Hankel Spectrum Analysis: A novel signal decomposition method and its geophysical applications

TL;DR

Hankel Spectral Analysis (HSA) is a new robust signal decomposition method for analyzing non-stationary harmonic signals in geophysical data, revealing new insights into Earth's dynamics and global observables.

Contribution

The paper introduces HSA, a novel state-space analysis technique based on Hankel matrices, TSVD, and shift-invariance, specifically designed for non-stationary signal decomposition in geophysics.

Findings

Confirmed triple jumps in Chandler wobble since 1900s.

Identified decadal signals linked to tide and solar activity.

Revealed interannual oscillations contributing to gravity anomalies.

Abstract

To analyze non-stationary harmonic signals typically contained in geophysical observables is a quest that has seen continual advances in numerical techniques over the decades. In this paper, based on transient z-pole estimation (in Hankel matrices), a novel state-space analysis referred to as Hankel Spectral Analysis (HSA), was developed. Depended on the Hankel total least square (HTLS), the HSA incorporates truncated singular value decomposition (TSVD) and its shift-invariant property in robustly decomposing the closely-spaced sinusoids. Resorted to a sliding window processing, HSA can be used to analyze non-stationary sequential structures, in the support of consecutive quaternary parameters {Ai, {\alpha}i, fi, {\theta}i}. Based on a series of experiments with special features commonly in real measurements, the availabilities of HSA in complex harmonic constituents (e.g., the time-variant amplitude/frequency, mutation, the episodic recording signals) with low Signal-to-Noise Ratio are confirmed. In real applications, we use HSA to analyze both global geophysical observables, including polar motion (PM) and earth's dynamic oblateness ({\Delta}J2), and some new findings are obtained. In the PM series since the 1900s, a total of triple jumps from Chandler wobble (CW) are firstly confirmed; and all of them are synchronized by the sharp decrease of Chandler intensity and period. In the {\Delta}J2 series, two decadal signals (18.6 yr, 10.5 yr) are identified to be associated with the tide effect, and solar activity; and its interannual-to-decadal oscillations contribute to multiple global gravity anomalies. These findings implied the great potential of the HSA in searching hitherto signals of geophysical observations.