Developing a New Paleosecular Variation Model

自高斯时代以来，对地球磁场的精确测量才进行了不到200年。即使我们算上之前对倾角和赤纬的稀疏测量，这些数据也只覆盖了几百年。另一方面，地磁场的典型时间常数是偶极子衰变的时间常数（15000年）。如果没有对这个时间常数进行多次观测，我们就不能指望对地磁场有一个完整的描述，这一事实可以通过古地磁的地磁倒转的发现而清楚地说明。古地磁资料具有：(1)误差大且分布差；(2)大多只有方向性信息；(3)全球数据集可能跨越几百万年。首席研究员成功地提出了“泰勒展开法”，通过统计处理，克服了古地磁资料的这些缺点。在该项目期间，该方法成功地应用于(1)磁场强度和虚拟偶极矩（Kono和Hiroi， EPSL,1996），(2)倾角和赤纬分布（Kono， JGG,1997），(3)磁场方向分布形状和虚拟地磁极（Kono， PEPI,1997）。这些研究表明，除了占主导地位的轴向偶极子项外，（2,1）次谐波在古磁场中也很重要。此外，对于非线性数据，如古磁方向，数据均值的反转不会导致高斯系数的平均值。在古强度数据中，避免了这些问题，可以得到平均场（Kono, Tanaka, and Tsunakawa, submitted to JGR）。至此，古长期变化的正演方法已经完成，现在是制定古地磁资料反演的时候了。

Precise measurements of the Earth's magnetic field has been carried out only for less than 200 years since the time of Gauss. Even if we count the sparse measurements of inclination and declination before that, the data covers only several hundred years. On the other hand, the typical time constant of the geomagnetic field is that of the dipole decay (15,000 years). The fact that we cannot hope for a complete description of the geomagnetic field without having observations for several times this time constant can be made clear by the discovery of the magnetic reversals from paleomagnetism. Paleomagnetic data have the characteristics of (1) large errors as well as bad distribution, (2) mostly only directional information, and (3) a few million years may be spanned in a global data set. The head investigator succeeded to formulate the "Taylor Expansion Method" which can overcome these shortcomings of paleomagnetic data by statistical treatment.Within the period of this project, this method was successfully applied to (1) magnetic field intensity and virtual dipole moment (Kono and Hiroi, EPSL,1996), (2)distributions of inclination and declination (Kono, JGG,1997), (3) the shape of distributions of magnetic field directions and virtual geomagnetic poles (Kono, PEPI,1997). These studies indicate that, apart from the dominant axial dipole term, the (2, 1) harmonics are important in the paleomagnetic field. Further, in the case of nonlinear data such as paleomagnetic directions, it was shown that inversiion of the mean values of the data will not lead to the mean Gauss coefficients. In the case of paleointensity data, these problems are avoided and the mean field can be obtained (Kono, Tanaka, and Tsunakawa, submitted to JGR). Thus far, the forward approach to the paleosecular variation was completed and now is the time for formulating the inversion of paleomagnetic data.