利用高分辨率DEM计算重力地形影响

发布时间：2018-03-10 12:41

本文选题：数字高程模型DEM　切入点：重力地形影响　出处：《山东科技大学》2017年硕士论文　论文类型：学位论文

【摘要】：随着科学技术不断向前发展,空间信息化测绘步入大数据时代。随着SRTM、ASTER-GDEM、World DEM等全球高分辨率数字高程模型的相继问世,地球重力场与垂直基准领域得到了革命性的变革与长足的发展,其中,利用高分辨率DEM计算重力地形影响已成为当前的热门研究领域。本文基于地形位理论,利用高分辨率DEM数据通过棱柱积分离散求和快速算法计算了重力地形影响,进而确定区域大地水准面与似大地水准面间距。论文的主要内容及结论如下:(1 )详细介绍了当前应用最广范的三款全球DEM产品,包括90米分辨率的SRTM、30米分辨率的ASTER-GDEM V2以及当前世界最高分辨率12米的World DEM;在左手坐标系中,基于牛顿万有引力公式,对棱柱体所产生的引力位及引力公式做了详细推导,最后给出了实用公式,并讨论了公式中无定义点的处理方法;探讨了地形位积分离散求和快速算法,使利用高分辨率DEM计算重力地形影响的运算在普通计算机上实现成为可能,也有力保证了足够长的积分半径。(2)系统性地阐述了精密高程系统基本理论,讨论了几何(水准)定义与物理(重力位)定义的正常高差距其实很小,基于重力位理论得出最终结论:大地水准面与似大地水准面间距其实并不大。(3)完整分析了基于地形位理论的大地水准面与似大地水准面间距的精密计算方法,利用高分辨率DEM计算重力地形影响,最重要的是对地面重力作地形改正,而本文在考虑此点的基础上,在垂线上平均重力的求取中考虑了被忽略的大地水准面之上的地形体在垂线上所产生的的平均重力,而此项可由棱柱积分法求得的地形位导出,进而导出大地水准面与似大地水准面间距的精密计算公式。(4)开发了大地水准面与似大地水准面间距计算软件,对试验区分别采用传统方法和精密方法进行了测试,结果显示:基于地形位理论利用高分辨率DEM顾及地形重力影响计算得到大地水准面与似大地水准面间距在振幅、坡度以及光滑性方面都更接近物理现实,在山峰处的效果尤为明显,传统方法得到的两面间距高达近40厘米,而精密方法得到的两面差距只有24厘米;精密公式中,DEM分辨率的高低直接决定了大地水准面与似大地水准面间距的精度,因此,重力地形影响的计算必须采用高分辨率DEM来进行地形模拟;对于低海拔地势平坦地区,传统公式与精密公式的计算结果精度相当。
[Abstract]:With the continuous development of science and technology, space information mapping has stepped into the era of big data. With the advent of global high-resolution digital elevation models such as SRTM TM, ASTER-GDEMN World DEM and so on, The field of earth gravity field and vertical datum has been revolutionized and developed greatly. Among them, it has become a hot research field to use high-resolution DEM to calculate the influence of gravity topography. The influence of gravity topography is calculated by using the prism integral discrete summation fast algorithm using high-resolution DEM data. Furthermore, the distance between regional geoid and quasi geoid is determined. The main contents and conclusions of this paper are as follows: 1) the three most widely used global DEM products are introduced in detail. It includes the ASTER-GDEM V2 with a 30-meter resolution of 90 m resolution and World DEM with the highest resolution of 12 m in the world at present. In the left-hand coordinate system, the gravitational potential and gravitational formula generated by the prism are derived in detail based on Newton's universal gravity formula. Finally, the practical formula is given, and the processing method of undefined points in the formula is discussed, and the fast algorithm of discrete summation of terrain potential integral is discussed, which makes it possible to use high resolution DEM to calculate the influence of gravity terrain on a common computer. The fundamental theory of precision elevation system is systematically expounded, and it is discussed that the normal height difference between the definition of geometry (leveling) and the definition of physical (gravity potential) is very small. Based on the theory of gravity potential, the final conclusion is drawn: the distance between geoid and quasi geoid is not large. (3) the precise calculation method of the distance between geoid and quasi geoid based on topographic potential theory is analyzed. Using high-resolution DEM to calculate the influence of gravity topography, the most important thing is to make topographic correction to the gravity of the ground. In this paper, based on the consideration of this point, The average gravity generated by a body above the neglected geoid on the vertical line is taken into account in the calculation of the mean gravity on the vertical line, which can be derived from the topographic potential obtained by the prism integration method. Furthermore, the precise formula for calculating the distance between geoid and quasi geoid is derived. (4) the software for calculating the distance between geoid and quasi geoid is developed, and the traditional method and precision method are used to test the test area. The results show that the distance between geoid and quasi geoid is closer to physical reality in amplitude, slope and smoothness by using high-resolution DEM to take into account the influence of terrain gravity based on topographic position theory, and the results show that the distance between geoid and quasi geoid is closer to physical reality. The effect is especially obvious at the peak. The distance between the two sides obtained by the traditional method is as high as 40 cm, but the gap between the two sides by the precision method is only 24 cm. The precision of the distance between geoid and quasi geoid is directly determined by the resolution of Dem in the precision formula. Therefore, the influence of gravity terrain must be simulated by high resolution DEM. The accuracy of the traditional formula is equivalent to that of the precision formula.
【学位授予单位】：山东科技大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：P208

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