Unification of vertical datums by GPS and gravimetric geoid models using modified Stokes formula

In general, neighboring vertical datums can be compared directly at one or more common points on the border between the datums. This direct methods requires leveling and gravity measurements. Such a direct connection is not possible if the datums are separated by an ocean or another body of water. Then a rigorous mathematical model, an indirect approach, may be useful. in order to connect regional vertical datums, a rigorous mathematical model is derived based on a method by Rummen and Teunissen. In this study, two vertical datums are connected indirectly by means of a combination of precise geocentric positions of tide gauge sites and their geoid heights in one geocentric coordinate system and their height values in the respective height datums. This method is used to connect the Swedish and the Finnish height systems. The difference between Swedish RH70 and the Finnish N60 height systems is estimated to -12.1(plus/minus)2.7 cm. The results are mostly in good agreement with those of the direct approach by Sjoberg and by Ekman and the indirect approach by Pan and Sjoberg.