ABSTRACT

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.

摘要

研究了重力场单元的分形行为。特别是，考虑了大地水准面高度、重力异常和垂直偏转分量。这些数据是根据超高程度的SGG-UGM-1位势模型合成的。埃及领土被选为研究区域。为了补充结果，对 GTM3A、Earth2012 和 SRTM30 地形数据进行了并行分形分析。正则化、变异函数和全局功率谱密度（PSD）概念被用作分形分析的不同工具。正则化和变差函数算法产生一致的分形维数。这两种算法保证了重力信号的分形性，包括大地水准面高度。全局 PSD 算法未能为地形和大地水准面高度提供有意义的分形维数。然而，它为其他元素提供了现实的尺寸。因此，分形维数可以表征不同重力数据的粗糙度和空间精度。此外，位势的多重分形建模可能是一项有前途的任务。