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

## TL;DR

This paper advances seismic signal processing by developing an enhanced sparsity-promoting polarization filtering method in the time-frequency domain to isolate earthquake body waves from surface wave interference.

## Contribution

It introduces a tailored filter set based on predicted seismic ray angles, improving automated extraction of body waves in complex seismic data.

## Key findings

- Effective separation of body and surface waves demonstrated on synthetic data.
- Successful application to real earthquake data from Guerrero, Mexico.
- Enhanced polarization filtering improves phase discrimination in seismic analysis.

## Abstract

Seismic waves generated by earthquakes consist of multiple phases that carry critical information about Earth's internal structure as they propagate through heterogeneous media. These phases provide constraints from different regions of the Earth, such as the crust, mantle, and even the cores. The choice of phase depends on the study target and scientific objective: surface waves are suited for imaging shallow structures, whereas body waves yield higher-resolution information at depth. A key challenge in body-wave studies is that the low-amplitude P and S arrivals are often masked by surface waves overlapping 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 information in the time-frequency domain. SP-TFF integrates amplitude, directivity, and rectilinearity to enhance phase discrimination. Here, we further develop SP-TFF by designing a filter set tailored to isolate body-wave arrivals otherwise masked by high-amplitude surface waves. The directivity filters are constructed from predicted seismic ray incidence angles, enabling focused extraction of body-wave energy and suppression of interfering phases. We evaluate the method on both synthetic tests and waveform data from the Mw 7.0 Guerrero, Mexico, earthquake of September 8, 2021, recorded by 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.