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[SSS12-15] Relationship between the fault rupture processes for small earthquakes and the systematic differences between moment and local magnitude
Keywords:moment and local magnitude, fault rupture processes, source spectrum, seismic radiated energy
Local magnitude (ML) is determined based on the maximum amplitude of observed seismic waveforms (Richter, 1935) and reflects fault rupture processes. In Japan, the Japan Meteorological Agency (JMA) routinely estimates JMA magnitude scale (Mjma), which is a type of ML. Moment magnitude (Mw) was introduced to precisely estimate the size of large magnitude (Hanks & Kanamori, 1979; Kanamori, 1977). Mw is directly related to seismic moment, which represents static characteristics of faulting. For moderate to large earthquakes (ML>3~4), Mw is generally consistent with ML. On the other hand, Mw tends to be systematically larger than ML for small earthquakes (ML<3~4) (e.g., Edwards et al., 2010; Edwards & Rietbrock, 2009; Goertz-Allmann et al., 2011; Uchide & Imanishi, 2018). Some studies have suggested that the inelastic attenuation along propagation path (e.g., Deichmann, 2017; Uchide & Imanishi, 2018) especially near the surface (e.g., Hanks & Boore, 1984) may cause the systematic differences.
In detail, even among small earthquakes with similar magnitude, the degree of discrepancy between Mw and ML tends to vary (e.g., Edwards et al., 2010; Uchide & Imanishi, 2018) However, the cause of this diverse discrepancy remains largely unclear. In this study, we investigated this discrepancy based on dynamic characteristics of faulting.
Around the Fukushima – Ibaraki border, many crustal earthquakes have been observed following the 2011 Tohoku-Oki earthquake, which enable us to systematically estimate source parameters for small earthquakes. We estimated radiated energy (ER), seismic moment (M0) and scaled energy (eR=ER/M0) using the source spectrum of each event and investigated how the differences of ER and eR affect the degree of discrepancy between Mw and ML. We analyzed approximately 15000 earthquakes with 2.0<Mjma<3.0 occurred after the 2011 Tohoku-Oki earthquake.
We determined the source spectrum by removing site and path effects from observed waveforms. We first estimated site and seismic attenuation factor Q-1 by applying the coda normalization method (Aki, 1980; Aki & Chouet, 1975). We then removed them from observed spectrum to calculate the source spectrum and obtained ER, M0, Mw and eR.
We obtained eR for 8949 earthquakes. The mean and standard deviation of the derived log10eR were -5.00 and 0.29, respectively, which is similar to average eR reported by previous studies (e.g., Abercrombie, 1995; Yoshida & Kanamori, 2023). The obtained eR varied by approximately one order of magnitude, suggesting the diverse rupture processes among earthquakes with similar M0.
The estimated Mw values were systematically larger than Mjma, consistent with previous studies (e.g., Edwards et al., 2010; Edwards & Rietbrock, 2009; Goertz-Allmann et al., 2011; Yoshida et al., 2017; Uchide & Imanishi, 2018). The systematic differences between Mw and Mjma may arise from the underestimation of the maximum amplitude caused by path effects attributed to inelastic attenuation and high attenuation near the surface (e.g., Deichmann, 2017; Hanks & Boore, 1984; Uchide & Imanishi, 2018).
We investigated the relationship between the derived eR and the discrepancy between Mw and Mjma. We found that the degree of the discrepancy decreases with increasing eR for earthquakes with similar M0. Both M0 and Mw reflect static deformation and is independent of rupture processes. On the contrary, since Mjma is derived from the maximum amplitude of seismic waveforms, Mjma may be correlated with ER reflecting dynamic rupture processes. Thus, the variations in the Mw - Mjma may for earthquakes with similar M0 may reflect the differences in the ER. Our result suggest that we can obtain the imformation about the differences in rupture processes between small earthqaukes based on observed waveforms.
In detail, even among small earthquakes with similar magnitude, the degree of discrepancy between Mw and ML tends to vary (e.g., Edwards et al., 2010; Uchide & Imanishi, 2018) However, the cause of this diverse discrepancy remains largely unclear. In this study, we investigated this discrepancy based on dynamic characteristics of faulting.
Around the Fukushima – Ibaraki border, many crustal earthquakes have been observed following the 2011 Tohoku-Oki earthquake, which enable us to systematically estimate source parameters for small earthquakes. We estimated radiated energy (ER), seismic moment (M0) and scaled energy (eR=ER/M0) using the source spectrum of each event and investigated how the differences of ER and eR affect the degree of discrepancy between Mw and ML. We analyzed approximately 15000 earthquakes with 2.0<Mjma<3.0 occurred after the 2011 Tohoku-Oki earthquake.
We determined the source spectrum by removing site and path effects from observed waveforms. We first estimated site and seismic attenuation factor Q-1 by applying the coda normalization method (Aki, 1980; Aki & Chouet, 1975). We then removed them from observed spectrum to calculate the source spectrum and obtained ER, M0, Mw and eR.
We obtained eR for 8949 earthquakes. The mean and standard deviation of the derived log10eR were -5.00 and 0.29, respectively, which is similar to average eR reported by previous studies (e.g., Abercrombie, 1995; Yoshida & Kanamori, 2023). The obtained eR varied by approximately one order of magnitude, suggesting the diverse rupture processes among earthquakes with similar M0.
The estimated Mw values were systematically larger than Mjma, consistent with previous studies (e.g., Edwards et al., 2010; Edwards & Rietbrock, 2009; Goertz-Allmann et al., 2011; Yoshida et al., 2017; Uchide & Imanishi, 2018). The systematic differences between Mw and Mjma may arise from the underestimation of the maximum amplitude caused by path effects attributed to inelastic attenuation and high attenuation near the surface (e.g., Deichmann, 2017; Hanks & Boore, 1984; Uchide & Imanishi, 2018).
We investigated the relationship between the derived eR and the discrepancy between Mw and Mjma. We found that the degree of the discrepancy decreases with increasing eR for earthquakes with similar M0. Both M0 and Mw reflect static deformation and is independent of rupture processes. On the contrary, since Mjma is derived from the maximum amplitude of seismic waveforms, Mjma may be correlated with ER reflecting dynamic rupture processes. Thus, the variations in the Mw - Mjma may for earthquakes with similar M0 may reflect the differences in the ER. Our result suggest that we can obtain the imformation about the differences in rupture processes between small earthqaukes based on observed waveforms.