Determination of the boundary values for the Stokes-Helmert problem

The definition of the mean Helmert anomaly is reviewed and the theoreticall y correct procedure for computing this quantity on the Earth's surface and on the Helmert co-geoid is suggested. This includes a discussion of the rol e of the direct topographical and atmospherical effects, primary and second ary indirect topographical and atmospherical effects, ellipsoidal correctio ns to the gravity anomaly, its downward continuation and other effects. For the rigorous derivations it was found necessary to treat the gravity anoma ly systematically as a point function, defined by means of the fundamental gravimetric equation. It is this treatment that allows one to formulate the corrections necessary for computing the 'one-centimetre geoid'. Compared t o the standard treatment, it is shown that a 'correction for the quasigeoid -to-geoid separation', amounting to about 3 cm for our area of interest, ha s to be considered. It is also shown that the 'secondary indirect effect' h as to be evaluated at the topography rather than at the geoid level. This r esults in another difference of the order of several centimetres in the are a of interest. An approach is then proposed for determining the mean Helmer t anomalies from gravity data observed on the Earth's surface. This approac h is based on the widely-held belief that complete Bouguer anomalies are ge nerally fairly smooth and thus particularly useful for interpolation, appro ximation and averaging. Numerical results from the Canadian Rocky Mountains for all the corrections as well as the downward continuation are shown.