全球磁場變化分析：應用經驗正交函數法

Abstract

我們利用 IGRF 模型提供的高斯係數，分析1900年至2020年的全球磁場長期變化。(i) 我們應用經驗正交函數法 (Empirical Orthogonal Functions, EOF) 在球諧函數階數至6的全球磁場上，並在地函為絕緣的假設下，向下恢復磁場至核幔邊界 (Core-mantle boundary, CMB)。前三個EOF模式呈現週期分別約為120、75及60年的時間變化及對應的空間特徵。這些振盪模式潛在支持接近外核CMB的穩定分層中，流體受磁力、浮力、科氏力造成的 MAC (Magnetic, Archimedes and Coriolis) 波動行為 (Buffett, et al., 2016)。(ii) 我們採用和 Yukutake 與 Shimizu (2015) 類似的方法，根據高斯係數的變化軌跡將全球磁場分解成穩定項和移動項，再利用複數EOF (Complex EOF, CEOF) 分析移動項磁場。結果顯示在研究時間區段內繞轉部分週期的西移現象。本研究呈現完整的分析，為將來低階的長期磁場變化提供更進一步的地球物理解釋基礎。

We examine the variations of the global geomagnetic field on long temporal scales using the IGRF model given in the Gauss coefficients for 1900 - 2020. (i) We apply the Empirical Orthogonal Function (EOF) analysis to the geomagnetic field truncated at spherical-harmonic degree 6, and downward continue it to the core-mantle boundary (CMB) under the assumption of an insulating mantle. The first three EOF modes show the periods around 120, 75 and 60 years. With corresponding spatial structures, these standing-oscillational modes potentially support the manifestation of the so-called MAC (magnetic, Archimedes and Coriolis) waves in the stably stratified layer near CMB (Buffett et al., 2016). (ii) We also model and decompose the geomagnetic field to standing and drifting components according to trajectories of the corresponding Gauss coefficients similarly as Yukutake and Shimizu (2015). We then use the Complex EOF (CEOF) analysis on the drifting field. The results indicate the presence of the westward drift phenomenon but only weakly, given the fact that the westward drift has only completed a fraction of a cycle during the studied timespan. This work represents the most updated complete analysis, and lends an insightful basis for further studies for geophysical interpretations, of the low-degree geomagnetic variations of long temporal scales.