Magnitude-Scaling Rate in Ground-Motion Prediction Equations for Response Spectra from Large, Shallow Crustal Earthquakes

Abstract We have evaluated the magnitude-scaling rates (MSRs, the rate of increase in the predicted spectrum with increasing moment magnitude) of five modern ground-motion prediction equations (GMPEs) for response spectra, including four Next Generation Attenuation (NGA) models and a model developed for data from Japan. We have found that MSRs for crustal earthquakes with a moment magnitude over 7 vary significantly among the five models, by a factor of 2–3 for some cases. The variation of MSRs among the four NGA models is alarmingly large, considering that they were derived from largely the same dataset and used the same site parameters. We have selected 641 strong-motion records from shallow crustal earthquakes with a moment magnitude over 7 from the NGA dataset and 69 from the 2008 Wenchuan, China, earthquake with a moment magnitude of 7.9, all within a short distance of 200 km from the fault rupture plane. To illustrate the extreme extent of magnitude scaling, we have fitted an attenuation model without a magnitude term to this dataset, based on an observation that an increase in one moment magnitude unit is related to an increase in fault length by a factor of 5–10, a significant increase in shaking duration, which cannot be fully accounted for by response spectra, and limited or no increase in ground-motion amplitude. The statistical analyses of the results indeed suggest that a zero magnitude scaling at spectral periods over 0.6 s may be reasonable for our dataset, while the required apparent magnitude scaling at short periods may be due to other factors such as stress drop, a parameter that is not used in any of the models considered. We will provide some plausible explanations for the possible zero magnitude scaling that can be considered as the lower limit of the uncertain magnitude-scaling rate.