Spherical Spectrum And Wavelet Analysis Of Satellite Magnetic Data

Fourier transform plays an important role in spherical harmonic function, at the same time it also restricts the development of spherical harmonic function in the frequency domain. This paper describes degree and order's physical meaning in the spherical harmonic function and their corresponding spherical wave property. Different from traditional researches most of which mainly focus on functions of harmonic degree n, this paper highlights the spherical harmonic order m's influences on the spherical wave. Different order m changes the direction of the spherical wave as well as the latitude where spherical field energy are concentrating. Based on the study of the order m, here introduces a new direction of spherical wave filtering concept, which can not only separate spherical wave of different directions but also field energy of different latitudes. Here introduces direction filtering results and combined direction and degree filtering results of main geomagnetic field POMME-6. These results confirm that if the order m is increasing with a constant degree n, the direction of spherical wave will rotate from north to east, while the direction of the magnetic anomaly will change from east to north, and the energy will concentrate from high latitude to low latitude.Although the spherical harmonic function has made great contribution to satellite data processing, the spherical harmonic function is built on the basis of Fourier transform. So we can only fit the low-frequency spherical field well, however, as to the medium and high frequency spherical field its effect is not very obvious. At the mean time spherical harmonic function does not have space locality. Satellite data mainly concentrate in low frequency, while ground, airborne and marine gravity and magnetic data are in medium and high frequency, which have very high resolutions due to height of measurement is much lower than satellite's. And most of the ground, airborne and marine data are measured in limited areas. In order to solve the contradictions among the satellite, ground, airborne and marine data, let every data can give full play to its role, people turn to the multi-scale wavelet method. This paper describes the Freeden et al's spherical wavelet theory based on the limited two-dimensional sphere. Spherical wavelet methods include wavelet-only approach and combined approach. Both of them are using spherical wavelet to decompose the input data to a certain number of frequency-dependent detail signals. If the low frequency part can not be ignored, it should be modeled by means of spherical harmonics first, and then the remaining medium and high frequency parts could be modeled by an expansion in spherical wavelet. The paper also describes the wavelet analysis and multi-scale analysis basic theory, followed by details of the spherical wavelet theory and pyramid algorithm used in calculation of coefficients of wavelet of different scales. The paper initially outline parameter and measurement data points selection procedure, then represents the application of spherical wavelet using POMME-6 and MF6 as input data. In the fifth chapter, model MF6 data in China are processed by the direction filtering and wavelet decomposition, followed by their preliminary interpretations. The magnetic energy in China mainly in the angle of 70°or less. The more similar of the direction of the filtering and structure, the better is the result to highlight the shape of the structure. In the wavelet method, structures of the earlier geological era are shown in the smaller processing scale result, which are mainly the plate position, deep faults and early Paleozoic suture zone; when wavelet scale is larger, structures of the later geological era are more prominent, in which positive magnetic anomalies are mainly located in Mesozoic and Cenozoic basins, negative magnetic anomalies are mainly located in orogenic belt.