Moment and energy magnitudes: diversity of views on earthquake shaking potential and earthquake statistics

The size of an earthquake can be defined either from the seismic moment (M0) or in terms of radiated seismic energy (Er). These two parameters look at the source complexity from different perspectives: M0 is a static measure of the earthquake size, whereas Er is related to the rupture kinematics and dynamics. For practical applications and for dissemination purposes, the logarithms of M0 and Er are used to define the moment magnitude Mw and the energy magnitude ME, respectively. The introduction of Mw and ME partially obscure the complementarity of M0 and Er. The reason is due to the assumptions needed to define any magnitude scale. For example, in defining Mw, the apparent stress (i.e. the ratio between M0 and Er multiplied by the rigidity) was assumed to be constant, and under this condition, Mw and ME values would only differ by an off-set which, in turn, depends on the average apparent stress of the analysed data set. In any case, when the apparent stress is variable and, for example, scales with M0, the value of ME derived from Mw cannot be used to infer Er. In this study, we investigate the similarities and differences between Mw and ME in connection with the scaling of the source parameters using a data set of around 4700 earthquakes recorded at both global and regional scales and belonging to four data sets. These cover different geographical areas and extensions and are composed by either natural or induced earthquakes in the magnitude range 1.5 ≤ Mw ≤ 9.0. Our results show that ME is better than Mw in capturing the high-frequency ground shaking variability whenever the stress drop differs from the reference value adopted to define Mw. We show that ME accounts for variations in the rupture processes, introducing systematic event-dependent deviations from the mean regional peak ground motion velocity scaling. Therefore, ME might be a valid alternative to Mw for deriving ground motion prediction equations for seismic hazard studies in areas where strong systematic stress drop scaling with M0 are found, such as observed for induced earthquakes in geothermal regions. Furthermore, we analyse the different data sets in terms of their cumulative frequency–magnitude distribution, considering both ME and Mw. We show that the b values from Mw (bMw) and ME (bME) can be significantly different when the stress drop shows a systematic scaling relationship with M0. We found that bME is nearly constant for all data sets, while bMw shows an inverse linear scaling with apparent stress.