TGF: A New MATLAB-based Software for Terrain-related Gravity Field Calculations

With knowledge of geometry and density-distribution of topography, the residual terrain modelling (RTM) technique has been broadly applied in geodesy and geophysics for the determination of the high-frequency gravity field signals. Depending on the size of investigation areas, challenges in computational efficiency are encountered when using an ultra-high-resolution digital elevation models (DEM) in the evaluation of Newtonian integration. This paper presents a new MATLAB-based program, terrain gravity field (TGF), for the accurate and efficient determination of the terrain-related gravity field based on an adaptive algorithm. Depending on the attenuation character of gravity field with distance, the adaptive algorithm divides the integration masses into four zones, and adaptively combines four types of geometries and DEMs with different spatial resolutions. The most accurate but least efficient polyhedron together with the finest DEM are only considered for the innermost zone, while prism approximation for the second zone, the third zone with the more efficient tesseroid and a coarse DEM, and the most efficient but least accurate point-mass with the coarsest DEM for distant masses. Compared to some publicly available algorithms depending on one type of geometric approximation, the TGF achieves accurate modelling of gravity field and greatly reduces the computation time. Besides, the TGF software allows to calculate ten independent elements of gravity field, supports two types of density inputs (constant density value and digital density map), and considers the sphericity of the Earth by involving spherical approximation and ellipsoidal approximation. Further to this, the TGF software is also capable of delivering the gravity field of full-scale topographic gravity field implied by masses between the Earth’s surface and mean sea level. Results from internal and external numerical validation experiments of TGF confirmed its accuracy of sub-mGal level. Based on TGF, the trade-off between accuracy and efficiency, values for the spatial resolution and extension of topography models are recommended. The TGF software has been extensively tested and recently been applied in the SRTM2gravity project to convert the global 3” SRTM topography to implied gravity effects at 28 billion computation points. This confirms TGF the capability of dealing with large datasets.