Alternative methods to smooth the Earth's gravity field
Alternative methods to smooth the Earth's gravity field
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发表时间：
1981-12
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通讯作者：
C. Jekeli
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作者：
C. Jekeli
对一维和二维函数给出了球面上的卷积及相应的卷积定理。这些结果中的一些被用于各向同性平滑算子或滤波器的研究。傅立叶频谱分析中的公知滤波器，例如矩形滤波器、高斯滤波器和汉宁滤波器，适用于球体上的数据。最常用于重力数据的低通滤波器是矩形（或Pellinen）滤波器。然而，它的频谱具有相对较大的旁瓣;因此，该滤波器通过重力频谱上端的相当大的一部分。高斯滤波器和汉宁滤波器的球面自适应在抑制重力场的高频分量方面更有效，因为它们的频率响应函数是强场的，因为它们的频率响应函数在高频处是强锥形的，没有旁瓣或旁瓣很小。这些新的过滤器的实际实施公式。
Convolutions on the sphere with corresponding convolution theorems are developed for one and two dimensional functions. Some of these results are used in a study of isotropic smoothing operators or filters. Well known filters in Fourier spectral analysis, such as the rectangular, Gaussian, and Hanning filters, are adapted for data on a sphere. The low-pass filter most often used on gravity data is the rectangular (or Pellinen) filter. However, its spectrum has relatively large sidelobes; and therefore, this filter passes a considerable part of the upper end of the gravity spectrum. The spherical adaptations of the Gaussian and Hanning filters are more efficient in suppressing the high-frequency components of the gravity field since their frequency response functions are strongly field since their frequency response functions are strongly tapered at the high frequencies with no, or small, sidelobes. Formulas are given for practical implementation of these new filters.