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СИСТЕМА ВЫСОТ МОНГОЛИИ
Энхтуяа Содном
АЗОСГК, Монголия, г.Уланбатор-211238, район Чингэлтэй, площадь Стройтелей-3, дом Правительства-12, ком-208, старший специалист отдела кадастра и информационных технологий, тел: 976-21)260546, моб: 97699018529, e-mail: enkhtuya_64@yahoo.com
В статье рассматривается нивелирная сеть Монголии 2-го класса, ее сгущение, уравнивание, анализ и обновление данных. Нивелирная сеть используется также для изучения деформаций земной коры.
Ключевые слова: нивелирная сеть, анализ, сгущение, уравнивание, невязка хода, обновление данных, карта, деформации земной коры.
MONGOLIAN HEIGHT SYSTEM
Enkhtuya Sodnom
Administration of Land Affairs, Construction, Geodesy and Cartography, Government Building XII, room 208, Barilgachdyn square-3, Chingeltei district, Ulaanbaatar-211238, Mongolia, senior expert of Cadastral and Information Technological Division, tel:(976-21)260546, mobile: 976)99018529, e-mail: enkhtuya_64@yahoo.com
The existing second order levelling network in Mongolia, its densification, adjustment, data updating and analysis are considered. This network is used for study of vertical crustal deformation.
Key words: levelling network, analysis, densification, adjustment, loop closure, data updating, map, vertical crustal deformation.
1. Background
The 2nd, 3rd and 4th order levelling Network of Mongolia was established during 1940-1949 for the purposed of mapping Mongolia at the scale of 1:100 000. Thus it was the first vertical control network of Mongolia.
This network was connected to 6 points of the second order-levelling network of Russia. The six Russian points were used as the starting point of the Mongolian network and were based on the level datum of Footstock in the Baltic Sea. The orthometric height method was adopted to calculate the first levelling network of Mongolia. The levelling equipment accuracy used for this survey was 3 ".84-11 ".40.
The first Levelling Network of Mongolia is shown in Fig. 1.
The State Administration of Geodesy and Cartography (SAGaC) did a review and extended the existing leveling network in a period of 1974-1991. The proposal to make the Levelling Network densification, to update the old levelling data and to study the vertical crustal movements was undertaken in 1974-1991.
Figure 1.
Between existing levelling points new points were established, which increased the number of lines to the network, and thus reduced the size of existing polygons and increased the number of levelling polygons.
Below in table form is figure information that explains this further.
Table 1.
Order Character of levelling network Second order levelling networks
First Re-levelling
1 Number of the route 46 51
2 Number of the polygons 13 17
3 Average perimeter of polygon 1200 km 1000 km
4 Average distance between neighboring benchmarks 7-10 km 4.5-7.5 km
5 Average distance between control ground points 70-150 km 57-75 km
6 Average depth of benchmarks 1.3-2.0 m 1.5-3.9 m
The total length of the Re-Levelling Network is 14030.5 km and the network comprises 3039 control ground points and benchmarks in total.
The second order Re-Levelling Network of Mongolia is presented below.
Figure 2. The second order Re-Leveling Network
2. Technology and Equipment of field survey for Second Order Leveling Network
Two Russian Surveying Regulation were used during survey. One is the “Regulation of the 1st, 2d, 3rd, 4th order Levelling Network” and the other is the “Regulation of the adjustment for the 1st, 2d, 3rd, 4th order Levelling Network.
The requirements of the specification are as follows:
- Forward and backward leveling for the same route must be survey at different time of the same day. I.e. if forward levelling survey was done in the morning, the backward levelling survey was to be done on the afternoon of that same day. The permissible value of different (diff = back - fore) between both levelling is ±5Vl km.
- Use the following formulas to calculate random and systematic error of levelling of 1 km line.
1 fd2 " 1 2 on
rf2 = — ; 52 = - —
8n r 4[L] L
Where:
n - number of station position in the route d - difference of forward and backward direction levelling data L - route distance
S - value from chart, which is related to “d” and “L”
- The permissible misclosure of levelling error in route and polygon is
±5Vl km.
3. Analysis of second order Levelling Network
Formula [1] was used to determine random and systematic errors of the new
data (1974-1991).
The permissible value of those errors are for random error ^ = 1.25 mm, and for systematic error 5 = 0.15 mm in Mongolia.
The gravimetric correction to be applied to the spirit-leveled height differences is called the orthometric correction that compensates for the nonparallelity of gravity equipotential surfaces.
Gravity was measured on all 2nd order levelling network points. By using those gravity results, the corrections of normal orthometric heights for all points were calculated using the formula as shown.
f=-(Yok-Yoi)*Hm/Ym+(g-Y)m ^k^m [2]
Where:
ym - approximately value of normal gravity, which is equal to 981000
mGal for whole territory of Mongolia.
yok;yoi - normal gravity of bench marks K and I on the ellipsoid.
