Finite volume method: a good match to airborne gravimetry?

IF 3.9 2区 地球科学 Q1 GEOCHEMISTRY & GEOPHYSICS
Xiaopeng Li, Robert Čunderlík, Marek Macák, Dana J. Caccamise, Zuzana Minarechová, Pavol Zahorec, Juraj Papčo, Daniel R. Roman, Jordan Krcmaric, Miao Lin
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Abstract

Numerical methods, like the finite element method (FEM) or finite volume method (FVM), are widely used to provide solutions in many boundary value problems. In previous studies, these numerical methods have also been applied in geodesy but demanded extensive computations because the upper boundary condition was usually set up at the satellite orbit level, hundreds of kilometers above the Earth. The relatively large distances between the lower boundary of the Earth's surface and the upper boundary exacerbate the computation loads because of the required discretization in between. Considering that many areas, such as the US, have uniformly distributed airborne gravity data just a few kilometers above the topography, we adapt the upper boundary from the satellite orbit level to the mean flight level of the airborne gravimetry. The significant decrease in the domain of solution dramatically reduces the large computation demand for FEM or FVM. This paper demonstrates the advantages of using FVM in the decreased domain in simulated and actual field cases in study areas of interest. In the simulated case, the FVM numerical results show that precision improvement of about an order of magnitude can be obtained when moving the upper boundary from 250 to 10 km, the upper altitude of the GRAV-D flights. A 2–3 cm level of accurate quasi-geoid model can be obtained for the actual datasets depending on different schemes used to model the topographic mass. In flat areas, the FVM solution can reach to about 1 cm precision, which is comparable with the counterparts from classical methods. The paper also demonstrates how to find the upper boundary if no airborne data are available. Finally, the numerical method provides a 3D discrete representation of the entire local gravity field instead of a surface solution, a (quasi) geoid model.

有限体积法:一个很好的匹配航空重力?
数值方法,如有限元法(FEM)或有限体积法(FVM),被广泛用于解决许多边值问题。在以往的研究中,这些数值方法也应用于大地测量学,但由于上界条件通常建立在距地球数百公里的卫星轨道水平,需要进行大量的计算。由于地表下界与上界之间的距离较大,两者之间需要进行离散化处理,从而加重了计算负荷。考虑到许多地区,如美国,航空重力数据的均匀分布仅在地形上方几公里处,我们将卫星轨道高度的上边界调整为航空重力测量的平均飞行高度。解域的显著减小极大地减少了FEM或FVM的大量计算量。本文通过对感兴趣的研究领域的模拟和实际现场案例,论证了在降域中使用FVM的优点。在模拟情况下,FVM数值计算结果表明,当将上边界从250 km移动到10 km时,可以获得约一个数量级的精度提高。根据不同的地形质量模拟方案,实际数据集可以获得2 ~ 3 cm的精确准大地水准面模型。在平坦区域,FVM解决方案可以达到1 cm左右的精度,与经典方法相当。本文还演示了在没有机载数据的情况下如何寻找上边界。最后,数值方法提供了整个局部重力场的三维离散表示,而不是表面解,即(准)大地水准面模型。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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来源期刊
Journal of Geodesy
Journal of Geodesy 地学-地球化学与地球物理
CiteScore
8.60
自引率
9.10%
发文量
85
审稿时长
9 months
期刊介绍: The Journal of Geodesy is an international journal concerned with the study of scientific problems of geodesy and related interdisciplinary sciences. Peer-reviewed papers are published on theoretical or modeling studies, and on results of experiments and interpretations. Besides original research papers, the journal includes commissioned review papers on topical subjects and special issues arising from chosen scientific symposia or workshops. The journal covers the whole range of geodetic science and reports on theoretical and applied studies in research areas such as: -Positioning -Reference frame -Geodetic networks -Modeling and quality control -Space geodesy -Remote sensing -Gravity fields -Geodynamics
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