Detection of Earth’s free oscillation and analysis of the non-synchronous oscillation phenomenon of normal modes

• Method to detect normal modes based on Normal Time-Frequency Transform. • The method is highly sensitive to frequencies of normal modes. • The method can reveal the phase distribution character of free oscillation modes • Phenomenon of phase inconsistency of free oscillation modes. Earth’s free oscillation can provide essential constraints for refining Earth models, inverting seismic source mechanisms, and studying the deep internal structure of the Earth. Large earthquakes can simultaneously excite numerous normal modes. Due to the Earth’s ellipticity, rotation, and internal heterogeneities, these normal modes undergo splitting, with the frequencies of singlets of normal modes becoming very close (only a few µHz apart). This imposes greater demands on the detection of normal modes. This paper introduces a novel method for normal mode detection based on the normal time–frequency transform (NTFT). Compared to classical FT spectrum methods and recent optimal sequence estimation (OSE), the proposed method not only detects more weak normal modes but also reveals the spatial distribution of the phase of each normal mode. Taking the detection of 0 S 2 as an example, the phase measurements of each singlet are spatially inconsistent. This phenomenon can provide prior information for other methods, such as product spectrum analysis (PSA), spherical harmonic stacking (SHS), multistation experiments (MSE), and OSE. Additionally, understanding the phase distribution patterns contributes to further study of geological structures, offering crucial foundational data and observational support.