A Study of Pre-earthquake Anomalies in Geomagnetic and Borehole Strain Data Based on the Pyraformer Model

Abstract. As a major natural hazard, earthquakes are accompanied by lithospheric stress accumulation and anomalies in multiple physical fields during their preparation process. Identifying pre-earthquake anomalies is therefore of great scientific significance for understanding earthquake preparation and improving earthquake prediction. Taking the 2013 Lushan earthquake in Sichuan, China (Ms 7.0), as a case study, this work presents a comprehensive analysis of geomagnetic and borehole strain observations to investigate the spatiotemporal evolution of pre-earthquake multi-physical-field anomalies. First, Variational Mode Decomposition (VMD) was applied to geomagnetic and borehole strain data to achieve multi-scale signal decomposition, thereby separating long-term background variations from short-period disturbance components. Subsequently, the Pyraformer model was employed to model and predict the high-frequency feature sequences, and the prediction residuals were extracted to quantify pre-earthquake anomalies. The results show that borehole strain anomalies first emerged along local fault segments during the pre-seismic stage and gradually accumulated, whereas geomagnetic anomalies subsequently intensified and accelerated at adjacent stations. Overall, the anomalies exhibited a spatiotemporal evolution pattern characterized by local-to-regional expansion and stage-wise accelerated accumulation. Further analysis indicates that borehole strain anomalies generally preceded geomagnetic anomalies, with a time lag ranging from several days to several weeks between the rapid accumulation stage of borehole strain anomalies and the strengthening stage of geomagnetic anomalies. In addition, the cumulative anomaly curves commonly displayed a pronounced S-shaped growth pattern, reflecting the gradual increase in stress-strain during earthquake preparation and its subsequent transfer to the electromagnetic field response. These findings reveal a coupling relationship between the stress-strain field and the electromagnetic field during the earthquake preparation process. The integrated VMD-Pyraformer framework proposed in this study demonstrates strong stability and reliability in identifying geomagnetic and borehole strain anomalies and provides new observational evidence and an effective analytical approach for multi-station, multi-parameter joint monitoring and pre-earthquake anomaly identification.