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《Chinese Journal of Geophysics》 1997-01
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SPHERICAL ISOTROPIC STOCHASTIC VECTOR FIELDS IN GEOMAGNETISM

Mi SHI-ZHUANG(Institute of Geophysics, Academia Sinica. Beijing 100101, China)  
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.
【Fund】: 国家自然科学基金;;中国科学院资源环境“八五”重点攻关项目
【CateGory Index】: P318
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