地球重力场的球面小波分析研究

RESEARCH ON THE SPHERICAL WAVELET ANALYSIS OF THE EARTH'S GRAVITY FIELD

高精度高分辨率地球重力场模型是地球科学、空间科学以及海洋科学发展的需要。目前的全球重力场模型的阶数已达 36 0阶、50km× 50km的分辨率。调和展开分析是当前高精度全球重力场模型的基础 ,由于全球外调和展开存在只有频域的局部性而缺乏空间域的局部性的缺陷 ,使得地球重力场模型向高频逼近时不可能在外调和框架下有效地进行。利用球面小波分析和多尺度分析理论可克服该缺陷。通过发展球面小波理论 ,来对地球重力场进行球面小波展开 ,获得地球重力场的多尺度结构 ,建立局部或全球重力场的多尺度模型 ,揭示地球重力场的多尺度结构与场源密度分布之间的响应 ,恢复重力场的空间域与频率域的精细结构 ,提高重力场的精度和分辨率 ,以推进地球重力场在相关学科的基础、战略作用。

High precision,high resolution geopotential model is necessary for developing the earth science,space science and marine science.At present there exist geopotential models with 360 degree and 50km×50km resolution.Harmonic expansion analysis is the fundament of present high precision geopotential model.Because of the shortcoming that there only exists the localization of frequency domain,while without the localization of space domain in global outer harmonic expansion,the geopotential model which approximates to high frequency could not effectively be carried out in the framework of outer harmonic.In this paper the author argues by using the theories of spherical wavelet analysis and multiresolution analysis to overcome this shortcoming.By developing the theories of spherical wavelets,the author may implement the spherical wavelet expansion of geopotential,gain the multiresolution structure of the earth's gravity field,establish the multiresolution models of local or global gravity field,find out the correspondence between the multiresolution structure of the earth's gravity field and the distribution of the source density causing the gravity field,recover the refined structures of the gravity field in the space domain and the frequency domain,improve the precision and resolution of gravity field,so that the fundamental,strategical roles of gravity field in the relative disciplines could be promoted.