Using High Resolution DEM To Calculate Gravity Topographical Effect

With the continuous development of science and technology, spatial information mapping have come into the era of big data. With the advent of SRTM, ASTER-GDEM, World DEM and other global high-resolution digital elevation models, the earth's gravity field and vertical reference field have been revolutionized and developed rapidly. Among them, the use of high-precision DEM to calculate the influence of gravity terrain has become a hot research area. In this paper, based on the terrain potential theory, the high precision DEM data is used to calculate the influence of gravity terrain by the fast algorithm of discrete summation of the prism integral, and then the distance between the geoid and the geoid is determined. The main contents and conclusions are summarized as follows:(1) We have Introduced the three global DEM products,including the 90 meter resolution SRTM, 30 m resolution ASTER-GDEM V2 and the world's highest resolution of 12 m World DEM. In the left hand coordinate system, based on the Newton formula,the gravitational potential and gravitational formula of prism is deduced.Finally a practical formula is given, and we discusses the processing method of no defined point. A fast algorithm for discrete sum of terrain points is discussed, and it makes use of high resolution DEM calculation of gravity terrain effect operation in a computer can be realized, and can guarantee the integral radius long enough.(2) The basic theory of precise elevation system is expounded,and the separation between geometric normal (level) high and physical(gravity) normal high is infactly very small. Based on the theory of gravity, it is concluded that the geoid-quasigeoid separation is not large.(3) The calculation method of the geoid-quasigeoid separation based on terrain potential theory is deduced. The most important thing is to use the high precision DEM gravity to calculate the terrain effect. On the basis of this point, the neglected average gravity of the terrain on the vertical line is considered in the calculation of the mean gravity on the vertical line which is induced by terrain potential of the prism.(4) The software for calculating the geoid-quasigeoid separation is developed. The test area was tested by traditional method and rigorous method. Results show: Based on the terrain potential theory, using the high precision DEM to take account of the influence of terrain gravity, it is found that the distance between the geoid and the geoid is closer to the physical reality in terms of amplitude, slope and smoothness. The effect at the peak is particularly obvious. The traditional method of the two sides of the pitch up to nearly 40 cm, while the tight method to get the gap between the two sides is only 24 cm; In the rigorous formula, the resolution of DEM directly determines the accuracy of the geoid and the geoid. Therefore, the calculation of gravity terrain effects must be carried out with high resolution DEM. For the flat terrain with low altitude, the precision of the traditional formula and the rigorous formula is quite accurate.