Determination of focal depths for the 2024 M 7.3 Hualien offshore and 2025 M 6.2 Tainan earthquakes in Taiwan, China: An enhanced method based on sPn phase and waveform cross-correlation techniques

Abstract

This study proposes a method for determining earthquake focal depths by combining the sPn phase with the waveform cross-correlation technique, based on waveform data recorded by the Fujian Seismic Network from the 2024 M 7.3 Hualien offshore earthquake and the 2025 M 6.2 Tainan earthquake. The Pn phase onset was precisely aligned using waveform cross-correlation, and the arrival time difference (Δt) between the sPn and Pn phases was extracted via a sliding time-window correlation method. The focal depths were derived using a layered velocity model for the Taiwan region. Results show that the calculated focal depth for the Hualien earthquake is 23.1 km (Δt = 6.9 s), with a relative error of 2.7% compared to the official result (22.5 km) from the Central Weather Administration of Taiwan. For the Tainan earthquake, the depth is 17.9 km (Δt = 6.1 s), with a relative error of 13.3%. In this study, we show that a cross-correlation threshold of 0.8 and a bandpass filtering of 0.1-0.3 Hz are efficient to suppress noise and significantly improve depth accuracy for shallow earthquakes with depth <30 km. Compared to traditional travel-time location methods, this approach exhibits superior noise resistance and computational efficiency. Future work will focus on optimizing 3D velocity structures, integrating multiple phases, and applying deep learning techniques such as convolutional neural networks, aiming to improve the results in a more reliable and automatic way, and to provide efficient support on earthquake emergency response.

Keywords

M 7.3 hualien earthquake / M 6.2 tainan earthquake / sPn phase / Focal depth / Waveform cross-correlation / Sliding time-window correlation method

CRediT authorship contribution statement

Huifang Chen: Conceptualization, Methodology, Software, Writing - original draft, Project administration. Binhua Lin: Software, Validation, Writing - review & editing. Tairan Xu: Writing - review & editing. Yanming Zhang: Data curation, Validation, Writing - review & editing. Yuanhong Yang: Data curation, Visualization, Validation.

Declaration of competing interest

The authors declare that they have no known competing financial interests or personal relationships that could have influenced the work reported in this paper.

Author agreement and acknowledgments

All authors agree to this publication. This research was funded by the National Key Research and Development Program of China (Grant No. 2024YFC3012804), and we hereby express our gratitude. The authors would like to warmly thank the anonymous reviewers for their valuable comments and suggestions on this paper. The reviewers' professional insights and meticulous review have significantly enhanced the scientific rigor and logical coherence of the manuscript, and further broadened the research perspectives. Meanwhile, we appreciate the editorial team for their responsible work attitude and professional editorial expertise, which ensured the smooth progress of the manuscript from submission to publication and provided strong support for the timely dissemination of research results. Finally, we extend our most sincere thanks to all individuals and institutions that have provided help and support for this study.

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