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This paper presents a new adaptive algorithm for topographic correction of gravity measurements based on a triangulated polyhedral representation of topographic surfaces. The adaptive grid resampling of topography is driven by the actual gravity effect on the station, which depends on the topographic mass and distance. This is a major improvement for accuracy and computational speed compared to some old algorithms that account only for distance. Today, global availability of gravity data allows the regional investigation (∼100 km anomaly wavelengths) of the lithosphere. The variety of different data sets (from terrestrial and aero surveys to satellite data), the size of possible investigation areas and the availability of high-resolution, digital terrain models ask for new approaches of topographic correction. Specifically, an algorithm for topographic correction should be useable on large-scale investigation areas, that is, correctly model the long wavelength signal of topography, work in spherical domain, be able to handle high-resolution topography data available and accurately represent topography. The new algorithm does consider sphericity of the Earth, calculates gravity gradients, deals with large data sets and uses an adaptive approach for resampling topography to save computation time significantly. The resampling uses an efficient quadtree representation of the topography grid. High resolution of the topography grid is only considered if it has a significant influence on the gravity effect at the station. This leads to an accurate representation of distant terrain and a massive speed up of computation time. The new algorithm is tested in an area of South America and Central Asia. The results are almost identical to calculations with constant grid resolutions, but need only 2 per cent of calculation time. This method enables to correct all gravity data sources (terrestrial, aero, satellite data) with the necessary topographic resolution with huge saving in computation time without presumptions by the user. [ABSTRACT FROM AUTHOR]