We estimate the Mw values of 1823 weak earthquakes (Mw4.0) occurred in northeastern Italy, an area with complex tectonics and moderate seismicity, using the method proposed by Atkinson et al. (2014). The Mw is obtained from the response spectra (SAs) at 1.0 and 0.3 s, which have been properly corrected for path effects. After tuning a relationship that describes log(SA) versus Mw for local events (those recorded at distances <80  km), we correlate the computed Mw values with available ML values to obtain an empirical relationship that correlates ML versus Mw in the investigated region. These relationships can be easily implemented in real time, within the routine analyses of seismicity. The ML values underestimate the energy released by weak events (ML<2.0); therefore, our results, and reliable estimates of Mw in general, are of utmost importance for enlarging the existing catalogs of seismic events and improving our knowledge of magnitude‐recurrence relationships. Our approach is shown to be very effective for the rapid estimation of Mw for weak events and can be efficiently implemented within real‐time control systems and traffic‐light protocols in the seismic monitoring of induced seismicity caused by human activities carried out underground.

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