地磁学中的球面各向同性随机矢量场

从地磁场随机模拟的需要出发，研究球面各向同性随机矢量场．首先指出，与三维空间中的随机矢量场不同，在球上均匀性蕴含于各向同性；三维均匀各向同性随机矢量场一定是球上各向同性随机矢量场，反之不真．其次，以地核磁场的随机模型为例，给出了球面各向同性模型的空间两点关联张量的并矢表示，并将其在不变坐标系分解；利用核幔边界地球主磁场的球谐功率谱的幂级数拟合模型，估算空间两点关联张量．因此，即使根据地球主磁场观测认定地核场具有球面各向同性，亦不能推定地核内部磁流体运动是三维均匀各向同性的．

SPHERICAL ISOTROPIC STOCHASTIC VECTOR FIELDS IN GEOMAGNETISM

Most geomagnetic observations are always related to a sphere, since they weretaken either on the earth's surface or by satellite. In addition, the remanentmagnetization vector field can not be transformed into potential field in general. Inthis paper, a spherical isotopic stochastic vector field (SISVF) has been considered. Itwas point out that there is no difference in meaning between the homogeneity andthe isotropy on 2-D spherical surface, while they are two distinguish concepts in a3-D space. A homogeneous and isotropic stochastic field in the 3-D space must bea spherical isotopic stochastic vector field, conversely is not true. For a SISVF, thespatial two-point correlation tensor depends on four independent correlation functions.The dyad presentation and the decomposition in the invariant coordinatesystem were given for the spatial two-point correlation tensor for spherical isotropicmodel of the core fie1d, as an example of above theory. A power series fitting modelof spherical harmonic power spectrum of the c0re field was established, and variouscomponents of spatial two-Point correlation tensor in the geographic polar sphericalcoordinate system and the invariant coordinate system were estimated. Results of thisstudy indicate that the magnetic field in the earth's core is not necessarilyhomogeneous and isotropic in the 3-D space, even the observed field has sphericalisotropic.