在地磁学与地球重力学中的球谐分析

球谐分析在地磁学与地球重力学中得到广泛的应用.由于地球磁场与地球引力场的不同，球谐表述有所不同.地磁场的高斯分析（球谐分析）的结果表明，地磁场没有单极子，而引力场有，地磁场有内外源场之分，而地球引力场只有内源场，地磁场的球谐级数收敛快，地磁场高斯级数所用的蒂合勒让德函数是Schmidt半标准化的，而地球引力场中用的是全标准化的，地磁场的高斯系数随时间变化快，每5年产生一个IGRF（国际地磁参考场）, 而引力场的变化是与地质变化有关，相对于地磁场来说，是缓慢的. 地磁场的高斯分析还存在一个唯一性问题.

The spherical harmonic analysis in geomagnetism and gravitation

The method of spherical harmonic analysis is using widely in geomagnetic and gravitation. There are some different characters in the two fields. In geomagnetism there are no monopole, two fields with internal and external sources, respectively. In gravitation there are a monopole, and only internal field. The Schmidt partly-normalized Legendre function are adapted in geomagnetism, but the normalized Legendre function in gravitation. The geomagnetic field change faster than the gravitational field. So there are some IGRF with interval of 5 years in geomagnetism. And there is a problem of Uniqueness in Gauss Analysis of the geomagnetic field.