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The fractal behaviour of gravity field elements was investigated. Particularly, the geoidal heights, gravity anomalies and vertical deflection components were considered. Such data were synthesized from the ultra-high degree SGG-UGM-1 geopotential model. The Egyptian Territory was selected as the study area. To supplement the results, parallel fractal analyses were performed on the GTM3A, Earth2012 and SRTM30 terrain data. The regularization, variogram and global Power Spectral Density (PSD) concepts were applied as different tools for fractal analysis. Consistent fractal dimensions resulted from the regularization and variogram algorithms. These two algorithms ensured the fractalness of the gravitational signals, including the geoidal height. The global PSD algorithm failed to give meaningful fractal dimensions for the topography and geoidal heights. However, it yielded realistic dimensions for the other elements. So, fractal dimensions could characterize the roughness and spatial precisions of different gravitational data. Also, multifractal modeling of the geopotential might be a promising task.

The fractal behaviour of gravity field elements: case study in Egypt