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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., Comment: 40 pages,10 figures