任意球冠下Stokes-Neumman混合边值问题的球谐函数有限逼近方法
Spherical Harmonic Finite Approximation Method for the Stokes-NeummanMixed Boundary Value Problem with a Sphere Cap
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摘要: 首先研究了任意球冠下Stokes-Neumman混合边值问题的求解方法,然后利用EGM08重力场模型对建立的求解方法进行模拟计算。结果表明,给出的解算方法能达到亚mm量级的精度。作为Stokes-Neum-man混合边值问题的应用拓展,用于精化局部大地水准面,结果表明,若不顾及边界效应,计算精度至少达到5cm。因此,本文建立的Stokes-Neumman混合边值问题的解法不仅理论上可行,而且能保持足够的计算精度,适用于多种类型重力观测数据的综合处理。Abstract: A method solving the Stokes-Neumman Mixed Boundary Value Problem(S-N MBVP)witha sphere cap is studied in this paper.First,we discuss the method for S-N MBVP with the polar cap.Then S-N MBVP with general sphere cap is solved with the help of coordinate transformation.Thetransformation between spherical coefficients in different coordinate systems is also studied.By mak-ing use of the imitation computation for the EGM08model,it is concluded that the solution methodgiven in the paper can be accurate to submillimeter level.S-N MBVP can be used to refine the localgeoid,our results show the recovered height of a geoid in the interior of the spherical cap can reach tothe accuracy of 5centimeters.Our results show that the proposed method not only is effective in theo-ry,but also has sufficient precision to deal with many kinds of gravity data.
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