Multivariate Conversion of Moment Magnitude for Small-to-Moderate-Magnitude Earthquakes in Iran

Abstract

Homogeneous estimates of moment magnitude (M) for small-to-moderate-magnitude (SMM) earthquakes are important to assess regional ground motion compared to global models. However, an estimate of M was available for only 6% of the shallow crustal earthquakes in Iran from 1973 to 2013 in the database developed by the Pacific Earthquake Engineering Research Center. Therefore, this study evaluates the existing conversion models, from ML, Ms, and mb, to M, for M ˃ 4.0 using the Iranian data set. Correlations between the residuals of these conversions were computed. A weighted estimate for M is presented that combines these conversion models using these correlations based on multivariate statistics. The conversion to M was improved with smaller standard deviations, especially when ML and mb were both available. The inverse-variance-weighted approach, which is common in practice, underestimates the standard deviations because it neglects the positive correlations between these variables.