS points did not achieve high accuracy and national quasi- geoid heights with the accuracy only at level ±1,6 m (Scientific report, p.125). This accura- cy satisfied requirement of reduction of meas- urements to ellipsoid for adjustment of the national astro - geodetic network, but did not meet the requirement of the construction of the high accurate national quasi-geoid model. In order to construct the high accurate na- tional quasi-geoid model, we must solve 03 problems: Problem 1. Based on n orientation points, accomplishing the orientation of the WGS-84 global reference ellipsoid under the condition of the best it’s fitting to the Hon Dau local quasi-geoid, we will get 03 coordinate trans- formation parameters , ,0 0 0dX dY dZ from ITRF according to the WGS-84 global refer- ence ellipsoid to VN2000 - 3D according to the WGS084 national reference ellipsoid and national quasi-geoid heights  of the n abovementioned points of orientation. This problem will be solved in 3.1. Problem 2. Creation of relationship be- tween the mixed quasi-geoid model and the national quasi-geoid model with the purpose of propagation of the national quasi-geoid model for the whole territory of Vietnam; Construction of the national quasi-geoid mod- el VIGAC2017 and estimation of the accuracy of this model. This problem will be solved in 3.2. Problem 3. Estimation of differential rota- tions , ,X Y Z   and differential scale change m between ITRF and VN2000 - 3D based on geodetic coordinates B, L in VN2000 2D, national normal heights ,H global geodetic coordinates , ,B L H of orien- tation points and results of solution of prob- lem 2. This problem will be solved in 3.3. 2. Data In order to solve the above-mentioned problems, we can have set of orientation points covering the whole territory of Vietnam. Accomplishing project “Con- struction of local geoid model on territory of Vietnam” in period 2009 - 2010 Vietnam De- partment of Surveying and Cartography car- ried out GPS observations on 290 first order benchmarks, 199 second order benchmarks and GPS data processing in ITRF by software Bernese on base of the using of satellite ephemeris with accuracy at level ±2,5 cm. Because of the displacement of some first and second orders benchmarks from so- cial - economic activities and Earth’s crustal movements, on base of Smirnov’s statistic criterion selected the 89 most stable first order benchmarks and the 75 most stable second order benchmarks (Ha Minh Hoa et al., 2016a; Luong Thanh Thach, 2016). Thus, we have all 164 first, second orders benchmarks, covering over the whole territory of Vietnam, with high accurate global geodetic coordinates Vietnam Journal of Earth Sciences 39(2), 155-166 159 , ,B L H according to the WGS-84 global reference ellipsoid, and use them as orientation points for solving abovementioned problems. Ha Minh Hoa, et al., (2012); Ha Minh Hoa, (2013b); Ha Minh Hoa et al., (2016a) determined geopotential 2 262636847, 2911 .0W m s of the Hon Dau local geoid and height 0,8900D m of the Hon Dau local quasi-geoid according to the global quasi-geoid. Estimation of height 0D shows that it is constant on whole territory of Vietnam (Ha Minh Hoa, et al., 2012; Nguyen Tuan Anh, 2015) and in global scale (Ha Minh Hoa, 2016b). With above-presented research results,we can calculate mixed quasi- geoid height * from global quasi-geoid height  by the following formula: * 0,8900D m      (1) where  is the global quasi-geoid height determined from the EGM2008. Formula (1) has been used for the construction of the mixed quasi-geoid model VIGAC2014 in the state order science - technological theme (Ha Minh Hoa et al., 2016a). The accuracy of mixed quasi-geoid model VIGAC2014 has obtained at level ±7 cm based on the 89 first-order benchmarks (Ha Minh Hoa et al., 2016a) and at level ±8 cm based on the 75 second order benchmarks (Luong Thanh Thach, 2016). Above-mentioned levels of accuracy fully correspond to levels of accuracy of the first and second orders national normal heights (Ha Minh Hoa, 2014b). However, those levels of accuracy do not satisfy the requirement of accuracy more than ±4 cm of the national quasi-geoid model used for the construction of the national spatial reference. Apart from that, the mixed quasi-geoid model VIGAC2014 is not the national quasi-geoid model. That is why we must solve problem of orientation of the WGS-84 global reference ellipsoid, best fitting to the Hon Dau local quasi-geoid, with purposes of transformation of the mixed quasi-geoid model VIGAC2014 to the national quasi-geoid model and it’s accuracy estimation. With the purpose of calculation of national normal heights by the mixed quasi-geoid model VIGAC2014 and GNSS technology, (Ha Minh Hoa, 2014b) constructed criterion for base points of mixed quasi-geoid model VIGAC2014. The result determined 09 base points such as I(HN-VL)6-1, I(HN- VL)28-1, I(HN-VL)64, I(HN-VL)72, I(VL- HT)98, I(VL-HT)158, I(BH-HN)33, I(BH- TH)65, I(BH-TH)122A. Those base points have been the accomplished transmission of national normal heights to 30 GNSS points of the North Vietnam geodynamic network, the Cuu Long delta geodynamic network and 02 GNSS points on islands Con Dao, Phu Quoc with the maximal distance of transmission at the level of 1,500 km. On every GNSS point deviation from 09 obtained normal heights does not exceed 1,5 cm (Ha Minh Hoa et al., 2016a). This shows that differences of mixed quasi-geoid heights between arbitrary two points from the mixed quasi-geoid model VIGAC2014 have very high accuracy. So the mixed quasi-geoid model VIGAC2014 is very important data resource for the construction of the high accurate national quasi-geoid model. 3. Applied methods By IAG resolution No.16 (June 1983) in Hamburg (Germany) (International Association of Geodesy (IAG), 1984), all geodetic data must be processed in the zero tide system. (Ha Minh Hoa, 2014b) presented formulas for conversion of normal height H from the mean tide system to the zero tide system, of global geodetic height H and global quasi-geoidheight  from the free - tide system to the zero tide system. In the next research of this article we understand that all normal heights, geodetic heights and quasi- geoidheights belonged to the zero tide system. Ha Minh Hoa/Vietnam Journal of Earth Sciences 39 (2017) 160 3.1. Method of orientation of WGS-84 ellipsoid for it’s best fitting to the Hon Dau local quasi-geoid It is assumed that we have set of n orientation points. By regulation of IERS, national reference ellipsoid must be oriented so that its axes are parallel to corresponding international axes. Because the main axes of the WGS-84 global reference ellipsoid are parallel to corresponding international axes, we must orient the WGS-84 global reference ellipsoid under the condition of the best fitting to the Hon Dau local quasi-geoid so that the axes of the WGS-84 national reference ellipsoid are parallel to the corresponding axes of the WGS-84 global reference ellipsoid. Then for i-th orientation point ( i = 1,2,, n) relationship between the local geodetic height Hi according to the WGS-84 national reference ellipsoid and the local geodetic height Hi according to the WGS-84 global reference ellipsoid is presented in the following form: (Ha Minh Hoa, 2013a): 0 . ,0 0 dX H H A dYi i i dZ          (2) where coefficient matrix A has form: (cos cos cos sin sin ),A B L B L Bi i i i i i   , ,B L Hi i i are global geodetic coordinates of i-th point according to the WGS-84 global reference ellipsoid. Symbolizing iH as national normal height of i-th orientation point, on account of ,H Hi i i   ,H Hi i i   where i is the mixed quasi-geoidheight of i-th point, from (2) we have the relation: .. 