Hankel Spectrum Analysis: A Decomposition Method for Quasi‐Periodic Signals and Its Geophysical Applications

Abstract To analyze quasi‐periodic signals (with time‐varying complex amplitudes/frequencies) typically contained in geophysical observables is a quest that has seen continual advances in numerical techniques over the decades. In this study, based on transient z ‐pole estimation (in Hankel matrices), a state‐space analysis referred to as Hankel Spectral Analysis (HSA) was developed. Based on the Hankel total least squares and incorporating truncated singular value decomposition and its shift‐invariant property, the HSA aims to decompose the closely spaced sinusoids robustly and orthogonally. Upon using a sliding windows process, the HSA can be used for decomposing and analyzing quasi‐periodic signals, in the support of consecutive parameter spectra { A i , f i , θ i }. Based on a series of experiments, we first confirmed the superiority of the HSA for decomposing different signal constituents (e.g., amplitude‐frequency modulation, mutation, and episodic signals). In real applications, as examples, we use HSA to analyze the polar motion (PM) and Earth's dynamic oblateness (Δ J 2 ). For the PM, we obtained the time‐varying Chandler wobble (CW) and Annual wobble, and first confirmed that there are four phase jumps in the CW since the 1900s; we find that all of those phase jumps are synchronized by the sharp decrease of Chandler intensity and period, and their random excitation mechanism was discussed. For the Δ J 2 , the 18.6 and 10.5 years signals were re‐extracted, and we found that its interannual‐to‐decadal oscillations contribute to multiple global gravity anomalies. These results indicate the great potential of the HSA in decomposing and extracting the recorded periodic/quasi‐periodic signals from geophysical observations.