Inverse Multiscale Geoid Computation

本文介绍了一种以大地电位值为实际地表资料，确定大地大地表面和大地大地大地扰动电位的多尺度方法。与标准方法不同，本文提出以旋转椭球面代替球面作为参考面。此外，电势本身打算用椭球面谐波小波从真实地球表面的给定电势值近似椭球面电势。求解过程采用椭球调和正则化小波的多分辨率分析。其基本思想是用合适的方法逼近（正则化）小波变换在椭球面上定义的积分，即参考椭球，通过评估函数，即实际地球表面上的点值。为了实现正则化，必须区分带限（即截断奇异值分解）和非带限（即Tikhonov）情况，并且对于带限和非带限方法，必须分别实现不同类型的金字塔模式进行快速小波变换。最后，利用物理大地测量学中著名的布伦斯公式，将扰动势用于大地水准面确定。利用越来越多的空间定域小波在大地水准线上的放大特性，从全球尺度到局部尺度的高精度大地水准面建模可以在理论和实践方面得到有效和经济的阐述。

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.