0 0 0          dZ dY dX Aiii  (3) From (3) we get observation equation in following form: ,. 0 0 0 iii l dZ dY dX A           (4) Where constant term .iil   Solving system of observation equations (4) under the condition of the best fitting of the WGS-84 global reference ellipsoid to the Hon Dau local quasi-geoid, i.e. under the condition 2 min,1 n ii   we will get coordinate transformation parameters , ,0 0 0dX dY dZ . From (4) we will obtain the national (local) quasi-geoid heights of the n orientation points. The estimation of the accuracy of the national (local) quasi-geoid heights  will be considered in 3.2. 3.2. Determination of relationship between mixed quasi-geoid model VIGAC2014 and national quasi-geoid model VIGAC2017 As above presented, model VIGAC2014 is only the mixed quasi-geoidmodel, but is not the nationalquasi-geoidmodel. With national normal height H of geodetic point, mixed quasi-geoid height * (1) from the VIGAC2014 is calculated by formula * ,H H   where H is the global geodetic height according to the WGS84 global reference ellipsoid, meanwhile, nationalquasi-geoidheight  is calculated by formula , HH  where H is the local geodetic height according to the WGS84 national reference ellipsoid. Model Vietnam Journal of Earth Sciences 39(2), 155-166 161 VIGAC2014 can be used for calculation of the national normal height H based on global geodetic height H obtained from GNSS technology, but can not be used for determination of local geodetic height H by formula .H H   In order to construct the national quasi- geoid model from the mixed quasi-geoid model VIGAC2014, taking account of formula (3), we get the formula of conversion of the mixed quasi-geoid height * to the national quasi-geoid height * in the following form: 0* * . ,0 0 dX A dY Ci i i dZ            (5) where coordinate transformation parameters , ,0 0 0dX dY dZ have been determined in 3.1, C is correction from existence of systenatic error in the VIGAC2014 model. The mixed quasi-geoid model VIGAC2014 is used for the construction of the national quasi-geoid model VIGAC2017 by formula (5) in taking account of two it’s outstanding advantages: - The mixed quasi-geoid model VIGAC2014created from the EGM2008 model allows getting difference of quasi- geoid heights between two arbitrary points with very high accuracy. - The mixed quasi-geoid model VIGAC2014 allows propagating quasi-geoid heights to big distances on the whole territory of Vietnam, even to territories of neighbor countries. With two independent series: series of national quasi-geoid heights obtained from the results of ellipsoid orientation in 3.1 and series national quasi-geoid heights * achieved by formula (5) from the VIGAC2014 model, based on method of double observation processing we will accomplish the accuracy estimation of the national quasi-geoid model VIGAC2017 and determine correction C in formula (5). 3.3. Determination of differential rotations ZYX  ,, and differential scale change m Although WGS84 national reference ellipsoid has axes, paralleling to corresponding axes of the WGS-84 global reference ellipsoid, but between ITRF and VN2000 - 3D exist differential rotations ZYX  ,, and differential scale change ,m with being arise from error accumulation and propagation in process of approximate calculation of coordinates of the national first and second orders astro - geodetic points in VN2000 - 2D. Values mZYX ,,,  with parameters ,,, 000 dZdYdX obtained in 3.1, creating 07 coordinate transformation parameters in Bursa - Wolf’s formula in the following form: 0 . ,0 0 mdX Z YX X X Y Y dY m YZ X Z Z ZdZ mY X                                                 (6) where , ,X Y Z are global geodetic coordinates of geodetic points according to the WGS-84 global reference ellipsoid, , ,X Y Z are national (local) geodetic coordinates of this geodetic point according to the WGS-84 national reference ellipsoid. In case of spatial coordinates , ,X Y Z of geodetic point are known in ITRF, but national spatial coordinates ZYX ,, of this geodetic point in VN2000 - 3D are calculated by formula: Ha Minh Hoa/Vietnam Journal of Earth Sciences 39 (2017) 162 2 ( ).cos .cos , ( ).cos .sin , [ .(1 ) ].sin . X N H B L Y N H B L Z N e H B        where LB, are geodetic coordinates of geodetic point in VN2000 - 3D; the prime vertical radius of curvature N of this point is calculated by formula: ;2 21 .sin a N e B   national geodetic height *  HH with national quasi-geoid height ,* determined by formula (5). With known coordinate transformation parameters 000 ,, dZdYdX in 3.1, from (6) we have observation equations: . . . , . . . , . . . , Y X Z Y Z X Y Z v Z Y X m lX Y Z X v Z X Y m l v Y X Z m l                        (7) where constant terms ,0l X dX XX    ,0l Y dY YY    .0l Z dZ ZZ    Based on the set of orientation points, we wiil solve system of observation equations in form (7) under condition  2 2 2 minv v vX Y Z   and wiil get unknown parameters , ,X Y Z   and .m By such way we will obtain the 07 coordinate transformation parameters , , , , , ,0 0 0dX dY dZ mX Y Z    for conversion of coordinates from ITRF according the WGS-84 global reference ellipsoid to VN2000 - 3D according the WGS-84 national reference ellipsoid. 3. Results Based on global geodetic coordinates iii HLB ,, on n = 164 orientation points (i = 1,2,,164) we solved system of observation equations (4) under the condition min164 1 2  i i  and had the following coordinate transformation parameters: ,417880,111,192468,42,511083,204 000 mdZmdYmdX  (8) national quasi-geoid heights  (4) of the 164 orientation points. Minimal national quasi-geoid height 0,042 m belongs to the second order benchmark II(PLK - PL)24 and maximal national quasi-geoid height 4,524 m belongs to the first order benchmark I(BH - TH)59. Accomplishing estimation of two independent series  nad * on the 164 orientation points by method of double observation processing, we had got correction C = -0,023 m. Differences ,*iiid   i = 1,2,..., 164, have been presented in Table 1. RMS of every from two abovementiond series is equal to 164 2 1, 2651 0,062 .2 164 328 diim m x       Limited maximal absolute value of defferences d has been determined by formula ..2.max mtd  With t = 2,0; ,062,0 mm  value .175,0max d In Table 1, number of absolute values of differenses d in interval (0 – 17,5 cm) is160 ( 97,56 %). With t = 2,5; 0,062 ,m m  limited maximal absolute value 0, 219.maxd  Mean while, number of differences d with absolute values in the interval (17,6 - 19,5 cm) is only 4 (2,46%). Hence, differences d in Table 1 satisfy limited value, in addition differences d with small absolute values occupy vast majority. That attestes reliability of the initial national quasi-geoid model VIGAC2017, with being constructed from the mixes quasi- geoidVIGAC2014 by formula (5). Vietnam Journal of Earth Sciences 39(2), 155-166 163 Based on the 164 orientation points with those geodetic corrdinates B, L in VN2000, we solved the system of observation equations in form (7) and had unknown parameters ZYX  ,, and m with following values: Ex = - 0”,011168229 or Ex = - 0,000000054 Ey = 0”,085600577 or Ey = 0,000000415 Ez = - 0”,400462723 or Ez = -0,000001941 Dm = 0,000000000 Abovepresented parameters mZYX ,,,  with parameters 000 ,, dZdYdX (8) created set of the 07 coordinate transformation parameters from ITRF to VN2000 - 3D and