Developing a New Paleosecular Variation Model

自高斯时代以来，对地球磁场的精确测量只进行了不到200年。即使我们把之前对倾角和倾角的稀疏测量计算在内，这些数据也只涵盖了几百年。另一方面，地磁场的典型时间常数是偶极子衰减的时间常数（15，000年）。如果没有几倍于这个时间常数的观测，我们就不可能希望对地磁场进行完整的描述，这一事实可以通过古地磁学中的磁反转的发现而清楚地表明。古地磁数据具有以下特点：（1）误差大、分布差;（2）大多只有方向信息;（3）全球数据集可能跨越数百万年。研究组长成功地制定了“泰勒展开法”，通过统计处理克服了古地磁数据的这些缺点，在本项目期间，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）倾角和倾角的分布（Kono，JGG，1997），（3）磁场方向和虚拟磁极的分布形状（Kono，PEPI，1997）。这些研究表明，除了主导的轴向偶极子项，（2，1）谐波是重要的古磁场。此外，在非线性数据的情况下，如古地磁方向，它表明，反演数据的平均值不会导致平均高斯系数。在古强度数据的情况下，避免了这些问题，可以获得平均场（Kono，Tanaka和Tsunakawa，提交给JGR）。到目前为止，古地磁变化的正演研究已经完成，现在是制定古地磁数据反演的时候了。

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.