1. Hankel Spectrum Analysis: A Decomposition Method for Quasi‐Periodic Signals and Its Geophysical Applications.
- Author
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Shi, Kunpeng and Ding, Hao
- Subjects
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DECOMPOSITION method , *SINGULAR value decomposition , *GEOPHYSICAL observations , *GRAVITY anomalies , *SPECTRUM analysis , *LEAST squares - 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 {Ai, fi, θi}. 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 (ΔJ2). 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 ΔJ2, 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. Plain Language Summary: In signal analysis, the refined extracting of the periodic and quasi‐periodic signals remains a considerable challenge. In this study, we propose a powerful time‐series separator, the Hankel Spectral Analysis (HSA), which supports instant structured detection that traditional methods cannot afford. We have designed multiple sets of simulations to show the HSA's well‐restored ability for various and complex quasi‐periodic signals. Although the HSA has some significant advantages, it has two fundamental limitations: (a) it is applicable only to data series which are physically constituted by a sum of harmonic components; (b) the number of harmonic components needs to know beforehand. In the real application, we focus on the study of polar motion (PM) and the Earth's dynamic oblateness (ΔJ2). Here, we mainly attempted to resolve their recent disputes about the Chandler wobbles (CW) phase jumps in PM and the long periodic signal in ΔJ2. Subsequently, the origins of CW phase jumps are re‐examined; and our results show that there is a particular consistency between the four‐phase jump events and the valleys of amplitude and period. In addition, we re‐extracted the ∼18.6 and 10.5 years signals in ΔJ2 and found that the famous "1998 anomaly" related to the fluctuations on interannual‐decadal timescales. Key Points: Hankel Spectrum Analysis is proposed for more exactly decomposing and parameterizing signals with time‐varying amplitudes/frequenciesMultiple phase jumps of the Chandler wobble accompanied by sudden drops in instantaneous amplitude and period are detectedWe access the Earth's oblateness ΔJ2 of the residual ∼18.6 years tidal signal, ∼10.5 years signal, and multiple global gravity anomaly peaks [ABSTRACT FROM AUTHOR]
- Published
- 2023
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