Abstract:
Long-period ground motions typically manifest as highly non-stationary features within seismic acceleration records, where low-frequency components frequently separate temporally from high-frequency strong-motion segments and exhibit significant delay, posing a critical threat to flexible structures with long natural periods such as high-rise buildings and long-span bridges. Traditional identification methods, which rely on manual visual inspection of time histories or the evaluation of response spectra, are inherently limited; manual inspection is subjective and struggles to automatically capture the specific evolutionary process of the long-period dominant interval, while response spectra condense the entire record into single maximum responses, causing the impact of late-arriving surface waves to be masked by earlier high-frequency body waves. Existing time-frequency tools present notable challenges: the short-time Fourier transform (STFT) cannot simultaneously balance high- and low-frequency resolutions, the continuous wavelet transform (CWT) suffers from boundary effects that distort low-frequency energy calculations, and the Hilbert-Huang transform (HHT) is prone to mode mixing when processing strong-motion records contaminated by complex environmental noise. This paper proposes a time-frequency analysis framework based on the multiple filter technique (MFT), aimed at achieving automated and precise identification of long-period ground motion components. The MFT method decomposes the signals into a series of narrow-band components utilizing logarithmically spaced central frequencies, generating a high-resolution time-frequency amplitude matrix. For each frequency, a Gaussian-type frequency domain filter is applied. After utilizing a Hilbert transform to extract instantaneous amplitudes, the framework establishes a 1.0 Hz physical boundary frequency to separate low-frequency energy from high-frequency energy. The instantaneous energy ratio is dynamically calculated to represent the proportion of low-frequency energy relative to total energy. When this ratio strictly exceeds 0.5, a long-period dominant state is triggered, indicating that low-frequency energy has physically surpassed high-frequency energy. To ensure engineering relevance and rigorously exclude ambient seismic noise, the methodology enforces a localized noise threshold. Furthermore, only segments continuously maintaining dominance for at least ten seconds are classified as long-period dominant zones, ensuring the identified signals possess the requisite time scale to accumulate substantial ground velocity and displacement. Recognizing that the energy ratio inherently lacks particle motion constraints, the framework incorporates the normalized inner product (NIP) method as an auxiliary tool for the physical verification of actual surface waves. The NIP quantifies phase consistency between the radial and phase-shifted vertical displacement components utilizing S-transform instantaneous phases with a rigorous threshold of 0.8. The robustness of this dual-analysis framework was extensively validated using three-component strong-motion acceleration records collected from the January 7, 2025,
MS6.8 Dingri, Xizang, earthquake. The automated analysis revealed that seismic waves underwent intense anelastic attenuation and wave-mode conversion during propagation. Notably, densely distributed stations in specific target regions demonstrated a strong full-range long-period characteristics across shear-wave signals. This phenomenon is mainly caused by near-surface low-velocity media and complex basin structures. The analysis also captured specific near-fault anomalies at the bedrock station XZ.RKZ, located at an epicentral distance of 163 kilometers, where long-period characteristics were linked to critical reflections triggered by the Moho discontinuity. This was mathematically verified using Snell’s law based on regional crustal and mantle velocities. The study further tracked the spatial evolution of the seismic wavefield by systematically comparing stations along the propagation path; at the closer stations, long-period motions were observed to be in an early stage, displaying mixed high-low frequency characteristics and dual-peak response spectra. Conversely, at the far-field station, the shear-wave signal evolved to be entirely dominated by low frequencies, featuring a wave group composed purely of low-frequency components. A stable Rayleigh wave elliptical motion was verified by NIP polarization analysis, which indicates that the low-frequency dominant intervals identified by the proposed method can effectively depict the evolution of low-frequency energy and provide a reliable reference for surface wave arrival. However, these intervals do not necessarily equate to the physical arrival time of the first surface wave. The proposed NIP polarization analysis method based on the long-period dominance identification satisfies the dual requirements of engineering application and physical phase verification. The method proposed in this paper can serve as an effective tool for the rapid screening and time-domain annotation of long-period records in strong-motion databases, providing technical support for the seismic analysis and input selection of long-period structures.