Determination of strain magnitude <italic>M</italic>_{<italic>ε</italic>} based on borehole strain observation and its application

Seismic waves can trigger the rupture of critically stressed faults, remotely and dynamically triggering of earthquakes or volcanic activities, which may result in casualties and significant property damage. Therefore, quantitatively explore the relationship between earthquake magnitude, epicentral distance and strain or stress changes is of great significance for effective earthquake disaster prevention and mitigation. The four-component borehole strainmeters, an ultra-broadband ground stress monitoring instrument, can theoretically complement observations with seismic instruments. This study utilizes second-by-second far-field waveform data from 13 sets of four-component borehole strainmeters deployed across China, capturing 108 M≥5.5 earthquakes between November 2022 and November 2023. By analyzing the maximum amplitude of the four strain components, we developed a magnitude calculation formula based on borehole strain observations. Comparing the derived strain magnitude with the magnitude provided by the China Earthquake Networks Center (CENC), yielding a correlation coefficient of 0.83, demonstrating a strong consistency between them. Furthermore, data from 22 M≥5 earthquakes recorded at 10 stations in Shanxi Province from January to May 2024 were selected to test the applicability of the strain magnitude formula Using Z-test, and the result showed |Z|=1.31 (<1.96), indicating that the difference between the strain magnitude and the CENC magnitude is not statistically significant, thus confirming the formula’s feasibility. Notably, the study found no magnitude saturation effect for magnitudes ≤7.8. Using the strain magnitude formula, the maximum strain wave amplitude at various epicentral distances can be predicted, which allows for the estimation of the maximum stress fluctuation amplitude induced by seismic waves. This provides a new and quantitative method for investigating the dynamic triggering mechanisms of earthquakes. This study lays a scientific foundation for understanding the relationship between epicentral distance and dynamic stress wave amplitudes for earthquakes of different magnitudes. It also introduces an innovative approach to earthquake magnitude determination, offering valuable insights and crucial support for the analysis of dynamic stress triggering mechanisms.