Hm - average height between bench marks K and I g - gravity survey data y - Normal gravity
(g-y)m - arithmetic average of anomaly gravity of bench marks K and I.
The computation of the orthometric correction f is done iteratively, since it involves the unknown orthometric heights.
Before the network adjustment, while carrying out pre-adjustment data screening for second order Re-Levelling Network, we determined levelling loop closures and route closures (Fig. 3).
The levelling loop closures for Re-Levelling Network show the following results.
Allowable closure 53.3% of the all polygon
(polygon № 6+9;7;8;11;13;14;15;17) Exceed allowable closure by 2-10 cm 26.6%
(polygon № 2; 5; 12; 16) Exceed allowable closure by 20-30 cm 20.1%
(polygon № 1,3,10)
The result a polygons error determines which levelling order a particular polygon route will belong /Table 2/.
Figure 3.
Table 2. Loop error of levelling
Polygon No Loop error Permissible misclosure Providing in which levelling class
1 420.10 ±555.84 4d
2 289.80 ±373.48 3rd
3 -379.50 ±358.29 3rd
4 1142.90 Not provide
5-9 See picture 2. 2d
10 -450.10 ±688.74 4d
11-17 See picture 2. 2d
Pre-adjustment data screening techniques are mainly based on the examination of condition equation misclosures together with the experiences and intuition of the surveyors.
4. Least squares network adjustment
Net adjustment of new data (1974-1991) for second order Leveling Network using “Nivelir” software.
The new data of second order levelling network was adjusted using the “Nivelir” software in 2000. Mr. B.Enkhbaatar was the programmer of the “Nivelir” software, whiles working for “MobiCom” corporation. This software based on the parametric method, which is one of least square methods.
The number of station position in line levelling or distance line levelling determined weight measurement. Following formula is:
P = °; or P = C; [3]
n L
c-constant number, It is choose c = 1 in calculation.
n-number of station position in the levelling route.
L-distance of levelling route, by kilometer.
For the 1974-1991 re-levelling project, it was instructed that the 6 Russian levelling points would be the starting points of re-levelling. Those same points were used as the starting points for the 1945-second order Levelling Network. The loop error of the resulting survey that consists of the Russian and Mongolian levelling route was 1 meter, which is not acceptable as per specification used.
Given the huge loop error for the said survey, the new data of second order Levelling Network survey adopted the gravimetric point 0012 Arvaikheer Province as the vertical datum since it was established by high accuracy GPS technology.
Given the loop error of levelling in table 2, the adjustment shows that the levelling route polygons in the central and eastern part of the territory were accurate to second order levelling whilst the levelling route polygon on the western part of the territory were accurate to third order leveling (Figure 3).
Error of mean square in 1-km levelling route calculated following formula is:
(a) (b)
m = M; by P = — ; and m = +M
VC l ’ JCy
Where:
M- Error mean square of unit weight,
M = V[PV2]/z-u;
z - number of line in network levelling, u - number of intersection point,
V - correction from calculation,
The resulting adjustment indicated that mean average square error of levelling in 1 km line was +6 mm in the second order and +10.1 mm in the third order Relevelling Network.
I took part in re-network adjustment using new data (1974-1991) and Japan adjustment software “Lev-3”.
Its purpose was to check on the accuracy and quality of “Nivelir” software results for first net adjustment, also analysis and confirm to it.
The “Nivelir” software result of the net adjustment for the re-levelling new data (1974-1991) was not accepted and restricted for public use related to the following reason:
; by P = £;
[L] n
[4]
- The difference between the 1st and 2nd survey shows that there is a difference of 10 to 60 cm.
As such, the result of the 1st survey was taken as the more correct thus continued to be adopted and made available for public use.
I carried out the re-net adjustment using “Lev-3” software of the re-leveling new data, the polygons in the central and eastern parts of the territory (blue polygons, Ref to Figure 3.) were adjusted by adopting the second order levelling network, while the polygons in the western part of territory (brown polygons, Ref to Figure 3.) were adjusted by the adoption of the third order Leveling Network.
The resulting calculation indicates that mean average square error of leveling in 1 km line was +7.05mm in the 2nd order and +11.51 mm in the 3d order Re-levelling network.
5. Quality analysis of the results
I mentioned the mean average square error of leveling in 1 km line was +6.0 mm, +7.05mm in the 2nd order and +10.1 mm, +11.51 mm in the 3d order Re-leveling network on the table 2.
Average square error is a main character or necessary element of the network quality. The result of the first net adjustment is seen to be more accurately (6 mm).