guarantee close connection between those spatial reference systems. Table 1. Estimation of the differences * d on the 164 first and second order benchmarks No Points Differences d (m) No Points Differences d (m) Differences with absolute values not more 17.5 cm 1 IBH-TH122A 0.029 50 IVL-HT158 0.023 2 IBH-TH119 0.049 51 IDN-BT74 0.045 3 IBH-HN33 0.032 52 IBH=-LS88-1 0.047 4 IBH-HN39 0.037 53 IVL-HT98 0.032 5 IBH-HN42 0.009 54 IBH-LS.85-1 0.051 6 IHN-VL4-1 0.046 55 IBH-LS93 0.049 7 IHN-VL6-1 0.017 56 IBH-LS71 0.054 8 IVL-HT152-1 -0.023 57 IBT-APD56 0.034 9 IHN-VL34- -0.049 58 IVL-HT87 0.051 10 IHP-MC48A -0.045 59 IVL-HT247A 0.045 11 IBH-TH3-1 -0.021 60 ILS-TY1 0.065 12 IVL-HT181 -0.061 61 IDN-BT83 0.052 13 ILS-TY4 -0.037 62 IVL-HT78 0.055 14 IVL-HT309A -0.058 63 ILS-HN36 0.065 15 IVL-HT317 -0.053 64 ILS-HN29 -0.022 16 IVL-HT187 -0.049 65 IHN-VL28-1 0.032 17 IVL-HT170-1 -0.048 66 IIDK-TM41 0.021 18 IHP-MC41 -0.019 67 IIBH-XL11-1 -0.045 19 IHN-VL56 0.051 68 IIBH-XL17 0.003 20 IBH-TH11 0.064 69 IIBS-CD12 -0.047 21 IHN-VL40-1 0.057 70 IIBS-CD3 0.001 22 IVL-HT130 -0.035 71 IICD-VC4-1 -0.020 23 IBH-TH5 -0.015 72 IICT-GD10 0.001 24 IHN-VL38-1 -0.019 73 IICT-GD15-1 -0.036 25 IVL-HT197 -0.032 74 IICF-VT1 -0.039 26 IBT-APD63 -0.032 75 IIGD-AB12 -0.057 27 IVL-HT127-3 -0.026 76 IIGD-AB9-1 -0.036 28 IBT-APD59-1 -0.029 77 IIGD-APD6-1 -0.036 29 IVL-HT278-1 -0.023 78 IIHN-AB11 -0.064 30 IVL-HT108 -0.015 79 IIHN-AB3 -0.062 31 IDN-BT77 -0.012 80 IIHN-MT5 -0.019 32 IBT-NH17-1 -0.015 81 IILC-TG19A -0.020 33 IVL-HT83 -0.009 82 IIMC-XM7-1 -0.056 34 IBH-HN17 0.006 83 IIMT-TH4 -0.026 35 IHN-VL45-1 0.053 84 IINB=HN15 0.060 36 IBH-TH65 0.015 85 IIPLK-PL12 -0.034 37 IVL-HT178 0.001 86 IIPLK-PL2 0.061 38 IVL-HT103 0.008 87 IIPLK-PL8 -0.037 39 IHN-VL64 0.017 88 IISC-VT3-1 -0.040 40 IVL-HT141- 0.009 89 IITX-TL25 -0.050 Ha Minh Hoa/Vietnam Journal of Earth Sciences 39 (2017) 164 41 IVL-HT329A 0.009 90 IITX-TL6 -0.048 42 IHN-VL72 0.024 91 IIYB-CN18 -0.055 43 IHN-VL10A -0.070 92 IVL-UT150 -0.072 44 IDN-BT16 -0.074 93 IBH-LS77 0.066 45 IDN-BT28 -0.068 94 IVL-HT71 0.074 46 IIBS-CD7-1 0.068 95 IIGD-AB3-1 -0.069 47 IIHN-AB23 -0.071 96 IILC-TG15 0.072 48 IINB-HN27-1 0.067 97 IILC-TG31 0.073 49 IINK-PT10 0.075 98 IIPLK-PL16 -0.067 99 IBH-LS97 0.116 130 IIMT-TH25 -0.148 100 IHN-HP7 0.082 131 IIMT-TH7 -0.148 101 IVL-HT121 0.082 132 IIMT-TV11 -0.141 102 IVL-HT325-1 0.098 133 IIMX-DC34 -0.148 103 ILS-HN7 0.078 134 IINB-HN11-1 0.089 104 IBT-APD49-1 0.115 135 IINB-HN24 0.102 105 IBH-TH59 0.097 136 IINK-PT13 0.139 106 IVL-HT173-2 0.079 137 IISC-PL29 -0.132 107 IBH-TH70A 0.098 138 IITL-TV5-1 -0.135 108 IHN-VL50 0.093 139 IITL-TV7 -0.129 109 IVL-HT123 0.087 140 IITX-TL14 -0.098 110 ILS-HN12 0.102 141 IITX-TL20-1 -0.129 111 IHP-MC4-1 0.108 142 IIYB-CN24-1 -0.135 112 IBH-LS80 0.110 143 IICD-HN6 0.085 113 IDN-BT86 0.092 144 IICD-VC4 -0.133 114 IVL-HT320A 0.090 145 IICT-GD1 0.130 115 IHP-NB14A -0.099 146 IICT-GD4 0.142 116 ILS-HN22 -0.094 147 IIDK-TM29 -0.101 117 IBH-HN16A 0.096 148 IIDK-TM45 -0.136 118 IBH-HN48 0.146 149 IIDL-PR31 -0.145 119 IHN-HP2A 0.136 150 IIGD-APD2-1 0.090 120 IIAB-CL5 -0.105 151 IIHN-AB17 -0.122 121 IIAS-KS10 -0.138 152 IIHN-AB20 -0.090 122 IIAS-KS16 -0.092 153 IIHN-AB7 -0.134 123 IIAS-KS22 -0.132 154 IIHN-MT15 -0.102 124 IIAS-KS32 -0.115 155 IIBMT-DT12 -0.112 125 IIBH-XL6 0.097 156 IIBS-CD14 0.147 126 IHN-HP5 0.170 157 IINK-PT6-1 -0.165 127 IIBMT-DT14 -0.158 158 IIPLK-PL24 -0.164 128 IIBMT-DT4 0.151 159 IITT-TK29 -0.153 129 IIBN-QT11-1 0.166 160 IIAS-KS35 -0.169 Differences with absolute values more 17.5 cm and not more 20 cm 161 IBMT-APD30 0.182 163 IINB-HN32-1 0.178 162 IVL-HT95 0.177 164 IVL-HT73 0.195 Experimental results show that in combination with the initial national quasi- geoid model VIGAC2017, the national geodetic coordinates