Study on pre-seismic anomaly extraction of borehole strain data based on Pyraformer model: a case study of the 2021 Yangbi Ms6.4 earthquake in China

Earthquakes are violent natural disasters triggered by the long-term accumulation and sudden release of crustal stress, and the accurate extraction of pre-seismic anomaly signals is of great significance for improving the timeliness and reliability of earthquake prediction. In this study, we propose an anomaly detection method for borehole strain data based on the combination of Variational Mode Decomposition (VMD) and the Pyraformer network, and take the 2021 Yunnan Yangbi Ms6.4 earthquake as a case study to analyse pre-earthquake anomaly identification. The VMD method is capable of performing adaptive mode decomposition of non-smooth time series signals, extracting Intrinsic Mode Functions (IMFs) at different time scales, and effectively separating key modal components containing seismic precursor information. It shows good decomposition accuracy and stability when dealing with complex borehole strain sequences, providing a solid foundation for subsequent anomaly identification. Meanwhile, the Pyraformer model combines a pyramid structure with a sparse attention mechanism, enhancing the sensitivity and recognition of weak pre-seismic signals while improving the efficiency of long sequence modelling. By processing and analysing four-component borehole strain data from three stations—Yongsheng, Tengchong, and Panzhihua—three stages of anomalous cumulative acceleration prior to the Yangbi earthquake were identified: the first phase starts about 10 months before the earthquake (mid-June 2020), with the number of anomalous days increasing. The second phase begins about 8 months before the earthquake (mid-August 2020), with a significantly increased rate of anomaly accumulation. In the third phase, the number of anomalous days increased sharply from 1 month before the earthquake (mid-April 2021) until the event, with the anomaly accumulation curve exhibiting a typical S-shaped growth trend. The above results show a high degree of temporal consistency with multiple sources of pre-seismic anomalies (e.g. subsurface fluid disturbances, geoelectric field changes, and ionospheric Total Electron Content (TEC) anomalies), which further verifies the significance of borehole strain anomalies as precursors in the earthquake development process.