Inverse Multiscale Geoid Computation

逆多尺度大地水准面计算

• 批准号: 5322860
• 负责人: Professor Dr. Willi Freeden
• 金额: --
• 依托单位: Fachbereich Mathematik
• 依托单位国家: 德国
• 项目类别: Research Grants
• 财政年份: 2001
• 资助国家: 德国
• 起止时间: 2000-12-31 至 2010-12-31
• 项目状态: 已结题
• 来源: https://gepris.dfg.de/gepris/projekt/5322860?language=en
• 关键词: Inverse; Multiscale; Geoid; Computation

Starting from geopotential values as data on the actual Earth's surface a multiscale method of determining the disturbing potential outside and on the telluroid is introduced. In contrast to the standard procedure an ellipsoid of revolution is proposed to act as reference surface instead of a sphere. Furthermore, the potential itself is intended to be approximated by ellipsoidal harmonic wavelets outside the telluroid from given potential values on the real Earth's surface. The solution process is performed by multiresolution analysis in terms of ellipsoidal harmonic regularization wavelets. The essential idea ist to approximate in suitable way the (regularization) wavelet transforms defined als integrals over the telluroid, i.e. the reference ellipsoid, by evaluation functionals, i.e. point values on the actual Earth's surface. The bandlimited (i.e. truncated singular value decomposition) case and the non-bandlimited (i.e. Tikhonov) case must be distinguished for regularization, and different types of pyramid schemata must be implemented for fast wavelets transform for the bandlimited and non-bandlimited appraoch, respectively. Finally, the disturbing potential is used for geoidal determination by using the well-known Bruns formula of physical geodesy. Both the theoretical and practical aspects can be formulated in such a way that high-precision geoidal modelling from global to local scale becomes efficiently and economically available by virtue of the zooming-in property of more and more space-localizing wavelets on the telluroid.

本文从实际地球表面的地球位值出发，介绍了一种确定类地体内外扰动位的多尺度方法。与标准方法不同，本文提出用旋转椭球代替球面作为参考面。此外，潜在的本身是打算近似椭球谐波小波外的碲线从给定的潜在值在真实的地球表面。求解过程采用椭球调和正则小波多分辨分析。其基本思想是以适当的方式近似的（正则化）小波变换定义的als积分的telluroid，即参考椭球，通过评估功能，即点值的实际地球表面上。对于正则化，必须区分带限（即截断奇异值分解）情况和非带限（即吉洪诺夫）情况，并且必须分别针对带限和非带限方法实现不同类型的金字塔模式以进行快速小波变换。最后，利用物理大地测量中著名的Bruns公式，将扰动位用于大地水准面的确定。理论和实践方面都可以制定这样一种方式，即从全球到局部尺度的高精度大地水准面建模变得有效和经济，凭借越来越多的空间局部化小波的放大属性的telluroid。