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 (M 0) or in terms of radiated seismic energy (E r). These two parameters look at the source complexity from different perspectives: M 0 is a static measure of the earthquake size, whereas E r is related to the rupture kinematics and dynamics. For practical applications and for dissemination purposes, the logarithms of M 0 and E r are used to define the moment magnitude M w and the energy magnitude M E, respectively. The introduction of M w and M E partially obscure the complementarity of M 0 and E r. The reason is due to the assumptions needed to define any magnitude scale. For example, in defining M w, the apparent stress (i.e. the ratio between M 0 and E r multiplied by the rigidity) was assumed to be constant, and under this condition, M w and M E 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 M 0, the value of M E derived from M w cannot be used to infer E r. In this study, we investigate the similarities and differences between M w and M E 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 ≤ M w ≤ 9.0. Our results show that M E is better than M w in capturing the high-frequency ground shaking variability whenever the stress drop differs from the reference value adopted to define M w. We show that M E accounts for variations in the rupture processes, introducing systematic event-dependent deviations from the mean regional peak ground motion velocity scaling. Therefore, M E might be a valid alternative to M w for deriving ground motion prediction equations for seismic hazard studies in areas where strong systematic stress drop scaling with M 0 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 M E and M w. We show that the b values from M w (b Mw) and M E (b ME) can be significantly different when the stress drop shows a systematic scaling relationship with M 0. We found that b ME is nearly constant for all data sets, while b M w shows an inverse linear scaling with apparent stress. [ABSTRACT FROM AUTHOR]