Multivariate conversion of moment magnitude for small-to-moderate-magnitude earthquakes in Iran

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 M_L, M_s, and m_b, 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 M_L and m_b 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.