Budget Amount *help 
¥7,700,000 (Direct Cost: ¥7,700,000)
Fiscal Year 1999: ¥2,800,000 (Direct Cost: ¥2,800,000)
Fiscal Year 1998: ¥4,900,000 (Direct Cost: ¥4,900,000)

Research Abstract 
First of all, we examined the problem which arise because of the fact that paleomagnetic data are mostly given by inclination and declination, which depend nonlinearly on the parameters (Gauss coefficients) of the magnetic field model. Gubbins and Kelly (1993) and Johnson and Constable (1995, 1997) already published models of the timeaveraged field for the last 5 million years. However, they implicitly assumed that there is a direct correspondence between the parameters and the data (I, D), which is not correct. By using the Taylor expansion method we showed that the mean of the nonlinear data depend not only on the means of parameters but on the variances of parameters. The variance of the data, on the other hand, depend only on the variance of the parameters, at the approximation to the second order terms. Next, in order to avoid the complexity discussed above, we applied the inversion only to paleointensity data for the last 5 million years. Paleointensity data are usually accompani
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ed by the directional information, so that they can readily be converted to the three components (X, Y, Z) which are linear functions of the parameters. In this case, it is possible to solve the inverse problem separately for the means and for the variances. The results show that the mean magnetic field is more axial dipole like than the present field, and that largest nodipole power is contained in the (2, 1) harmonics. The inversion of variances resulted in a large g【0!1】 component, which is about 30% of the mean value. For other terms, unambiguous results were not obtained possibly because of the number of paleointensity data were not enough. Thirdly, we developed a threedimensional dynamo code in this research period and studied the origin of the geomagnetic field. Using the simulation results obtained by this code, we analyzed the behavior of dynamo magnetic field from the point of view of paleosecular variation. The comparison with the observed field show that dynamo field has many similar properties such as the dominance of the axial dipole component, about the same power on the surface of the core in harmonics of different degrees, and Gauss coefficients behave as random variates following zeromean normal distributions. Other interesting properties such as the westward and eastward drift of surface features was seen only in the models. Less
