Application of Stabilized AR‐z Spectrum in Harmonic Analysis for Geophysics

Abstract

AbstractThe AR‐z spectrum devised in Ding and Chao (2015a) for analyzing harmonic signals (an extension of the frequency domain autoregressive AR algorithm developed by Chao and Gilbert (1980) based on Prony's method) proves to have significantly higher sensitivity and spectral resolution than the Fourier and maximum‐entropy spectra, especially when the signal‐to‐noise ratio is low. As such, it can be prone to random fluctuations in the form of spurious variances of the noise spectrum. Here we develop a stabilized AR‐z spectrum taking advantage of a Monte Carlo noise‐assisted bootstrap scheme, and demonstrate its effectiveness in obtaining more robust spectral estimates for single record. We apply the stabilized AR‐z spectrum, and compare it with the Fourier and maximum‐entropy spectra, to a number of global geophysical observables of the Earth, including the elastic free oscillations, length of day variation (ΔLOD), dynamic oblateness (ΔJ2), polar motion, Earth's nutation, and global mean sea level variation. We report the findings about hitherto unresolved fine structures, including those for the Mf and Mm tidal clusters in the ΔLOD, ΔJ2, polar motion and the Earth's nutation, and the modal splittings of the Earth's free oscillations. Furthermore, a number of long‐period signals of certain nominal periodicities are detected (or confirmed) in the stabilized AR‐z spectra, including the 6‐year signals in ΔLOD, the 18.6‐year signals expected in ΔLOD and ΔJ2, and certain quasiperiodic interannual to decadal periodicities whose origins have yet to be identified. Overall, the stabilized AR‐z spectrum demonstrates a momentous performance in the quest for numerical harmonic analysis methods.