Hotine-Helmert boundary-value calculation model for quasi-geoid determination

doi:10.11947/j.AGCS.2019.20170594

Abstract

Abstract:

The development of the space geodesy techniques has made it possible to obtain the ellipsoidal height, thus bringing new opportunities for the research of the second geodetic boundary value problem. The Hotine-Helmert boundary value problem, i.e. the second boundary value problem based on the Helmert's second condensation method, is studied in this paper. The definitions and algorithms for the direct and indirect topographic effects are presented at first. Then a calculation model for the Hotine-Helmert boundary value problem is presented in this contribution. The secondary indirect topographic effect on the gravity caused by the terrain condensation is unnecessary in the Hotine-Helmert boundary-value model, making it easier than the Stokes-Helmert boundary-value model. Furthermore, a kind of spheroidal Hotine kernel function whose low degrees are modified is introduced, which can effectively improve the accuracy of the quasi-geoid compared with the traditional spheroidal kernel. In order to verify the validity and practicability of the Hotine-Helmert boundary-value calculation model, the gravimetric quasi-geoid in central China with the area of 6°×4° and the resolution of 1.5'×1.5' is solved according to the Hotine-Helmert boundary-value model, using the first 360 degrees of EIGEN-6C4 model as the reference model. The accuracy of the determined gravimetric quasi-geoid in the test area is ±4.8 cm.

Key words: Hotine-Helmert boundary-value calculation model, the direct and indirect topographic effects, the low-degree modified spheroidal Hotine kernel, quasi-geoid

CLC Number:

P223

MA Jian, WEI Ziqing, REN Hongfei. Hotine-Helmert boundary-value calculation model for quasi-geoid determination[J]. Acta Geodaetica et Cartographica Sinica, 2019, 48(2): 153-160.

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