B, L, H of geodetic point in VN2000 - 3D allow getting the national normal height H with the second order national normal height accuracy on the whole territory of Vietnam. In addition, the national geodetic coordinates , ,B L H of geodetic pointreceived from conversion of the global geodetic coordinates , ,B L H of this geodetic point, obtained from the processing of GNSS data in ITRF according to the WGS- 84 global reference ellipsoidwith the using of satellite ephemeris with accuracy at level ±2,5 cm, to VN2000 - 3D. Experimental results will be presented in the next scientific article. It is necessary to pay attention to the Vietnam Journal of Earth Sciences 39(2), 155-166 165 factthat, at present, more 60% first and second orders benchmarks have been displaced on the terrain surface of Vietnam’s territory. So with the purpose of development of the national spatial reference system in Vietnam, we must perfect the national first and second orders leveling networks in the near future. 4. Discussions Abovepresented research results show that the initial national quasi-geoid model VIGAC2017 has the high accuracy and allows starting the construction of the initial spatial reference system, which guarantees to get the second order normal height by GNSS technology. That is seenas the first step to the perfectible construction of the national spatial reference system in the future. However, with the accuracy at level ±0,062 m the inital national quasi-geoid model VIGAC2917 does not satisfy the requirement of accuracy more than ±0,040 m for the construction of the national spatial reference system by international regulation. An increase of accuracy of the final national quasi-geoid model will be accomplished by an increase of accuracy of the mixed quasi- geoidmodel VIGAC2014 based on usage of detailed gravimetric data on territory of Vietnam. The physical geodesy exists two methods for determination of quasi-geoid height by gravimetric data: - The first method: Calculation of quasigeoif height by Stokes’s integral. - The second method: Correction of spherical harmonic coefficients of Earth’s Gravitational Model (EGM) by approach of Colombo O. The first method requires existence of gravimetric data around computational point with radius of near zone at 3°. This requirement can’t be sastified for narrow and long country like Vietnam in the near futute. In addition, at present, there is no detailed gravimetric data in Lao and Campuchia. So the second method becomes more realistic and has been proposed to use (Ha minh Hoa, 2013c; Ha Minh Hoa, 2014a; Ha Minh Hoa, 2014b; Ha Minh Hoa et al. 2016a). Apart from that correction of spherical harmonic coefficients of EGM can be carried out based GNSS data on the first and second orders (Ha Minh Hoa, Nguyen Thi Thanh Huong, 2015a). Vietnam Institute of Geodesy and Cartography will carry out project “Detailed gravimetric measurement in mountainous regions of Vietnam” in the near future. 5. Conclusions In the epoch of application of GNSS technology, the task of the construction of the national spatial reference system becomes the most important research content of high geodesy, that concentrates in itself the most important achievements in fields of the physical geodesy and geometrical geodesy. The key problem of the aforementioned task is the construction of the high accurate national quasi-geoid model. This scientific article presented results of the construction of the initial national quasi-geoid model with accuracy at the level of ±6,2 cm and determination of the 07 coordinate transformation parameters from ITRF according to the WGS84 global reference ellipsoid to VN2000 - 3D according to the WGS84 national reference ellipsoid. 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