Abstract—Studies on astronomical historic archives are very important for understanding and promoting the progress of astronomy and astrophysics. For long-term solar data sets, they are the oldest topics in statistical astrophysics during the last four hundred years. To reveal the complex physical behavior of solar magnetic structures, a relatively novel time series analysis technique is applied here to investigate the multi-scale oscillation modes and the secular trend of yearly solar sunspot areas during the time interval from 1611 to 2005. Based on the empirical mode decomposition technique, the following results are found: 1) the time series of 395-year solar sunspot areas is decomposed into four intrinsic mode functions with different quasi-periodic oscillations, which could be understood four dynamic processes that have different periodic-scales; 2) for the secular trend of solar magnetic activity, the level of the Sun has a rapid decrease from 1611 to 1670, and then the activity level increases during the period of 1670-2005. The analysis results indicate that the utility of the empirical mode decomposition technique for the study of solar historic archives and could provide some very important information on the understanding of solar magnetic activity variations.

Index Terms—Time-frequency analysis, signal processing, empirical mode decomposition, intrinsic mode function.

Yongyan Zuo, Yuanyong Liu, Xinan Tian, Jianmei An are with Chongqing University of Arts and Sciences, Chongqing, China (email: 407837032@qq.com).
Yunfang Cai is with Yunnan Observatories, Chinese Academy of Sciences, Kunming, China.

Cite: Yongyan Zuo, Yunfang Cai, Yuanyong Liu, Xinan Tian, Jianmei An, "Multi-scale Oscillation Modes and Secular Trend Analysis of Astronomical Historic Archives," International Journal of Applied Physics and Mathematics vol. 9, no. 4, pp. 189-195, 2019.