Since the inception of the optimal sequence estimation (OSE) method, various research teams have substantiated its efficacy as the optimal stacking technique for handling array data, leading to its successful application in numerous geoscience studies. Nevertheless, concerns persist regarding the potential impact of aliasing resulting from the choice of distinct station distributions on the outcomes derived from OSE. In this investigation, I employ theoretical deduction and experimental analysis to elucidate the reasons behind the immunity of the Yl'm'-related common signal obtained through OSE to variations in station distribution selection. The primary objective of OSE is also underscored, i.e., to restore/strip a Yl'm'-related common periodic signal from various stations. Furthermore, I provide additional clarification that the ‘Yl'm'-related common signal’ and the ‘Yl'm'-related equivalent excitation sequence’ are distinct concepts. These analyses will facilitate the utilization of the OSE technique by other researchers in investigating intriguing geophysical phenomena and attaining sound explanations.
H. Ding, W.B. Shen, Search for the Slichter modes based on a new method: optimal sequence estimation, J. Geophys. Res. Solid Earth 118 (9) (2013) 5018-5029, https://doi.org/10.1002/jgrb50344.
H. Ding, B.F. Chao, Data stacking methods for isolation of singlets of the Earth's normal modes: extensions comparisons and applications, J. Geophys. Res. Solid Earth 120 (2015) 5034-5050, https://doi.org/10.1002/2015JB012025.
H. Ding, B.F. Chao, The Slichter mode of the Earth: revisit with optimal stacking and autoregressive methods on full superconducting gravimeter data set, J. Geophys. Res. Solid Earth 120 (10) (2015) 7261-7272, https://doi.org/10.1002/2015JB012203.
S.Y. Zeng, W.B. Shen, Observations of the singlets of higher-degree modes based on the OSE, J. Earth Sci. 5695 (2018) 1-11.
H. Ding, Z.F. Chen, Y.J. Pan, C.Y. Zou, The complex Love numbers of long-period zonal tides retrieved from global GPS displacements: applications for mantle anelasticity, J. Geophys. Res. Solid Earth 126 (2021) e2021JB022380, https://doi.org/10.1029/2021JB022380.
H. Ding, B.F. Chao, Solid pole tide in global GNSS and superconducting gravimeter observations: signal retrieval and inference for mantle anelasticity, Earth Planet Sci. Lett. 459 (2017) 244-251, https://doi.org/10.1016/jepsl201611039.
H. Ding, B.F. Chao, A 6-year westward rotary motion in the Earth: detection and possible MICG coupling mechanism, Earth Planet Sci. Lett. 495 (2018) 50-55, https://doi.org/10.1016/j.epsl.2018.05.009.
H. Ding, X.Y. Xu, Y.J. Pan, W.P. Jiang, T. Van Dam, A time-varying 3D displacement model of the ~5.9-year westward motion and its applications for the Global Navigation Satellite System positions and velocities, J. Geophys. Res. Solid Earth 125 (4) (2020), https://doi.org/10.1029/2019JB018804.
H. Ding, X.Y. Xu, Y.J. Pan, M.K. Li, Array processing techniques for analyzing global geophysical observation networks: comprehensive analysis and typical applications, Earth Sci. Rev. 221 (2021) 103807, https://doi.org/10.1016/j.earscirev.2021.103807.
G. Backus, R. Parker, C. Constable, Foundations of geomagnetism, Cambridge University Press, Cambridge, 2005.
B. Hofmann-Wellenhof, H. Moritz, Physical Geodesy, Springer, Verlag Wien, 2006.
F. Gilbert, A.M. Dziewonski, An application of normal mode theory to the retrieval of structural parameters and source mechanisms from seismic spectra, Philos. Trans. R. Soc. London, Ser. A 278 (1975) 187-269.
A.R. Edmonds, Angular momentum in quantum mechanics, Princeton University Press, Princeton, Jersey, 1957.
H. Ding, T.Y. Jin, J.C. Li, W.P. Jiang, The contribution of a newly unraveled 64yr common oscillation on the estimate of present-day global mean sea level rise, J. Geophys. Res. Solid Earth 126 (6) (2021), https://doi.org/10.1029/2021JB022147.