Advances in the numerical solution of the linear molodensky problem

The solution of the linear Molodensky problem by analytical continuation to point level is numerically the most convenient of all the theoretically equivalent solutions. It is obtained by successively applying the same integral operator and it does not depend explicitly on the terrain inclination. However, its dependence on the computation point restricts somehow the computational efficiency. The use of the Fourier transform for the evaluation of the integral operator in planar approximation lessens significantly the burden of computations. Using this spectral approach, the problem has been reformulated and solved in the frequency domain. Moreover, it is shown that the solution can be easily split into two steps: (a) “downward” continuation to sea level, which is independent of the computation point, and (b) “upward” continuation from sea to point level, using the values computed at sea level. Such a treatment not only simplifies the formulas and increases the numerical efficiency but also clarifies the physical interpretation and the theoretical equivalence of the continuation solution with respect to the other solution types. Numerical tests have been performed to investigate which terms in the Molodensky series are of significance for geoid and deflection computations. The practical difficulty of differences in the grid spacings of gravity and height data has been overcome by frequency domain interpolation. Presented at theXIX IUGG General Assembly, Vancouver, B.C., August 9–22, 1987.