On the Solution of the Inverse Stokes Problem Including Ellipsoidal Effects
Abstract

the nonradial direction of the derivative appearing in the boundary condition,

terms in the reference potential depending on J _{ 2 } (zonal harmonic of degree 2) and ω (angular velocity of the earth’s rotation), and

deviations of the true boundary surface from a sphere.
As a consequence of these ellipsoidal terms the solution of the inverse Stokes problem can no longer be represented by a simple spherial integral formula. Starting from an approximation of the boundary condition of order 0(f) the solution of the inverse Stokes problem is provided in the frequency domain, using spherical harmonics as base functions. Special attention is given to the null space of the boundary operator as well as to small eigenvalues related to the harmonics ot first degree. The results are transformed from the frequency domain into the space domain, resulting in two alternatives for the procedure of evaluation. In the first alternative the altimetryderived disturbing potential (or geoidal height) data are inserted into the inverse Stokes formula, and a correction term is applied to the resulting gravity anomalies. In contrast, in the second alternative a correction term is added to the disturbing potential data, and this reduced data is inserted in the inverse Stokes formula. A numerical evaluation based on the EGM96 geopotential model results in estimates of the order of magnitude of the correction terms, which is ±3 • 10^{6} ms^{2} and ±2m, respectively; these numbers mirror the approximations existent in the ”spherical” inverse Stokes problem. The correction terms show a lowfrequency behaviour, dominated by spectral terms of degree ≤ 20.