Accurate Measurement Methods of Frequency Eigenquantities in High-Speed Railway Seismic Wavefields and Applications to Distributed Acoustic Sensing Data

High-speed railways (HSRs) generate repeatable and spatially extended seismic wavefields, providing useful signals for distributed acoustic sensing (DAS)-based vibration analysis. This study develops an integrated measurement framework for two characteristic frequency eigenquantities in HSR-induced seismic wavefields: train frequency and bridge frequency. Building on established spectral-line, cepstral, and Doppler descriptions of HSR seismic wavefields, we systematize the relevant theoretical expressions, compare frequency-domain correlation and cepstral strategies for train-frequency estimation, and derive a velocity-independent bridge-frequency estimator from paired Doppler-shifted components. DAS data collected along viaduct sections of the Beijing–Guangzhou HSR are used to evaluate the framework across single trains, dense observation traces, and multiple train events. The results show that bridge frequency is more stable than train frequency, with lower measurement variance. The frequency-derived train speeds and carriage lengths fall within typical operating ranges of Chinese HSR trains, and the observed spatial periodicity in frequency measurements is consistent with bridge pier spacing. These findings support accurate frequency measurement and preliminary estimation of train speed, carriage length, and wave velocity from DAS records. Together, they clarify measurable frequency parameters of HSR seismic sources and establish a quantitative source-characterization basis for DAS-based railway vibration analysis and future multi-source monitoring studies.