High-Precision Detection of Earth’s Free Oscillation Signals with Consideration of Phase Consistency

High-precision detection of normal modes is crucial for revealing Earth's deep internal structure. Using superconducting gravimeter data, this study achieves high-precision normal mode detection by combining Normal Time-Frequency Transform (NTFT) and Optimal Sequence Estimation (OSE). Experiments show that OSE detection results vary significantly with the number of stations or different station combinations, indicating the existence of normal mode asynchronous oscillations that notably impact OSE accuracy. NTFT is then applied to extract each station's instantaneous phase spectrum, confirming asynchronous oscillations and highlighting the necessity of considering phase consistency in OSE-based detection. Finally, by integrating NTFT and OSE, a high-precision detection method that accounts for phase consistency is proposed. For the ₃S₁ model, the singlet frequencies of the <i>m</i> = -1, 0, and 1 states were detected to be 0.9424 mHz, 0.944 mHz, and 0.9455 mHz, respectively. The detection results are in excellent agreement with the PREM theoretical values, which validates the effectiveness of the proposed method. This research provides foundational data and key technical support for further exploring Earth's deep structure and optimizing Earth models.