The Second Geodetic Boundary Value Problem Based on Molodensky Theory

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.