On the relationship between ML and MW in a broad range: an example from the Apennines, Italy

Abstract

Being tied to a physical quantity, moment magnitude (Mw) should be the reference estimate of earthquake size and used whenever possible. Local magnitude (ML) represents a simple alternative for a reliable estimate of size, its best use being either for quick outcomes or when the computation of Mw is difficult (e.g., for small earthquakes). However, ML and Mw are profoundly different and not interchangeable. Here, we analyze a large set of 1509 ML–Mw data points from earthquakes of the central and northern Apennines (CNA), quantify the empirical scaling, and look for features of global validity. Our data set is made of 449 unpublishedMws from moment tensor solutions of events from the Amatrice-Visso-Norcia (AVN) sequence, 170 published Mws from moment tensor solutions of events from the L’Aquila seismic sequence (2009), and 890 published ML–Mw data points from earthquakes of the Altotiberina fault (ATF, 2010–2014; Mws from spectral correction). We integrate our empirical data set by computing the local magnitudes of the events from the AVN and L’Aquila sequences. Our analysis of CNA earthquakes shows that, for earthquakes up to a crossover magnitude MLco ≈ 4:3: Mw = 2/3 ML + C′; C′ = 1.14. Moreover, for earthquakes with ML > MLco, up to ML 6.5, our data suggest Mw = bML + C′′; b = 1.28; C′′= −1:50, in which b depends on the combined effects of source scaling and crustal attenuation, and C′ and C″ on regional attenuation (G (r) , Q (f) , κ0), focal depth, and rigidity at source. Finally, a synthetic study calibrated on the crustal attenuation and the source characteristics of the AVN data set reproduces the observed scaling between ML and Mw, predicting that MLs in the analyzed region saturate above ML ∼ 6:5. Smooth transitions are predicted between the different regimes.