基于Legendre函数的超高阶次地磁场建模方法

Legendre函数是超高阶地磁场模型球谐展开的重要组成部分,是解决高纬度地区数据溢出问题的关键。针对Legendre函数在超高阶地磁场建模中的解算问题,从Legendre函数的递推方法出发,优化了Legendre函数的解算过程,提高了效率和精度,解决了数据溢出问题,并给出了Legendre函数的递推过程、函数值和精度检验值。仿真结果表明,该方法提高了磁场模型数值稳定性及精度,为建立更高阶次的地磁场模型和地磁导航基准图的制备提供理论依据。通过将模型计算的各磁场要素与EMM2010模型相比较,验证了方法的有效性,并生成了全球的地磁图。

Method for ultra high-order magnetic model based on Legendre function

Legendre function is an importance part of ultra high-order geomagnetic model spherical harmonics,and is key to solve the overflow date of high latitude.Starting from the recursion methods of Legendre functions,the calculation process of Legendre function for ultra-high order magnetic model is optimized to improve the efficiency and accuracy and solve the overflow of high latitude data.The recursive process of Legendre functions are given,and the variation and accuracy test are presented.Simulation experiments prove that this method has improved the numerical stability and accuracy of the magnetic model and provides the theory basis for building up higher-order geomagnetic model and preparing the geomagnetic navigation matching map.Comparison on the magnetic elements calculated by the improved magnetic model with those calculated by EMM2010 shows that the proposed method is effective and has created a global geomagnetic map.