Earthquake body-wave extraction using sparsity-promoting polarization filtering in the time–frequency domain

Seismic waves generated by earthquakes consist of multiple phases that carry critical information about Earth’s internal structure as they propagate through heterogeneous media. Each seismic phase follows its own propagation path and sampling depth, bringing constraints from different regions of the Earth such as the crust, mantle, or even the outer and inner cores. The choice of phase for analysis therefore depends on the study target and the scientific objective: surface waves are particularly suited for imaging shallow, large-scale structures, whereas body waves provide higher-resolution information at depth, inaccessible to surface-wave methods. However, a persistent challenge in body-wave studies is that the relatively low-amplitude P and S arrivals are often obscured by stronger, slowly attenuating surface waves that overlap in both time and frequency. Although body waves typically contain higher frequency content, their spectral overlap with surface waves limits the effectiveness of conventional filtering approaches. Addressing this issue requires advanced signal processing techniques. One such method, Sparsity-Promoting Time–Frequency Filtering (SP-TFF; Mohammadigheymasi et al., 2022), exploits high-resolution polarization characteristics in the time–frequency domain to separate seismic phases. SP-TFF combines amplitude, directivity, and rectilinearity constraints to enhance phase discrimination. In this study, we further develop SP-TFF by designing a filter set specifically tailored to isolate body-wave arrivals that are otherwise masked by high-amplitude surface waves. The directivity filters are constructed based on the predicted incidence of seismic rays from the earthquake hypocenter to each station, enabling focused extraction of the incoming body wave energy and suppression of interfering phases, including surface waves and scattered wavefields. We demonstrate the method using both synthetic tests and waveform data from the Mw 7.0 Guerrero, Mexico, earthquake of September 8, 2021 (depth 21.8 km, reverse-thrust faulting), recorded by stations of the United States National Seismic Network (USNSN). Our results show that SP-TFF provides a robust computational framework for automated body-wave extraction, integrating polarization-informed filtering into seismological data processing pipelines. The approach is scalable to large waveform datasets and can enhance both real-time and retrospective seismological analyses, positioning it as a valuable informatics tool for Earth science. The codes required to reproduce the synthetic and observational examples are openly available on GitHub for the broader geoscience community.