Some modifications of Stokes' formula that account for truncation and potential coefficient errors

Stokes' formula from 1849 is still the basis for the gravimetric determinat ion of the geoid. The modification of the formula, originating with Moloden sky, aims at reducing the truncation error outside a spherical cap of integ ration. This goal is still prevalent among various rnodifications. In contr ast to these approaches, some least-squares types of modification that aim at reducing the truncation error, as well as the error stemming from the po tential coefficients,, are demonstrated. The least-squares estimators are p rovided in the two cases that (1) Stokes' kernel is a priori modified (e.g. according to Molodensky's approach) and (2) Stokes' kernel is optimally mo dified to minimize the global mean square error. Meissl-type modifications are also studied. In addition, the use of a higher than second-degree refer ence field versus the original (Pizzetti-type) reference field is discussed , and it is concluded that the former choice of reference field implies inc reased computer labour to achieve the same result as with the original refe rence field.