Astronomical-topographic levelling using high-precision astrogeodetic vertical deflections and digital terrain model data

Abstract

At the beginning of the twenty-first century, a technological change took place in geodetic astronomy by the development of Digital Zenith Camera Systems (DZCS). Such instruments provide vertical deflection data at an angular accuracy level of 0.̋1 and better. Recently, DZCS have been employed for the collection of dense sets of astrogeodetic vertical deflection data in several test areas in Germany with high-resolution digital terrain model (DTM) data (10–50 m resolution) available. These considerable advancements motivate a new analysis of the method of astronomical-topographic levelling, which uses DTM data for the interpolation between the astrogeodetic stations. We present and analyse a least-squares collocation technique that uses DTM data for the accurate interpolation of vertical deflection data. The combination of both data sets allows a precise determination of the gravity field along profiles, even in regions with a rugged topography. The accuracy of the method is studied with particular attention on the density of astrogeodetic stations. The error propagation rule of astronomical levelling is empirically derived. It accounts for the signal omission that increases with the station spacing. In a test area located in the German Alps, the method was successfully applied to the determination of a quasigeoid profile of 23 km length. For a station spacing from a few 100 m to about 2 km, the accuracy of the quasigeoid was found to be about 1–2 mm, which corresponds to a relative accuracy of about 0.05−0.1 ppm. Application examples are given, such as the local and regional validation of gravity field models computed from gravimetric data and the economic gravity field determination in geodetically less covered regions.