Body-Wave Magnitude mb Is a Good Proxy of Moment Magnitude Mw for Small Earthquakes (mb<4.5-5.0)

Abstract

Body‐wave magnitude m b is usually considered a poor proxy of moment magnitude M w because it saturates for moderate and large earthquakes ( M w>5.5–6) and generally shows a poor correlation with M w. On the other hand, the observed distribution of data at the global scale also seems to indicate an inverse saturation at low magnitudes ( M w<4.5–5.0) in which M w appears to be almost uncorrelated with m b. We show here that the latter is an artifact of the incompleteness of the global M w datasets for M w<4.5–5.0 and that disappears considering lower M w estimates available from regional centroid moment tensor (CMT) catalogs and/or using general orthogonal regression methods. In these cases we show that m b well corresponds to M w<4.5–5.0 and hence can confidently be used for approximating the M w of small earthquakes. Conversion relations between the band‐limited short‐period body‐wave magnitude m b (Gutenberg and Richter, 1956) and moment magnitude M w (Hanks and Kanamori, 1979) have been obtained in the past by several authors using ordinary least‐squares (OLS) regression methods (e.g., Heaton et al. , 1986; Johnston, 1996; Scordilis, 2006). Such a computational approach, however, is inappropriate when the error in the independent variable (predictor) is not negligible compared with that of the dependent variable (response). Castellaro et al. (2006) have shown that the use of OLS in conversion relations produces a bias of the frequency–magnitude distribution law (Gutenberg and Richter, 1944), which can be avoided using the general orthogonal regression (GOR) method described by Fuller (1987). The latter method has been used in numerous studies of this type, both at the global and regional scale (Ristau, 2009; Wang et al. , 2009; Deniz and Yucemen, 2010; Das et al. , 2011, …