The Spherical Wavelet Expansion Of The Earth's Gravity Field And Its Application

This dissertation focuses on the spherical wavelet expansion of the earth gravity field and its application. Based on the concept of the integration approaches and radial basis functions the spherical wavelet is put forward, with that the earth gravity field is described in a new way, and some other researches are conducted, they are: spherical wavelet regularization, multiscale approximation of satellite gravity measurement, down continuation of airborne geavimetry data, the least squares properties of geopotential wavelet approximation, the spherical wavelet solution of two kinds of BVP and spherical selective multiscale reconstruction. Author main work and contributions are as following:I.As the basis of following works, the spherical harmonic analysis method and radial basis functions technology are introduce in detail.2.In the following part the classic wavelet and the second generation wavelet and its transformation are introduced, with the theory of classic wavelet the spherical wavelet is put forward, and external space of the earth is proved a space of multiscale space.3.Main attention is paid on the third part; in this part several kinds of method to physical geodesy regularization problem are discussed, which are Tikhonov regularization, truncated singular value decomposition, biased estimation and least squares collocation. A new mothod based on the spherical wavelet named spherical wavelet regularization is set up, with this method we can approximate the solution bit by bit. At the end the test of ground gravity solution from simulated satellite data and down continuation of airborne gravimetry are conducted.4.It is proved that using radial derivative or tangential derivative to solve the ground gravity is the same ill-posed problem, we can get the solution with the spherical wavelet regularization. So the theory is performed to SST problem and the multiscale solution is achieved at the end.5.Based on the redundancy of spherical wavelet transformation we proved that using spherical wavelet to approximate the earth gravity field has the least square properties.6.The practical spherical wavelet solutions of the Dirichlit I3VP and Neumann BVP are given out.7.Based on the spherical wavelet theory, we establish a new de-noise method named selective multiscale reconstruction, with that we discuss how to get rid of the noise of satellite measured data.