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<p>Local magnitude (M<sub>L</sub>), the earliest magnitude scale developed in southern California, enables rapid earthquake characterization based on observed amplitudes and zero-magnitude reference amplitudes (A<sub>0</sub>) derived from local events. However, amplitudes are sensitive to path and site effects, motivating the development of the physically robust moment magnitude (M<sub>W</sub>). Previous studies have demonstrated an approximately 1:1 relationship between M<sub>L</sub> and M<sub>W</sub> for M<sub>L</sub> &lt; 6.5 in southern California. In contrast, M<sub>L</sub> in Taiwan systematically overestimates M<sub>W</sub>, reflecting distinct regional attenuation characteristics. Although prior work has recalibrated the logA<sub>0</sub> attenuation model for shallow earthquakes in Taiwan, deep events for focal depth larger than 35&#xa0;km exhibit even larger overestimation, with an average bias of 0.5 magnitude units. In this study, we investigate deep earthquakes in Taiwan and establish a new depth-dependent logA<sub>0</sub> attenuation model. A model relying solely on hypocentral distance produces depth-dependent residuals; therefore, a depth term (logD) is incorporated to logA<sub>0</sub> attenuation model. The final regression model is logA<sub>0</sub> = 0.097–1.587logR − 0.0014R + 0.417logD ± 0.273, where R is hypocentral distance and D is focal depth. The results demonstrate that logA<sub>0</sub> attenuation varies systematically with both distance and depth, consistent with Richter’s description that earthquakes at different depths require distinct logA<sub>0</sub> values. The recalibrated M<sub>L</sub> shows no depth dependence and exhibits a stable 1:1 relationship with M<sub>W</sub>, with a standard deviation of 0.16. The proposed logA<sub>0</sub> attenuation model enables rapid and reliable M<sub>L</sub> estimation for deep earthquakes in Taiwan, enhancing real-time hazard assessment and reducing magnitude conversion uncertainty in combined earthquake catalogs.</p>

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Discussion of local magnitude scale for deep earthquakes in Taiwan

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年6月20日

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  • Xin-Yu Lin,
  • Ting-Chung Huang,
  • Yih-Min Wu

摘要

Local magnitude (ML), the earliest magnitude scale developed in southern California, enables rapid earthquake characterization based on observed amplitudes and zero-magnitude reference amplitudes (A0) derived from local events. However, amplitudes are sensitive to path and site effects, motivating the development of the physically robust moment magnitude (MW). Previous studies have demonstrated an approximately 1:1 relationship between ML and MW for ML < 6.5 in southern California. In contrast, ML in Taiwan systematically overestimates MW, reflecting distinct regional attenuation characteristics. Although prior work has recalibrated the logA0 attenuation model for shallow earthquakes in Taiwan, deep events for focal depth larger than 35 km exhibit even larger overestimation, with an average bias of 0.5 magnitude units. In this study, we investigate deep earthquakes in Taiwan and establish a new depth-dependent logA0 attenuation model. A model relying solely on hypocentral distance produces depth-dependent residuals; therefore, a depth term (logD) is incorporated to logA0 attenuation model. The final regression model is logA0 = 0.097–1.587logR − 0.0014R + 0.417logD ± 0.273, where R is hypocentral distance and D is focal depth. The results demonstrate that logA0 attenuation varies systematically with both distance and depth, consistent with Richter’s description that earthquakes at different depths require distinct logA0 values. The recalibrated ML shows no depth dependence and exhibits a stable 1:1 relationship with MW, with a standard deviation of 0.16. The proposed logA0 attenuation model enables rapid and reliable ML estimation for deep earthquakes in Taiwan, enhancing real-time hazard assessment and reducing magnitude conversion uncertainty in combined earthquake catalogs.