DOWNWARD CONTINUATION OF HELMERTS GRAVITY

The aim of this contribution is to show that mean Helmert's gravity an omalies obtained at the earth surface on a grid of a 'reasonable' step can be transferred to corresponding mean Helmert's anomalies on the g eoid. To demonstrate this, we take the 5' by 5' mean Helmert's anomali es from a very rugged region, the south-western corner of Canada which contains the two main chains of the Canadian Rocky Mountains, and for mulate the problem of downward continuation of Helmert's anomalies for this region. This can be done exactly because Helmert's disturbing po tential is harmonic everywhere outside the geoid, therefore even withi n the topography. Then we solve the problem numerically by transformin g the Poisson integral to a system of 53,856 linear algebraic equation s. Since the matrix of this system is well conditioned, there is no th eoretical obstacle to the solution. The correctness of the solution is then checked by back substitution and by evaluating the contribution of the downward continuation term to Helmert's co-geoid. This contribu tion comes out positive for all the points. We thus claim that the det ermination of the downward continuation of mean Helmert's gravity anom alies on a grid of a 'reasonable' step is a well posed problem with a unique solution and can be done routinely to any accuracy desired in t he geoid computaion.