引用本文: 马健, 魏子卿. 利用Molodensky理论求解第二大地边值问题[J]. 武汉大学学报 ( 信息科学版), 2019, 44(10): 1478-1483.
MA Jian, WEI Ziqing. The Second Geodetic Boundary Value Problem Based on Molodensky Theory[J]. Geomatics and Information Science of Wuhan University, 2019, 44(10): 1478-1483.
 Citation: MA Jian, WEI Ziqing. The Second Geodetic Boundary Value Problem Based on Molodensky Theory[J]. Geomatics and Information Science of Wuhan University, 2019, 44(10): 1478-1483.

## The Second Geodetic Boundary Value Problem Based on Molodensky Theory

• 摘要: 过去由于无法获得大地高数据，传统的第三大地边值问题采用重力异常作为边值条件。GNSS技术的发展为第二边值问题的研究带来了契机。研究比较成熟的第三边值理论无疑为第二边值问题提供了很好的参考和借鉴，对此开展将第三边值问题中计算似大地水准面的Molodensky理论方法应用于第二边值问题的研究。首先推导了Hotine算子与梯度算子的关系，然后给出了基于Molodensky理论求解第二边值问题的算法。实验结果表明，该算法与传统第三边值问题中Molodensky理论的边值解精度相当，说明基于Molodensky理论求解第二大地边值问题是完全可行的。

Abstract: Due to the inability to obtain ellipsoidal height data in the past, gravity anomaly is chosen as the boundary condition in the traditional third geodetic boundary value problem. The development of GNSS technology brings opportunities for the development of the second boundary value problem. The relatively mature third boundary value theory provides undoubtedly a good reference for the second boundary value problem. Therefore, this paper deals with how to use the Molodensky theory for the third boundary value problem to calculate the quasi-geoid for the second boundary value problem. In this paper, the relationship between the Hotine operator and gradient operator is deduced. Then the method of solving the second boundary value problem based on the Molodensky theory is presented. Experiments show that the accuracy of the quasi-geoid by this method is equivalent to that by the traditional Molodensky method in the third boundary value problem. Thus it is feasible to solve the second boundary value problem based on the Molodensky theory.

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