Ellipsoidal representation of the topographical potential and its vertical gradient
Ellipsoidal representation of the topographical potential and its vertical gradient
复制标题
地形势及其垂直梯度的椭圆体表示
DOI：
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发表时间：
2005
期刊：
影响因子：
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通讯作者：
E. Grafarend
中科院分区：
文献类型：
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作者：
P. Novák;E. Grafarend
摘要。由于全球定位系统（GPS），地球表面上和上面的点很容易通过高斯表面法坐标L，B和H的三重体分别称为椭球经度，椭球纬度和椭球高度来给出。对于大地测量应用，这些曲线坐标参考国际参考椭球GRS80，它是Somigliana-Pizzetti参考势场的等势面。在这里，我们的目标是用高斯表面法坐标（L，B，H）表示GRS80上方“地形”质量产生的引力势及其垂直梯度，即对测量重力的影响。地形势及其垂直梯度的空间（积分）公式为球面项和相应的椭球修正量之和。在加拿大落基山脉的测试区域，使用区域有限的离散积分来评估地形贡献的公式。本文还介绍了地形势的谱（级数）表示，并用简单的层密度讨论了参考椭球上或参考椭球内地形质量的凝聚。鉴于目前可获得的地形数据，特别是质量密度数据的精度相对较低，椭球面修正似乎意义有限。然而，利用GPS直接观测到的高精度坐标来表示地形势及其垂直梯度当然具有优势。
Abstract.Due to the Global Positioning System (GPS), points on and above the Earth’s surface are readily given by means of a triplet of the Gauss surface normal coordinates L,B and H called ellipsoidal longitude, ellipsoidal latitude, and ellipsoidal height, respectively. For geodetic applications, these curvilinear coordinates refer to the international reference ellipsoid GRS80, which is an equipotential surface of the Somigliana–Pizzetti reference potential field. Here, we aim at representing the gravitational potential, that is generated by the ‘topographical’ masses above GRS80, and its vertical gradient, i.e. an effect on measured gravity, in terms of the Gauss surface normal coordinates (L,B,H). The spatial (integral) formulas for the topographical potential and its vertical gradient are presented as a sum of a spherical term and corresponding ellipsoidal correction. The formulas for the terrain contribution are evaluated over the test area in the Canadian Rocky Mountains using an area-limited discrete integration. The spectral (series) representation of the topographical potential is also introduced, and the condensation of the topographical masses on or inside the reference ellipsoid is discussed in terms of a simple layer density. The ellipsoidal corrections might seem to be of limited significance in view of a relatively low accuracy of currently available topographical data, especially the mass density. However, the representation of the topographical potential and its vertical gradient using the coordinates that are directly observable with a high level of accuracy by GPS certainly has advantages.