Abstract
Abstract
Local magnitude (M
L
), the earliest magnitude scale developed in southern California, enables rapid earthquake characterization based on observed amplitudes and zero-magnitude reference amplitudes (A
0
) derived from local events. However, amplitudes are sensitive to path and site effects, motivating the development of the physically robust moment magnitude (M
W
). Previous studies have demonstrated an approximately 1:1 relationship between M
L
and M
W
for M
L
L
in Taiwan systematically overestimates M
W
, reflecting distinct regional attenuation characteristics. Although prior work has recalibrated the logA
0
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 logA
0
attenuation model. A model relying solely on hypocentral distance produces depth-dependent residuals; therefore, a depth term (logD) is incorporated to logA
0
attenuation model. The final regression model is logA
0
= 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
0
attenuation varies systematically with both distance and depth, consistent with Richter’s description that earthquakes at different depths require distinct logA
0
values. The recalibrated M
L
shows no depth dependence and exhibits a stable 1:1 relationship with M
W
, with a standard deviation of 0.16. The proposed logA
0
attenuation model enables rapid and reliable M
L
estimation for deep earthquakes in Taiwan, enhancing real-time hazard assessment and reducing magnitude conversion uncertainty in combined earthquake catalogs.