Abstract The secular variation spatial pattern of geomagnetic cutoff rigidity, Rc, is analyzed considering analytical expressions. Stormer analytic Rc equation in terms of geomagnetic latitude is used considering a pure dipolar field for the centered and eccentric dipole coordinates, together with a dipole-quadrupole superposition simplified equation. Linear Rc time trend for the period 1900–2020 in a 5 ° × 15 ° latitude-longitude grid is assessed in each case and a comparative analysis is made with trends based on trajectory based Rc estimations. Common features with some analytic approaches are the two patches of Rc positive and negative trends in the western hemisphere, even though maximum and minimum trend values are underestimated in all analytical cases. Global mean values are almost coincident, except for the dipole-quadrupole superposition case. The salient patches pattern may be due mainly to the dipole axis rotation, more than to its center displacement, its decreasing momentum or the increasing quadrupolar component role. Even though with the advent of better computational tools the trajectory based estimation would be a natural choice to analyze Rc variations, we still consider that an appropriately modified Stormer equation, with its natural advantages of its analytical form and extremely fast way of computation, is sufficient for many applications.

中文翻译：

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使用分析方法的地磁截止刚度长期变化的空间特征

摘要 考虑解析表达式，分析了地磁截止刚度Rc的长期变化空间格局。考虑到中心和偏心偶极坐标的纯偶极场以及偶极-四极叠加简化方程，使用地磁纬度方面的 Stormer 解析 Rc 方程。1900-2020 年期间在 5°×15° 经纬度网格中的线性 Rc 时间趋势在每种情况下都进行了评估，并与基于轨迹的 Rc 估计的趋势进行了比较分析。一些分析方法的共同特征是西半球的 Rc 正负趋势的两个补丁，尽管在所有分析案例中都低估了最大和最小趋势值。全球平均值几乎一致，除了偶极-四极叠加情况。突出的斑块图案可能主要是由于偶极轴旋转，而不是其中心位移、其减小的动量或增加的四极分量作用。尽管随着更好的计算工具的出现，基于轨迹的估计将是分析 Rc 变化的自然选择，我们仍然认为适当修改的 Stormer 方程具有其分析形式和极其快速的计算方式的天然优势，就足够了对于许多应用程序。