BVP, Global Models and Residual Terrain Correction

Abstract

The integral of Stokes or similar formulae, used to estimate global models of the gravity fields, are based on the solution of the external boundary value problem (BVP) for the disturbing potential T. This approach presupposes the disturbing potential T to be harmonic on the geoid, which implies that there are no masses outside the geoid (Vaníček and Krakiwsky, Geodesy: the concepts, 1986; Bajracharya, Terrain effects on geoid determination, 2003).When solving this problem with the remove-restore procedure, we have to compute the long wavelengths provided by a set of spherical harmonic coefficients (global model) and the short wavelengths calculated using topographic heights and residual terrain correction (RTC) (Forsberg, International School for the Determination and Use of the Geoid, 2005). When performing this operation two inconsistencies arises: first the reference surface used is not a continuos surface, but a set of horizontal planes; second this set of surface is different from the one implied in the global model. This paper suggests a new procedure to better harmonize the various steps involved in solving the geodetic boundary value problem. First, the difference between using a block or a moving average operator as reference surface for smoothing g is evaluated. Second, we shall look more closely to the procedure of reducing data to the reference surface. Particularly a new sequence that allows moving data always in free air is proposed. Numerical tests proved that there are significant differences between choosing the reference surface either computed from block or moving average operator. The residual field estimated using the second approach seems to be smoother than the one obtained with the first one. Moreover, a possible influence on the procedure of computing global models, due to the new method described in the paper, has been proved. © Springer-Verlag Berlin Heidelberg 2009.