用于区域地磁场模型计算的三维Taylor多项式方法

The three dimension Taylor polynomial method for the calculation of regional geomagnetic field model

地磁场具有复杂的时空分布特点.地磁场模型是研究地磁场空间分布与时间变化规律的主要手段,包括全球和局部地区两类模型.局部模型精度满足了反映小尺度磁异常的需要.Taylor多项式模型是用于区域地磁场模型计算的常用方法,但至目前为止所用的都是二维Taylor多项式方法.本文提出了既能表示出地磁场在地球表面的分布,又能表示出地磁场随高度变化的三维Taylor多项式完整展开方法,这个方法能描述地磁场三维结构的特点.文中指出,相对于经典展开(局部三角阵展开),更一般的Taylor多项式展开应该为完整展开(矩阵展开)方法,文中详细分析了两种方法的截断阶数的选取和边界效应问题,并利用1980年的中国地磁观测资料,计算了中国区域的磁场总强度F,磁偏角D,磁倾角I.结果表明:(1)三维Taylor多项式方法计算的中国区域地磁场要素与实际观测资料有较好的一致性,能反映地磁异常的分布细节;(2)三维Taylor多项式方法能较好地克服区域模型中的边界效应问题;(3)三维Taylor多项式方法与计算区域模型的其他三维方法相比,具有计算简单,精度基本一致的特点.在一些对实时性要求很高的应用领域,如高速弹道飞行器导航等,可以得到比较好的应用.

Geomagnetic field has a complex spatial and temporal distribution characteristics. The model of geomagnetic field is main method to study the field spatial distribution and temporal variation, including two types of models of global and local areas. The regional geomagnetic model represents the magnetic anomalies of small-scale. Taylor polynomial model is the commonly used for calculation of regional geomagnetic field model, and two- dimensional Taylor polynomial method has been used up to now. In this paper, three-dimensional Taylor polynomial expansion method is put forward first. It can express the distribution of geomagnetic field on Earth＇s surface, but also geomagnetic field changed with height. It describes the characteristics of three-dimensional structure of the geomagnetic field. The paper points out that the more general Taylor expansion should be complete polynomial expansion （matrix expansion） method. It should replace the classical expansion （local triangular matrix to expand）. This paper analyzes the comparison of the truncation order and the boundary effect of the two methods. The total intensity （F）, declination （D）, inclination （I） of China region are calculated by using China＇ s geomagnetic observation data in 1980. The results show that： （1） Geomagnetic elements field calculated by three-dimensional Taylor polynomial method is in good agreement with actual observation data. It can describe the details of the distribution of magnetic anomalies; （2） Three-dimensional Taylor polynomial method can overcome the boundary effects in other regional model; （3） Comparing three-dimensional Taylor polynomial method with other three- dimensional methods, it has the same accuracy and three-dimensional Taylor polynomial method has simpler calculation process. In some of the real-time applications such as aircraft or high-speed missile navigation, it can have a good prospection.