The quality of the input observations was very grossly. Because error of mean square is a too big and a 46.7% of all loop error was exceeded allowable closure by 2-30 cm.
But I assumed the result of last re-net adjustment (B on the table 3.) that is more optimal and accurately than other results.
6. Study on Vertical Crustal Movements of Mongolia using Levelling data
The rate of the vertical crustal deformation is very important and useful in the field of seismology, geophysics, geomorphology, construction and other subjects of the infrastructure.
In Mongolia, determination of the rate of the vertical crustal deformation is very significant and beneficial for both theory and practice, which include the following.
- Determination of the seismic zone in the territory;
- Determination of the micro-zone in the territory of big city and region of industrial;
- Study of the symptom of pre- earthquake;
- Mineral research;
- Determination of the area for construct the industrial and the water construction;
- Determination of relationship of the geophysical field and the vertical crustal deformation;
- Study on the structure of the crust, and
- Monitoring of environment. Etc.
The rate of the vertical crustal deformation was determined by following formula:
hnew — hold
dV =................; [5]
dT
Where:
hnew - new data or measuring difference of height in 1974-1991
hold - old data or measuring difference of height in 1940-1945
dT - time between two survey.
The allowable value of different of the two surveying is ±9^L km. There are a several sections that were exceeded allowable value by 7.9 - 715.6 mm on the different routes. The total distance of these routes is 604.6 km. It is 4.31% of the total distance of the second orders Levelling Network.
Below 7 sections exceeded allowable value by 10 - 71.5 cm.
Table 4.
route number Name of section Distance of section, km hnew hold mm Allowable value, mm
005 BM 0141-BM 1557 54.8 173.0 66.6
023 BM 186 - BM 42 7.7 -240.8 24.9
038 BM 1556 - BM 1743 99.9 -805.5 89.9
039 BM 1521 - BM 1524 49 -192.4 63
041 BM 1256 - CGP 371 12.8 157.5 32.2
041 BM 1346 - BM 1363 10 -147.2 28.5
046 BM 1030 - BM 1087 8.6 -381.5 26.3
7. Vertical Crustal Movement Map
I prepared Vertical Crustal Movement Map (Figure 4) using the difference of the old (1940-1945) and the new (1974-1991) levelling data.
The quality of the data use is not accurate and, the points number are too few and distance between two benchmarks is too far in the some place (especially in west of territory), and the length of time between old and new levelling is a too long which is 35-45 years.
Moreover, the different of the two surveying is exceeded allowable value on the several sections of the different routes.
This map is very necessary and serves as basis for the research of the Vertical Crustal Movement. Also The Vertical Crustal Movement Map is a very important for planning and management of the Levelling Network.
50 25 0.0 2.5 5-0
Figure 4. The Vertical Crustal Movement Map The contour interval is a 25 m.
8. Conclusion
The updating and maintenance of the Leveling Network is very difficult and very important activities for Mongolia with wide territory.
Disadvantage of the results:
a. Starting point is a not actual. There don’t have a vertical datum.
b. The quality of the observation data is not accurately.
Because there is a 46.7% of all polygons loop error was exceeded allowable closure by 2-30 cm and error of mean square is too big - 7.05 mm in the second order and 11.51 mm in the third order.
c. Density of the common points of two surveying is not enough. Especially in western part of the territory have a very few points.
d. There are a two survey conducted and It is not enough for study on the Vertical Crustal Movements.
e. The length of time between old and new levelling is a too long or 35-45 years.
Advantage:
a. The result of the re-net adjustment is giving us a possibility to update the old data (1940-1945). It is a very necessary for second order Leveling Network of Mongolia.
b. The Vertical Crustal Movement Map is a first try for research of the vertical motions using leveling data.
c. Also the Vertical Crustal Movement Map is very necessary for planning and management of the Leveling Network.
The reason of the disadvantage:
- Starting point of two leveling networks (old and new) was different. The first leveling network’s vertical datum was based on the heights of the 6 points of the Russian second order-leveling network. The possibility of error of height transfer might have been accumulated due to the fact that the datum used was thousands of km away. Re-leveling network’s vertical datum was a the Gravimetric point 0012 of Arvaikheer province /Central area of Mongolia/
- There were a many earthquakes. For example: In the Southern part of Mongolia, there had been earthquakes with magnitude between 3.3 to 8 on the Richter’s scale which had occurred for about 130 times between 1944 and 1990. Movement of landmass due to these earthquakes may have also contributed to the differences previously mentioned.
- Re-measurements work took 15 years to be completed and during that time many people measured one line of levelling network at various times which is a wrong approach to height measurement.
- The re-levelling was completed 13 years. Re-measurement usually took place every 5 to 10 year. It is now 21 years down the track with out a re-levelling.
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© Enkhtuya Sodnom, 2012
