Gravity field terrain effect computations by FFT
Gravity field terrain effect computations by FFT
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DOI：
10.1007/bf02521068
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发表时间：
1985-12
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影响因子：
--
通讯作者：
R. Forsberg
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文献类型：
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作者：
R. Forsberg
由于地球许多地区的详细网格地形和测深数据广泛可用，因此需要有效的地形影响计算技术，特别是用于重力场建模。与传统的积分技术相比，由于快速傅立叶变换（FFT）的速度，傅立叶变换方法提供了极其有效的计算。傅立叶技术依赖于基本非线性地形效应积分的线性化和级数展开，通常涉及高度/深度及其平方的变换。FFT方法特别适用于陆地重力数据和卫星测高大地水准面数据的地形简化，本文将概述FFT的基本公式，并着重讨论FFT的实际实现，其中必须采用特殊的粗/细网格对公式，以减少FFT不可避免的边缘效应，FFT的特殊性质被用来限制所需数据转换的实际数量。在美国、格陵兰岛和北大西洋的试验区，给出了重力和大地水准面地形效应的实际结果。对结果进行评估，对传统的集成程序：因此，例如，在东格陵兰的一个地区（地形校正高达10 mgal），使用来自详细摄影测量数字地形模型的高度数据，在实际重力站中FFT计算的地形校正的精度显示出0.25 mgal的均方根误差。同样，法罗群岛地区的均衡海洋大地水准面效应的计算均方根误差约为0.03米
The widespread availability of detailed gridded topographic and bathymetric data for many areas of the earth has resulted in a need for efficient terrain effect computation techniques, especially for applications in gravity field modelling. Compared to conventional integration techniques, Fourier transform methods provide extremely efficient computations due to the speed of the Fast Fourier Transform (FFT. The Fourier techniques rely on linearization and series expansions of the basically unlinear terrain effect integrals, typically involving transformation of the heights/depths and their squares. TheFFTmethods will especially be suited for terrain reduction of land gravity data and satellite altimetry geoid data.In the paper the basic formulas will be outlined, and special emphasis will be put on the practial implementation, where a special coarse/detailed grid pair formulation must be used in order to minimize the unavoidable edge effects ofFFT, and the special properties ofFFTare utilized to limit the actual number of data transformations needed. Actual results are presented for gravity and geoid terrain effects in test areas of the USA, Greenland and the North Atlantic. The results are evaluated against a conventional integration program: thus, e.g., in an area of East Greenland (with terrain corrections up to10 mgal), the accuracy ofFFT-computed terrain corrections in actual gravity stations showed anr.m.s.error of0.25 mgal, using height data from a detailed photogrammetric digital terrain model. Similarly, isostatic ocean geoid effects in the Faeroe Islands region were found to be computed withr.m.s.errors around0.03 m