Local Geoid Determination in Mountain Regions.

Abstract
The present report reviews and interrelates various methods for the local or regional determination of the geoid or of height anomalies according to Molodensky (i.e, of the quasi-geoid) from deflections of the vertical -- the astrogeodetic method -- or by a combination of vertical deflections with gravity anomalies by least-squares collocation. The classical astrogeodetic determination of the geoid by integration of vertical deflections reduced to sea level is compared with Molodensky's determination of height anomalies by integration of vertical deflections along the earth's surface. Extensive consideration is given to the reduction for curvature of the plumb line and to topographic-isostatic reduction of vertical deflections in the classical sense, which is a reduction to sea level, and in the modern sense, where the point remains on earth's surface. Then the application of collocation to the present problem is discussed. Finally, some results concerning geoid computations for Austria by collocation are outlined.

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