Discussion of Local Magnitude (ML) Scale for Deep Earthquakes in Taiwan

The Local Magnitude (M_L), was the earliest proposed magnitude scale, allows for rapid determination based on observed amplitudes and a zero magnitude reference amplitudes (A₀) derived from local events. However, the amplitudes are susceptible to external factors, the physically robust Moment Magnitude (M_w) was proposed. The previous studies showed a 1:1 relationship between M_L and M_w for M_L < 6.5 in Southern California; however, M_L in Taiwan tend to overestimate when compare to M_w due to different regional attenuation characteristics. Although the previous study has recalibrated the logA₀ attenuation model for shallow earthquakes in Taiwan, deep events exhibit an even more significant overestimation, averaging overestimate 0.528. Therefore, this study aims to discuss deep earthquakes in the Taiwan and establish a new logA₀ attenuation model for deep events. Since models relying solely on hypocentral distance (R) result in depth-dependent residuals, a depth term (D) was incorporated to account for the physical characteristic of deep seismic waves often propagating through high-Q plates. The derived regression model is:

logA₀ = 0.097 - 1.587logR - 0.0014R + 0.417logD ± 0.273

The results demonstrate that logA₀ attenuation varies distinctly with distance at different depths, aligning with Richter mentioned that different depth events require distinct calibration. Furthermore, the logA₀ value at a hypocentral distance 100 km differs from that of shallow event models, indicating the difference in attenuation properties. The recalibrated M_L demonstrates no depth dependency and a consistent 1:1 relationship with M_w, with a standard deviation ±0.160. This study proposed model provides a rapid and precise M_L calculation. This new model enhances the reliability of real-time hazard assessment and reduces magnitude conversion errors in catalog combination.